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ELECTRICAL METERS 




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ENGINEERING EDUCATION SERIES 



ELECTRICAL METERS 



PREPARED IN THE 

EXTENSION DIVISION OF 
THE UNIVERSITY OP WISCONSIN 



aBY-^ 
CYRIL Mi'lANSKY, B. S., B. A. 

ABBOCIATB PB0FB880R OF BLBCTBICAL BNGINBBRINa 
THB UNIVBBSITT OF WI8CONBZN 



Second Edition 
Revised and Enlarged 



Third Impression 



McGRAW-HILL BOOK COMPANY, Inc. 

NEW YORK: 239 WEST 39TH STREET 
LONDON: 6 & 8 BOUVERIE ST., E. C. 4 

1917 



T^ t. 



JsiT 



I ' 



CoPTRliiHT, 1913, 1917, BY THE 

McCiRAw-Hux Book Company, Inc. 



TSa MAPLiE PKE88 T O K K !>▲ 



PREFACE TO SECOND EDITION 

The many new developments in electrical meter design, since 
the publication of the first edition of this text, has necessitated 
the omission of some and the addition of much new material in 
the revised edition. 

The description of most obsolete meters has been omitted and 
several new designs are explained. The chapter on Instrimient 
Errors has been almost entirely rewritten and expanded so as to 
include many experimental results. The influence of frequency 
and wave form in producing errors in different classes of meters 
has been added. There has also been added a chapter on In- 
strument Transformers. Only so much of the theory of instru- 
ment transformers is given as is necessary for an understanding 
of their function in connection with meters and their testing. 

C, M. J. 

University op Wisconsin, 

Madison, Wisconsin, 

AprU, 26, 1917. 



358781 



PREFACE TO FIRST EDITION 

Efficiency is the shibboleth of the modern industrial worid. 
From a physical viewpoint the efficient operation of any plant 
is mainly a correct appUcation of the laws of conservation and 
transformation of energy, and hence, the operation of an in- 
dustrial plant cannot be efficient unless data are available for 
determining the relation between energy generated or delivered 
and energy utilized in any manufacturing process. 

The data necessary for efficient operation cannot be had 
unless proper and accurate instruments are used to determine 
the various quantities that enter into the operation. In any 
industry where electrical energy is generated or utilized, elec- 
trical measuring instruments are necessary for efficient operation. 

When the author decided to offer a course treating of Electrical 
Measuring Instruments, he was surprised to discover that no 
suitable text was available, and in fact in this country very 
little had been published treating, in a comprehensive and 
systematic way, of the various kinds of electrical measuring 
instruments. The articles in the technical journals and pro- 
ceedings of technical societies are, of course, numerous and 
valuable, but they are inaccessible to the average man who may 
want information concerning the characteristics and principles 
of operation of some type of measuring instrument. 

This text is written primarily to supply the author's needs in 
correspondence instruction, although it is hoped that others also 
may find it useful. 

Since, in this country, instruments of foreign make are used 
to such a limited extent, this work is confined almost entirely 
to instruments made in the United States, and to American 
practice. 

In classifying electrical measuring instruments, the main divi- 
sions have been made in accordance with the quantities to be 
measured, and minor subdivisions according to the principles of 
operation. Although such a classification necessitates some repe- 
tition in describing different instruments whose operation is based 
on the same principles, nevertheless, for the sake of clearness and 
simpUcity such a classification appears justifiable 

• • 
Vll 



viii PREFACE 

The attempt has been made to explain the fmidamental prm- 
ciples in an elementary way, and for this reason many line draw- 
ings and vector diagrams are used. The. manner in which these 
fundamental principles are applied in practice is usually exem- 
plified by means of cuts of actual instruments. The illustra- 
tions used were selected not because the author considers the 
instruments better than others not shown, but because they are 
typical, and used quite extensively. 

Great care has been taken to eliminate all errors, yet it is 
too much to expect that no mistakes will be found. The author 
will be very grateful to anyone who may discover and report 
any error. 

The author is under great obligations to Dr. M. G. Lloyd, 
of Chicago; Professor J. P. Jackson of the Pennsylvania State 
College, and Professor R. C. Disque of The University of Wis- 
consin for reading the manuscript and for many valuable sug- 
gestions. Thanks are also due to Mr. F. C. Thiessen and Mr. G. 
R. Wells for making the line drawings and vector diagrams; to 
the several manufacturers of electrical measuring instruments 
for their kindness in supplying information and electrotypes of 
their instruments. 

C. M. J. 
The Univbrsity op Wisconsin, 

Madison, Wisconsin, 

November 26, 1912. 



CONTENTS 

Paqb 
Preface. . , % v 

CHAPTER I 

Fundamental Electrical Principles 1 

Energy — Forms of Energy — Conservation of Energy — ^Electricity 
and Electrical Energy — ^Analogies — Magnetism — Properties of 
Magnetic Fields — Strength of Magnetic Field — Relation between 
Tension and Flux Density — Magnetic Field Surrounding an 
Electric Wire — Field of a Circular Coil — Solenoids — ^Law of the 
Magnetic Circuit — Force Exerted upon a Wire in a Magnetic 
Field — Force between Parallel Wires Carrying Currents — Electro- 
lytic Conductors — Faraday's Laws — Heat Effect — Practical Elec- 
trical Units — Resistance — Change of Resistance with Tempera- 
ture — Electric Current — Electromotive Force — Quantity — Energy 
— Power — Inductance — Capacity — Ohm*s Law — Pressure Drop in 
D.-C. Circuits — Energy Loss. 

CHAPTER II 

Classification of Instruments. 26 

Classes of Meters — Groups of Instruments-^Electromagnetic 
Instruments — Electrodynamic Instruments — Electrostatic Instru- 
ments — Thermal Instruments — Controlling Forces — Magnetic 
Shielding — Friction of Supports. 

CHAPTER III 

Current and Pressure-mbasurinq Instruments 32 

Ammeters and Voltmeters — Uses of Ammeters and Voltmeters — 
Range of Instruments — Ammeter Shunts — Range of Voltmeters — 
Voltmeter Multipliers — The Movable Core Type — Approximate 
Equation for Pull on Iron Core — Movable Coil Permanent Magnet 
Type — Damping — Torque Exerted by a Magnetic Field upon a 
Rectangular Coil. 

CHAPTER IV 

Fundamental Principles op Alternating Currents 47 

Introduction — Alternating Current — Generation of an Alternating 
Pressure — ^Law of Fluctuation of Alternating Pressure and Current 
— Cycle, Frequency, Period, Alternation — Instantaneous Value — 
Maximum Value — Average Value — Effective Value or Root-mean 
Square Value — ^Effect of Capacity — Phase Difference — Power in 
Alternating-current Circuits — Phase Angle. 

ix 



X CONTENTS 

CHAPTER V 

Paob 

Alternatino-gurrbnt Circuits 61 

Single-phase circuits — Polyphase Circuits — Three-phase Circuits 
— Current and Voltage Relations in Three-phase Circuits. 

CHAPTER VI 

Induction Principle 67 

Introduction — Rotating and Revolving Magnetic Fields — Pro- 
duction of Rotating Field — Rotating Field Produced by Unequal 
Component Fields — Production of a Revolving Magnetic Field — 
Speed of Revolving Field. 

CHAPTER VII 

Induction Type Ammeters and Voltmeters 75 

Application of Induction Principles to Meters — Induction Am- 
meters and Voltmeters — Series Transformer Principle — Relation 
between Current and Torque — Influence of Frequency — Influence 
of Temperature — Scale — Damping. 

CHAPTER VIII 

Electrodynamic Ammeters and Voltmeters 83 

Introduction — Electrodynamometer Type — Operation of Electro- 
dynamometer Ammeter — ^Voltmeters — Eflfect of Inductance Upon 
Beading of Electrodynamometer Voltmeter — Construction — ^Am- 
pere Balance — ^Uses of Kelvin Balance as a Voltmeter — Westing- 
house Dynamometer Ammeter and Voltmeter — Influence of 
Earth's Magnetic Field — Advantages — Disadvantages. 

CHAFFER IX 

Miscellaneous Ammeters and Voltmeters 97 

Electrostatic Voltmeter — Westinghouse Electrostatic Voltmeter — 
Operation — Insulation — Damping — Advantages — Hot-wire In- 
struments — Hot-wire Voltmeter — Hot-wire Ammeter — Damping 
— ^Thermoammeter. 

CHAPTER X 

Power Measuring Instruments 109 

Wattmeters — ^Electrodynamometer Type — Theory uf Electrodyna- 
mometer Wattmeter — Compensation for Power Consumed in 
Instrument — Influence of the Inductance of the Voltage C<m1 — 
Correction Factor — Range of Wattmeters — Induction Type Watt- 
meters — Westinghouse Induction Wattmeter — ^^ct"C Inductiooi 
WattmeiterB — Scale — Mercury Wattmeter. 



CONTENTS xi 

CHAPTER XI 

Page 

Phase Rblatton and Frequency Instruments 127 

Introduction — Power-factor — Power-factor Meter — Analytical 
Proof of Principles — Polyphase Power-factor Meter — Westing- 
house Power-factor Meter — Frequency Meters — Resonance Fre- 
quency Indicator — Campbell Frequency Meter — Hartmann and 
Braun Frequency Meter — Induction Type Frequency Meter — 
Weston Frequency Meter — Synchronizing Devices — Weston Syn- 
chroscope — Westinghouse Synchroscope — ^Lincoln Type Syn- 
chroscope. 

CHAPTER XII 

Recording or Graphic Meters 148 

Introduction — Direct Acting — Bristol Recording Instruments — 
General Electric Recording Meters — General Electric Recording 
Voltmeters and Wattmeters — Esterline Graphic Meters — Relay 
Type of Recording Meters — Principles of Operation — Construction 
— Operation — Damping — Sensibility — Westinghouse Recording 
Ammeters, Voltmeters, and Wattmeters — Westinghouse Recording 
Frequency Meters — Westinghouse Recording Power-factor Meter 
— Operation — Sangamo Graphic Meters — Right Line Pen Move- 
ment — Advantages and Disadvantages. 

CHAPTER XIII 

Integrating Meters, Watt-hour Meters 168 

Introduction — Watt-hour Meters — Electrodynamometer Type 
(without iron) — Counter-torque — Summation of Power — ^Large 
Current Capacity Watt-hour Meters — Electro-dynamometer Type 
(with iron) — Friction Compensation — Creeping — Brushes — The 
Commutator — Armature — Bearings — Jewels — Magnets — Register- 
ing Mechanism — Electrodynamometer Type on Alternating-current 
Circuits — ^Lagging — Value of Shunt Circuit Resistance — Three-wire 
Direct-current Meters — Mercury Watt-hour Meter — Operation — 
Compensation for Friction — Full-load Adjustment — Induction 
Type Watt-hour Meters — Operation — Shifting Magnetic Field — 
Practical Construction — Sangamo Induction Meter — Balance of 
Elements — Duncan Induction Watt-hour Meter — Full-load Adjust- 
nent — Relation between Torque and Power — ^Lagging Induction 
Watt-hour Meters — The Effect of Over and Under Lagging — ^Light 
Load Compensation — Flux Shunting Method — Influence of Fre- 
quency — Double Lagging — Single-phase Watt-hour Meters on Poly- 
phase Circuits — Three-wire Single-phase Induction Watt-hour 
Meters — Voltage Coil Connected Across Outside Wires — ^Load Un- 
balanced — Voltage Coil Connected between One Outside Wire and 
Neutral — Polyphase Watt-hour Meters — Watt-hour Meters for 
Two-phase and Three-wire Three-phase Circuits — Relation of 



xii CONTENTS 

Page 

Power to Torque in a y-connected System — Relations between 
Power and Torque in a A-connected System — Polyphase Meters 
for Four-wire Three-phase Systems — Balance of Metering Ele- 
ments — Interference of Elements — Effect of Power-factor on 
Operation — ^Effect of Improper Connections — Prepayment Watt- 
hour Meters — Prepayment Device — Operation — Bases of Energy 
Rates — Two-rate Meters. 

CHAPTER XIV 

Inteoratinq MeterSi Ampere-hour Meters 241 

Introduction — Electromagnetic Type Ampere-hour Meter — 
Accuracy Characteristics — Electrolytic Ampere-hour Meters — 
Edison Electrolytic Ampere-hour Meter — The Bastian Ampere- 
hour Meter. 

CHAPTER XV 

Demand Indicators 247 

Introduction — ^Thermal Type — Induction Type — Time Lag — 
Westinghouse Demand Indicator, Mechanical Type — Operation — 
Graphic Demand Meter, Type G — General. 

CHAPTER XVI 

Instrument Testing 263 

Introduction — General Precautions — Kinds of Tests — Apparatus 
for Instrument Testing — ^The Standard Cell — Galvanometer — 
Potentiometers — Slide-wire Type — Operation — ^Leeds & Northrup 
Potentiometer — Operation — Deflection Type Potentiometer — 
Theory and Operation — Standard Resistances or Shunts — Vari- 
able Resistance Rheostat — Lamp Bank — Water Rheostat. 

CHAPTER XVII 

Testing Ammetersv 278 

Introduction — Comparison of Ammeters — Calibration Curve — 
Calibration of D. C. Ammeters by Means of Standard Resistance 
and Voltmeter — Deflection Potentiometer Method — Difference 
between D. C. and A. C. Ammeters and Voltmeters — Calibration 
of A. C. Ammeters. 

CHAPTER XVIIi 

Testing Voltmeters, Wattmeters, Power-factor, and Frequency 

Meters 290 

Introduction — Comparison of D. C. Voltmeters — Potentiometer 
Method — ^Testing A. C. Voltmeters — Calibration Curves — Test of 
Electrodynamometer Type Wattmeter — Testing Single-phase 



CONTENTS xiii 

Paqb 

Power-factor Meters — Testing Polyphase Power-factor Meters — 
Testing Frequency Meters — Testing Recording Meters. 

CHAPTER XIX 

Testing Watt-hottr Meters 303 

Introduction — Rotating Standard Watt-hour Meter — Meter 
Timing Device — Kinds of Tests — Shop Tests — Installation Tests — 
Periodic Tests — Complaint Tests — Inquiry Tests — Retests — ^Re- 
pair Tests — Special Tests — Meter Constants — Dial Constant — 
Test Constant — Watt-hour Constant — Watt-minute or Watt- 
second Constant — Use of Constant in Testing — Methods of Loading 
— ^The Consumer's Load — Portable Lamp Bank Method — Special 
Load Box Method — Portable Storage Battery Method — ^Low Volt- 
age Transformer Method — Determination of Watt-hour Constant, 
Experimentally — Method of Procedure — Test for Percentage of 
Accuracy — Test of a D. C. Three-wire Meter — Test for Balance — 
Test of Ampere-hour Meters. 

CHAPTER XX 

Methods op Qbtaininq Different Power-factors 325 

Introduction — Reactance Coil Method — Two Transformer Method 
— Two Resistance Method — Two Generator Method — Phase-shift- 
ing Transformer — Ammeter Method of Measuring Power-factors 
— Ammeter Method on Two-phase Circuits — ^Ammeter Method on 
Three-phase Circuits. 

CHAPTER XXI 

Special Tests op A. C. Watt-hour Meters 338 

Test for Quarter-phasing — Test of Single-phase Mater on Non- 
inductive Load — Test of Single-phase Watt-hour Meter on Induc- 
tive Load — Testing with Standard Test Meter — Testing of Poly- 
phase Meters — Test for Interference of the Two Metering Elements 
— Test to Determine Torque — Test of Influence of Friction — 
Test to Determine Influence of Stray Field — Test to Determine 
Loss in Potential Coil — Test for Proper Connections. 

CHAPTER XXII 

Instrument Errors 365 

Sources of Error — Inherent Errors — Inherent Temperature Errors 
— Inherent Errors Due to Time and Use — Inherent Mechanical 
Errors — Defective Performance of Springs — ^Errors Due to Balanc- 
ing — Errors of Use — ^Electrostatic Effect — Contact Errors — Errors 
Due to Thermo-electromotive Forces — ^Errors Due to Combina- 
tion of Instruments — ^Errors Due to Voltage and Current Trans- 
formers — Errors Due to Frequency and Wave Form — Errors of 
Observation. 



xiv CONTENTS 

CHAPTER XXIII 

Paqb 

Instrument Transformers 385 

Definitions — Reasons for Use — General Theory — Current Trans- 
former — Potential or Voltage Transformer — Influence of Trans- 
former Constants in Power Measurements — Variation of Error 
with Power-factor — Variation of Error with Phase Angle — Testing 
Instrument Transformers — Watt-hour Meter and Standard Trans- 
former Method — Test for Ratio of Transformation, Watt-hour 
Meter Method — Test for Phase Angle, Watt-hour Meter Method 
— Ratio by Wattmeter and Standard Transformer Method — Phase 
Angle by Wattmeter Method — Potential Transformer Comparator 
Voltmeter. 

Index 405 



ELECTRICAL METERS 

CHAPTER I 

FUNDAMENTAL ELECTRICAL PRINCIPLES 

Before taking up in detail the discussion of electrical measur- 
ing instruments and their application, it wUl be well to review 
some fundamental electrical principles with special reference to 
their application. 

1. Energy. — The industrial application of electricity is mainly 
a process of utilizing energy, and the industrial use of electrical 
measuring instruments is primarily to secure efficient genera- 
tion, distribution, and conversion of energy. Energy is thus the 
important entity in all industrial operations. In fact, the whole 
series of physical phenomena consists in the transfer and trans- 
formation of this entity. 

Physicists define energy as the ability of a body or a system 
of bodies to do work; and work is defined as overcoming resist- 
ance through space, or in other words, the motion of a body 
against a force. Every moving body possesses the ability of 
doing work, because by virtue of its motion it can set other 
bodies into motion. 

2. Forms of Energy. — For purposes of clearness in discussion 
and calculation, energy is usually considered under two heads 
which are determined by the manner in which energy manifests 
itself. As pointed out, a body in motion is capable of causing 
motion in another body and hence, a body possesses energy by 
virtue of its motion. Such energy is called kinetic. 

Again, energy may also be possessed by a body in such a 
position, or condition, that it is capable of motion and ready to 
do work when the occasion arises. Such energy is called 
potential. 

These two forms are not distinct in kind, and one form may 
readily be converted into the other. Perhaps the simplest 
illustration of the two kinds of energy and the conversion of one 
form into the other is a vibrating pendulum. At the extreme 

1 



2 ELECTRICAL METERS 

positions of its swing the pendulum comes momentarily to rest, 
hence, its energy of motion, or kinetic energy, is zero. All of 
the energy is in the potential form. At the lowest or middle 
point of its swing the energy of the pendulum is wholly kinetic, 
and at intervening points it is partly kinetic and partly potential. 

3. Conservatioii of Energy. — ^Throughout all transformations of 
energy^ no body or system of bodies can acquire energy except 
at the expense of energy possessed by some other system. Henc6, 
to do work is to transfer energy from one system to another, and 
the amount of energy lost by one system is the exact equivalent 
of that acquired by the other. This means that no electric 
generator can ever be made to give out more energy than it 
receives. Some energy is always dissipated in every trans- 
formation, and hence, no machine can have an efficiency of 100 
per cent. 

4. Electricity and Electrical Energy. — Wc know not what 
electricity fundamentally is, we know it only through its mani- 
festations or effects. It matters not, so far as practical results 
are concerned, whether electricity is a form of energy, or only a 
vehicle of energy. The fact is that energy always is manifest in 
connection with the electrical current, and that this energy can 
be transformed into other forms of energy. It may also be trans- 
ferred from point to point without the necessity of mass motion. 
It is this ability to transfer energy without mass motion that 
makes electricity the only successful medium for transferring 
energy over long distances. 

The transformation of electrical energy is electrical work and 
is accomplished in many ways. The rate of transformation is 
power just as in the case of an expenditure of mechanical energy. 

6* Analogies. — ^The kinetic energy of a body in motion is pro- 
portional to the square of its speed. If m represents the mass 
of the body and Vi its speed, its kinetic energy is given by 

Kinetic energy ==*>J^m Fi* 

When a force acts upon a body in motion, its eflfect is to acceler- 
ate the speed of the body, that is, to change its speed from V\ 
to 72. The kinetic energy then is equal to y^mV^^. If the 
action of the force is such as to increase the speed there is an 
accumulation or storage of energy equal to 3^m(F2^ — Fi*). 
In an analogous way whenever a current in a circuit is increased, 
the energy in the magnetic field is increased. The mechanical 



FUNDAMENTAL ELECTRICAL PRINCIPLES 3 

energy is recovered when the body slows down to its former 
speed, and the electrical energy is returned to the circuit when 
the ciurent decreases to its former value. 

Another similarity between mechanical and electrical energy 
is found in their conversion from kinetic into potential form and 
vice versa. Mechanical energy can be changed to the potential 
form by compressing a spring. Electrical energy beoomes 
potential when a condenser is charged. 

This similarity or analogy is brought out more forcibly by 
writing the expressions for energy in the following algebraic 
forms: 

- f Mechanical energy of rotation = }4 ^^^ 

\ Energy of magnetic field = 3^ LI^ 

^ J Potential energy in compressed spring =^ l^Px 
\ Potential energy in charged condenser = 3^^ QE 

The letters in the above expressions have the following sig- 
nificance: 

K is the moment of inertia, a> the angular velocity, L the coef- 
ficient of induction and I the current strength. In the second 
set of expressions P is the maximum pressure to which the 
spring is subjected, x the distance through which the spring 
has been compressed, Q the quantity of electricity in condenser, 
and E the difiference of electrical pressure between the terminals 
of the condenser. The terms here used will be explained more 
fully later. 

6. Magnetism. — ^Magnetic bodies, or magnets, are bodies which 
attract or repel each other with a force other than gravitation and 
which tend to set themselves in a definite direction with reference 
to the earth's surface. The most obvious property of a magnet 
is its power to attract iron at a distance. A permanent magnet 
may be made by placing a bar of hardened steel within a solenoid 
and sending a current of electricity through the solenoid. The 
immediate space or region surrounding the magnet possesses 
unique properties. Some of these may be conveniently shown 
by placing a sheet of paper over a bar magnet and sprinkling 
iron filings on the paper. On examining the pattern produced 
on the paper by the filings, it will be discovered that they are 
arranged in Unes radiating from one end of the magnet and con- 
verging at the other end. Fig. 1. Another method of exploring 
the field surrounding a bar magnet is by the aid of a small pocket 



ELECTRICAL METER.<. 



When a small pocket compass is placed near one end 
of a magnet, the needle of the compass will point toward the 
magnet. When the compass is moved along one of the magnetic 
lines, it will remain parallel to the line. When the compass is 
brought near the other end of the magnet, the compass needle 
will be reversed, showing that the properties of the two ends are 
different at least in one respect. This fctperimental fact has led 
to a conventional statement that the magnetic lines leave the 
north-seeking pole of the bar magnet and reenter the south- 
seeking pole. According to this explanation the ma^etic 
lines are closed curves leaving the north pole, curving through 




the air, reentering the south pole, and completing the circuit 
through the metal. The magnetism about the bar is said to be 
due to a magnetomotive force analogous to electromotive force. 
The magnetomotive force sets up a difference of magnetic pres- 
sure between the two ends of the bar, which causes magnetism or 
magnetic flux from one end of the bar to the other. 

7. Properties of Magnetic Fields.- — When unUke poles of two 
magnets are placed near each other the arrangement of the mag- 
netic lines will be as shown in Fig, 2, The lines pass directly 
from the pole of one to the unlike pole of the other magnet. 
The attraction between unlike poles may, therefore, be considered 
as due to a tendency of the lines to shorten. 

When two like poles are brought near each other the resulting 
field is shown by Fig. 3. An inspection of this Bgure will show 



FUNDAMENTAL ELECTRICAL PRINCIPLES 



that the lines from one pole do not connect with those of the 
other pole. The repulsjon between unhke poles is therefore, due 




1^^^^ i--- %^ .^^ if^^t^ 



to a tendency of the lines to repel each other. These figures show 
that a tension or stress exists in a magnetic field parallel to the 




ines, and a pressure at right anglei 
more, the force of attraction and 



to their direction. Further- 
■epulsion has its seat outside 



6 ELECTRICAL METERF^ 

of the iron bar, and within the space surrounding it. This 
principle should be kept in mind. 

8. Strength of Magnetic Field. — The strength of a magnetic 
field is measured by the force it exerts upon a unit magnet pole. 
When this force is 1 dyne the field is said to have unit strength. 
Since iron filings arrange themselves in lines when subjected to 
the influence of a magnetic field, it is customary to express the 
field strength in lines per square centimeter; that is, graphically 
the density of lines is a measure of the field strength. A field of 
unit strength is represented by one line per square centimeter 
in a plane perpendicular to the lines. A field of 10 units would 
then be represented by 10 lines per square centimeter, etc. 

If the cross-sectional area of the field be S sq. cm. and if the 
field strength or density be represented by B, the total number 
of magnetic lines is equal to SB. The total number of lines 
through a given area is called the magnetic flux. Algebraically 

f>(flux) = SB 

9. Relation between Tension and Flux Density. — When a mag- 
netic circuit is made of iron, only a small magnetomotive force 
is necessary to maintain the magnetic flux. When one or more 
air gaps intervene, most of the magnetomotive force is utilized 
in forcing the flux through or across the air gap. As a result, 
there is manifest a force of attraction between any two parts of a 
magnetic circuit which are separated by an air gap. Both from 
experiinental and theoretical considerations, it has been deter- 
mined that this force is proportional to the square of magnetic 
flux per unit cross-section, or put in algebraic form the tension 
may be expressed as follows: 

F = KSB^ 

where F is the force, B the flux density, S the area, and K a 
constant. If F is to be expressed in dynes per square centimeter, 

the expivssion becomes 

B^ 

F (dynes) = ^ 

In pounds per square inch 

^. .^ (2.54)2^2 

F (pounds) = 445^000 >r8T 

10. Magnetic Field Surrounding an Electric Wire. — The be- 
havior of a compass needle near a wire through which a current 



P//W- — 



FUNDAMENTAL ELECTRICAL PRINCIPLES 7 

ifi flowing is much the same as when near a magnet. This 
showa that the space surrounding a current carrying wire is a 
magnetic field. 

The magnetic lines surround the wire in concentric circles as 
shown in Fig. 4. The dark spot m the center of the figure repre- 
sents a cross-section of the wire The 
direction of the magnetic hnes is de 
termined in accordance with the e\ 
periment shown in Fig. 5. If a cur 
rent passes from south to north along 
a wire held above a pivoted magnet r 
needle, the iV-end of the needle will be 
deflected westward. 

The north-seeking end of the mag- 
netic needle is pushed aside by the 
field surrounding the wire. The direc- 
tion of the hnea below the wire must 

then be westward. In any given case the direction of the lines 
may be determined by the following rule: 

Grasp the wire with the right hand, the thumb pointing in the 
diredion of the current, the finders will then point in the direc- 



-^ 



Fio. 4. 




Fio. 5. 

tion of the magnelic lines. The magnetic field surrounding a 

straight wire may be considered aa a series of concentric cylinders. 

11, Field of a Circular Coil. — When the wire is coiled into a 

circular loop, the magnetic lines enter one side of the loop, pass 



8 



ELECTRICAL METER/? 



through, and spread oiit at the other side, Fig. 6. The loop of 
wire thus haa the properties of a magnet; the north-seeking pole 
being where the l)ne« leave, and thu south pole where the lines 
enter the coil. A magnet brought near the loop will be attracted 
or repellnd, depending on whether unlike or like poles are brought 
near each other. 

12. Solenoidd.— It haa already been pointed out that, when an 
eJePtric wire in wound into a coil, all or nearly all the magnetic 
lincB pa«B in at one end and out at the other. Many types of 
inntninKnite make iiae of some form of a solenoid. When the 
solenoid [XtsscsMS an iron ctjre, the combination is called an 
electroningnet. Figs. 7 and 8 ahow the general distribution of 




tho magnetic linus in both a solenoid and electromagnet. Upon 
rofcrring tt) tho flgurca in question, it will be noticed that the 
linos do not all go tho whole length of the solenoid, but aomo 
(«u(ipe between the convolutions. The magnetic field is thus not 
uniform throughout the length of the solenoid. In fact, the 
Guil hati to be of considerable length to got a uniform field of 
10 em. length. 

When the Bolcnoid has an iron core, fewer magnetic lines take 
"short cuts" between tho convolutions of the coil, but raore lines 
continue throughout the whole length of tho solenoid. This is 
due to tho fact that the iron offers less opposition or reluctance, 
tui it is culled, to the estiiblishment of the miignctic hnes, than air. 
It requires less magnotoniot ive force to establish a given number 
uf magnetic lines in irun than in air, so when a doSoitc magnetic 



FUNDAMENTAL ELECTRICAL PRINCIPLES 9 

field is estabUshed within a solenoid, the introduction of an iron 
core will greatly increase its strength. 

The strength of magnetic field within a aolenoid is given by the 
formula 

4 



H 



10 



TTlI 




Fio. 7. 

where n is the number of turns per unit length — 1 cm. — of 
solenoid, and / is the current in amperes. This formula applies 
only to the middle portion of the solenoid where the field is 
uniform. Toward the ends the value falls off rapidly. When 




an iron core is placed within the solenoid, the fiux density within 
the iron is 

4 

/t is a quantity depending upon the quahty of the iron and may 



10 ELECTRICAL METERS 

have many values under different conditions. It is always 
greater than one and may be as large as 10,000. 

The cores of electromagnets should be made of the softest and 
purest iron, but for alternating currents the core niust be made of 
laminated iron or iron wire. The laminations prevent the forma- 
tion of eddy currents which tend to flow at right angles to the 
direction of the magnetic lines. The elimination of eddy ciurents 
prevents excessive heating of the core. 

13. Law of the Magnetic Circuit. — The relation between the 
magnetizing force of a solenoid and the resulting magnetic flux 
may be conveniently expressed in the form of Ohm^s law. 

Analogous to resistance in an electrical circuit there is a quan- 
tity called reluctance in the magnetic circuit. The readiness 
with which any given magnetizing force will build up a magnetic 
field depends upon the permeabiUty, length, and cross-section 
of the circuit. 

The higher the permeability and the greater the cross-sectional 
area of the circuit the more readily will the magnetic field be 
established. On the other hand, the longer the circuit the 
stronger will the magnetizing force have to be to establish a 
given field. The effect of these physical properties of a magnetic 
circuit is called reluctance and is equal to 

T 

31 = 



iiA 

Where L is the length of circuit, /x the permeability, and A the 
cross-section. 

The magnetomotive force due to a solenoid carrying a current 

/is 

4 
m.m.f. = -T^irNI 

Where N is the total number of turns on solenoid. 

4 

in m f To '^''^^ 
Analogously to Ohm's law the flux $ = — ~^~ = — j 



1^ 

When the magnetic circuit is not uniform, the reluctance of 
each part must be determined separately. The reluctance of 
the whole circuit is the sum of the reluctances of its parts. 

14. Force Exerted upon a Wire in a Magnetic Field. — Since a 
wire carrying a current is surrounded by a magnetic field, a force 



FUNDAMENTAL ELECTRICAL PRINCIPLES 11 

of attraction or repulsion will be experienced when the wire is 
introduced into a field due to a magnet; this force will act at 
right angles to the wire, and to the field of the magnet, Fig. 9. 

If / represents the current fiowing in the wire, H the strength 
of magnetic field, and I the length of wire at right angles to field, 
the force is given hy F = IIH. 

The direction of the force, as indicated by the arrow, may be 
determined by the following rule: 

If the thumb, index, and middle fingers of the left hand be held 
at right angles to each other, the thumb pointing in the direction 
of the field, the index finger in the direction of the current, the 
middle finger will point in the direction of the force acting upon 



li 



¥ 



'v:.k>.?s> -,:--■'- ^. 



Fio. 9. 



the conductor. If this conductor is free to move it will move in 
the direction of the force. Thus in F^. 9 the direction of the 
field is from N to S, and if the current fiows up through the paper 
the force will be in direction indicated. 

15. Force between Parallel Wires Carrying Currents. — Two 
parallel wires carrying electric currents will be either attracted 
or repelled depending upon whether the currents are fiowing in 
the same or opposite directions. 

If the currents flow in the same direction the magnetic lines 
will combine sq as to encircle both conductors. Fig. 10. The 
tension along the lines will be manifest aa a force tending to 
draw the wires together. 

When the currents are in opposite directions, the direction of 
the fields between the conductors is the same, and hence, the 
pressure at right angles to the lines will tend to force the wires 
farther apart. 



12 ELECTRICAL METERS 

The intensity of the force in either case is proportional to the 
product of the currents in the two wires. This relation is derived 
as follows: 

At a distance x from a wire carrying a current 7, the strength 
of field is 

X 

The force between a field // and a current per unit length of 
conductor is 

F = HT, r is the current in the second conductor 

Since H = — 

X 

F = , per unit length of conductor. 

X 

When I and /' are in absolute units, x in centimeters, the 
force is in dynes. 

1 ( o o } ) 

Fia. 10. 

When the two currents are equal, / = /', the expression becomes 

F = KP 

where K is a proportionality factor. 

These relations are very important as they have numerous 
applications in electrical measuring instruments. 

16. Electrolytic Conductors. — The passage of an electric cur- 
rent through some liquids is accomplished by different phenomena 
from its passage through solids. In fact, in regard to their 
conductivity, liquids may be divided into three groups, viz. : 

1. Those which make fairly good insulators, or which are non- 
conductors for practical purposes such as paraffin, mineral oil, 
etc. 

Note. — Tho studont can find tho dorivations of the two assumod oqua- 
tionfl, //---• and F - ///' in books on Physics. 



FUNDAMENTAL ELECTRICAL PRINCIPLES 13 

2. Those which conduct like solids without undergoing any 
chemical change, such as molten metal, mercury, etc. 

3. Those in which the passage of the current is accompanied 
by chemical decomposition, such as solutions of acids, salts of 
the metals, and some other chemical compounds. 

Liquids of the latter class are called electrolytes. The process 
of their decomposition by the passage of the electric current is 
called electrolysis, and the cell in which electrolysis is carried 
on is called an electrolytic cell. 

17. Faraday's Laws. — During the years 1833 and 1834 Faraday 
investigated the relation between the quantity of electrolyte 
decomposed by an electric current, and the strength of the current. 
The result of his investigations he expressed as follows: 

1. The mass of the solution decomposed is proportional to the 
quantity of electricity which passes through it. 

2. The mass of any substance Uberated by a given quantity of 
electricity is proportional to the chemical equivalent of the 
substance. 

The first law means that a given current of electricity flowing 
for a given time will deposit the same mass or weight of a given 
element from a solution, irrespective of the concentration of the 
solution that contains the element, or of other conditions. 

According to the second law, the mass of substance deposited 
will depend upon its combining weight, which is called chemical 
equivalent. Thus, when a solution of copper salt is used as the 
electrolyte, the mass of copper deposited will depend on whether 
a cupric or cuprous salt is used. The chemical symbol for cupric 
chloride is CuCU, and for cuprous chloride CuCl. From this it 
will be seen that two atoms of copper in the cuprous compound 
take the place of one atom in the cupric compound. The com- 
bining weight is twice as great, and twice as much copper will be 
deposited by a given current from a cuprous solution as from the 
cupric solution. The law also states that if solutions of different 
compounds be decomposed, the weight of material deposited by 
a given current is proportional to the combining weight of the 
materials or elements forming the compounds. Thus, 1 ampere 
sent through a solution of silver nitrate for 1 hr. will deposit 
4.025 grams of silver. The same current sent through a solu- 
tion of copper sulphate will deposit only 1.184 grams of copper 
in 1 hr. These laws are the fundamental principles of the 
operation of electrochemical measuring instruments. The elec- 



14 



ELECTRICAL METERS 



trochemical equivalents of some metals are given in the following 
table: 

Table I 



Metal 



Electrochemical equivalent in 
milligrams per coulomb 



Aluminum. 
Copper. . . 
Copper. . . 

Gold 

Iron 

Iron 



Lead.. . 
Nickel. 
Silver. . 
Zinc. . . 



0.0936 
0.6588 
0.3290 
0.6818 
0.2894 
0.1929 
1 . 0731 
0.3040 
1.1180 
0.3385 



It is noticed that two values are given in the table for copper 
and iron. This is because each of these has different valencies 
as explained above. The value 0.3290 for copper usually applies 
when copper is deposited in an electrolytic cell. The table may 
be reduced to English units by remembering that 1 gram is 
equal to 0.0353 oz. avoirdupois. 

18. Heat Effect. — The physical principle made use of in some 
instruments is the expansion of the metals by heat. When the 
temperature of a wire is raised, it expands; and since some of the 
energy of a current is always converted into heat, the strength 
of current may be measured by means of the expansion of a 
wire suitably arranged. Hot-wire instruments are due to an 
adaptation of this principle. 

19. Practical Electrical XTnits. — In the application of electricity 
many terms are constantly met, and a clear comprehension of the 
meaning of these terms will aid materially in understanding their 
industrial application. Among the most important terms are 
the names of the fimdamental electrical units: ohm, ampere, 
volt, coulomb, watt, joule, henry, and farad. 

20. Resistance. — ^Every electrical conductor offers a resistance 
to the flow of electricity. This resistance depends upon the 
material of which the conductor is made, the length of the con- 
ductor, and its cross-sectional area. The resistance of a con- 
ductor is analogous to the resistance a water pipe offers to the 
flow of water. This resistance will depend upon the roughness 



FUNDAMENTAL ELECTRICAL PRINCIPLES 16 

of its surf ace, or upon the material of which it is made. A long 
pipe will oflfer more resistance than a short pipe of same diameter, 
and a pipe of large diameter will oflfer less resistance than one of 
same length but of smaller diameter. It must be remembered, 
however, that the cause of the resistance of a conductor to the 
flow of electrical current is not the same as the cause of the resist- 
ance of a water pipe to the flow of water. They are analogous 
only. 

The resistance of any conductor can then be written in the 
following form: 

rl 
R = -~ 
^^ A 

where R is the total resistance, r, the resistance of a piece of 
the conductor of unit length and of unit cross-section, A its cross- 
sectional area, and I its length. 

The ohm is the unit of resistance and is defined as the resistance 
oflfered to an unvarying electric current by a column of mercury 
at the temperature of melting ice, 14.4521 grams mass, of a 
constant cross-sectional area and of a length of 106.3 cm. 

The ohm is thus a definite quantity and the resistance of any 

rl 
conductor is expressed in terms of it. In the formula R = -jy 

I and A may be expressed in any units, provided r expresses a 
resistance based on these units. The definition given for the 
ohm assumes Z to be in centimeters and A in square centimeters. 
In this country the Brown and Sharpe, or American wire gage 
has been generally adopted where a gage is to be used. In 
many cases it is better to specify the actual diameter or cross- 
section of a wire, and for this purpose the "mil system'' has been 
introduced. In this system the mil is the unit of length and is 
equal to 0.001 in. 

Since the areas of any two circles are proportional to the squares 
of their diameters, if the area of a circle 1 mil in diameter be 
taken as the unit area, the area of any other circle may be ex- 
pressed as the square of its diameter in mils. The unit area is 
called the circular mil (circ. mil) and is, as above expressed, the 
area of a circle 0.001 in. in diameter. Area in circular mils is 
equal to diameter squared, and the area expressed in square 
measure is equal to 0.7854 X d^ (diameter squared). The 
circular mil is, therefore, equal to 0.7854 sq. mil. 

It is seldom necessary to convert the area of round conductors 



16 ELECTRICAL METERS 

into square measure. The wire tables which are in common use 
usually give the sizes in the American wire gage, its diameter 
in mils, its area in circular mils, and various other properties of 
wire depending on the completeness of the tables. 

Wires larger than 0000 A.W.G,, that is, of a greater diameter 
than 0.46 in., are usually designated by their diameters in mils 
or their cross-sectional area in circular mils. 

The unit of a conductor most commonly used is a conductor 
1 ft. long and 1 mil in diameter called the mil-foot. The resist- 
ance of a mil-foot of copper of 98 per cent, conductivity is 9.61 
ohms at 0**C. or 32®F. This value may be used in our resistance 
formula, which then becomes 

R = '-f I 

I being expressed in feet and A in circular mils. 

21. Change of Resistance with Temperature. — The resistance 
of most conductors changes with the temperature. The resist- 
ance of pure metallic conductors increases with increase in 
temperature For pure metals the increase per ohm per degree 
is practically the same for all. This increase per ohm per degree 
change in temperature is called temperature coefficient of resist- 
ance, and for pure metals is nearly 0.00393 per degree Centigrade. 
The resistance of a conductor at any temperature i®C. is given 
by the following: 

Rt = Roil + at) 

Ro is the resistance of conductor in ohms at 0®C., a the tempera- 
ture coefficient, and i the temperature. The resistance of most 
alloys also increases with increase in temperature, but to a much 
smaller extent than pure metals. Thus an alloy of 84 parts by 
weight of copper, 12 parts by weight of nickel, and 4 parts by 
weight of manganese, called manganin, has a tempc^rature coeffi- 
cient of resistance which is negligible for practical purposes. 
Although the temperature coefficient of manganin is very slight, 
it is positive between 0° and about 50®C. When the temperature 
is increased above 50°C. the resistance of manganin slightly 
decreases. 

Carbon and all acid salt solutions have negative tempera- 
ture coefficients of resistance. That is, the resistance of these 
decreases as the temperature increases. 



FUNDAMENTAL ELECTRICAL PRINCIPLES 17 

22. Electric Current — The term ''electric current" has already 
beeiL used several tnMrwithout explanation, and perhaps an 
explanation will not aid much in giving a clear understanding of 
the quantity. 

Since the transfer of energy by water through pipes is in many 
ways analogous to the transfer of energy by electrical means, 
the terminology in one case is used to some extent in the other. 

When water flows through pipes the energy transferred by it 
in a given time depends upon the current and head, or pressure. 
The current is the number of gallons or cubic feet of water per 
second, or some other unit of time. The current is then the rate 
of flow of water. 

Electrical energy may be transferred along a conductor, and 
while the energy is being transferred the conductor is surrounded 
by a magnetic field. The transfer of energy is said to be by 
means of a current of electricity. Thus, the rate of flow of 
electricity is also called a current. The two cases are evidently 
analogous. 

In measuring a water current it is possible to measure the 
quantity of water discharged and thus, the rate of flow. It is 
not practical to measure an electric current in this way. The 
electric current is measured by means of its effect, and any effect 
which is proportional to some power of the current strength 
may be used for determining unit current, and hence, for measur- 
ing the current. The practical unit current has been defined in 
accordance with Faraday's first law as follows: 

The Ampere is the unvarying electric current which, when 
parsed through a standard solution of nitrate of silver in water, 
deposits silver at the rate of 0.00111800 gram per second. An 
ampere will thus deposit 4.025 grams of silver per hour. 

Absolute Unit of Current. — Another definition of unit current 
rests upon the fundamental principle that about every electric 
current there is a magnetic field. The intensity of this magnetic 
field at any point varies directly as the current strength and 
inversely as the distance of the point from the conductor (see 
Article 16). 

If a magnet be introduced into such a field, a force will be 
exerted upon it. The unit current is defined in terms of this 
force. According to these principles, unit current is defined as 
that current which, when flowing through a conductor 1 cm. long, 
bent into an arc with 1 cm. radius, will exert a force of 1 dyne 



18 



ELECTRICAL METERS 



on unit magnet pole placed at the center of the circle of which 
the arc is a part. The ampere is one-tenth of this absolute unit, 
23. Electromotive Force. — The real cause of an electric current 
is called electromotive force. Without going into details, we 
may say that electromotive force can be generated in three ways: 

1. Chemically, as in voltaic cell. 

2. Thermally, as when the junction of two metals is heated. 

3. Mechanically, as in the case of the static induction machine 
or when a wire is moved across a magnetic field. 

Of these three methods the last is the all-important one in 
industrial practice. It consists in the application of the principle 
that a wire moved in a magnetic field in such a direction aa to 
cut across the magnetic lines has an electromotive force induced 
in it. That is, the reaction between the magnetic field and the 
mechanical force causing the motion is manifest as an electro- 
motive force between the terminals of the wire. The value of 
this electromotive force will depend upon the strength of the 
magnetic field, the length of wire, and the speed with which it 
is moving across the field. This principle is used in the con- 
struction of all dynamo-electric machines, which form the main 
means for the conversion of mechanical into electrical energy 
and vice versa. 

Volt. — Since the resistance of a conductor is comparable 
to the resistance offered by a pipe to the flow of water, and the 
electrical current is comparable to the current of water, we may 
compare the electromotive force or electrical pressure to the 
water pressure causing a flow of water. Although this com- 
parison is not exact, it still serves to give, a better understanding 
of the relation of the electrical quantities involved. Water 
pressure can be measured in terms of pounds per square inch, 
but usually it is expressed as a head of so many feet. In the 
same way, the difference of electrical pressure between the termi- 
nals of a battery may be considered as a difference of electrical 
level. The current will then flow from a point of higher to a 
point of lower electrical level, when the circuit is closed. This 
difference of electrical pressure or electromotive force, is ex- 
pressed in volts, and the volt is defined as that difference of pres- 
sure which will cause a current of 1 amp. to flow through a 
resistance of 1 ohm. 

24. Quantity. — The quantity of water flowing through any 
given pipe in a given time may be expressed as the strength of 



FUNDAMENTAL ELECTRICAL PRINCIPLES 19 

current multiplied by the time. That is, if a unit current gives 
a cubic foot of water per second, a two-unit current would give 
2 cu. ft. per second, or 4 cu. ft. in 2 sec. 

Similarly, a unit current of electricity flowing for 1 sec. gives 
a definite quantity of electricity. This quantity is called 
the coulomb and is defined as the quantity of electricity conveyed 
by a current of 1 amp. in 1 sec. of time. The total quantity 
conveyed by a current of / amp. in t sec. is then given by 

Q = It, assuming / to be constant. 

26. Energy. — Referring again to our analogy we may consider 
unit work to be done when a cubic foot of water is delivered 
under a head of 1 ft. The amount of work done by a head of h 
ft. delivering q cu. ft. of water will then be hq. 

In our electrical analogy, the head was analogous to electrical 
pressure, and the number of cubic feet of water is analogous to 
the number of coulombs. A current delivering Q coulombs of 
electricity under a pressure of E volts will then do EQ units of 
work. The unit of electrical work is the joule and is defined as 
the work expended in a circuit when 1 coulomb is transferred 
under a pressure of 1 volt. Since the number of coulombs 
delivered by a current of I amperes in the time t is It, the amount 
of work expended by a current of I amperes in the time t and under 
a pressure of E volts is 

Work = Elt joules. 

Watt-hour, — One watt-hour equals 3,600 joules. 

26. Power. — The watt is the unit of power and is equal to 

1 joule per second. The watt is also equal to ».^ hp. The 

number of joules of work expended by a current of I amperes in t 
sec, as above expressed, is Elt; the niunber of joules per second 
will then be Elt -i- t or EI. That is, the power of a current of 
/ amperes flowing under a pressure of E volts is EI watts. 

27. Inductance. — It was briefly pointed out in Article 23 that 
when a conductor moves across a magnetic field an electro- 
naotive force is induced in the conductor. Evidently it is im- 
material whether the field is stationary and the conductor moves, 
or the conductor is stationary and the magnetic field moves; the 
necessary condition is relative motion between conductor and 
field. 

3 



20 



ELECTRICAL METERS 



This relative motion may be secured in several ways; the one 
in which we are at present interested consists in changing the 
magnetic flux around a conductor by means of the current in 
the conductor. 

Consider the case represented by Fig. 11 where a battery B 
supplies current through a variable resistance R to an electro- 
magnet M. Let us suppose the circuit open and no initial or 
residual magnetism in the core. Upon closing the circuit a 
current will begin to flow through the electromagnet coil. This 



• 1 • • 

* . • .' 
\ • • / 



\ \ ' ! • •' 




Fig. 11. 



current will magnetize the core and thus cause a number of 
magnetic lines to thread through the coil. If the resistance R 
is varied, the current will change and consequently the number 
of magnetic lines threading through the coil is either increased or 
decreased. In other words, any change in the current is accom- 
panied by a change in the magnetic flux passing through the 
coil. 

According to the principle of electromagnetic induction, when- 
ever the number of magnetic lines linked with a circuit is changed 
an electromotive force is induced in the circuit. Consequently, 
every time the current in the coil changes, an electromotive 
force is induced in it. The electromotive force induced by the 
building up or decay of the magnetic field within the coil, due 



FUNDAMENTAL ELECTRICAL PRINCIPLES 21 

to the variation of current in the coil, is called self-induction. 
The induced electromotive force is in such a direction as to 
oppose the applied electromotive force. In other words, while 
the current is changing the electromotive force of self-induc- 
tion opposes any change. If the magnetic lines threading 
through the coil are due to a current in an adjacent coil, the 
phenomenon is the same, but it is called mutual induction. 

From Fig. 6 it is evident that each magnetic line through the 
center of the coil is linked with each turn; or what amounts to 
the same thing, the lines due to each turn are linked with every 
other turn as well. The electromotive force of self-induction then 
depends not only upon the current but also upon the arrangement 
of conductors in the coil. If <^ is the total flux due to one turn 
through the coil, and if n is the number of turns, the total flux 
is n<^. This total flux is proportional to the current and hence 
we may write 

n4> = LI 

The constant L is called the coefficient of self-induction, or 
simply the self-inductance of the coil. 

The electromotive force of self-induction depends upon the 
rate of change of magnetic field. This may be expressed by 

„ d^ .dl 

^^^^^'-dt-'^dt 

Where -it represents the rate of change of current. 

According to this expression the inductance L is defined as 
the ratio of the induced counter electromotive force to the time 
rate of change of current. 

Henry. — Self- and mutual-inductances are physical quantities 
of the same nature, and hence the same unit must be used for 
both. This unit is called the henry and is defined as the induct- 
ance in a circuit in which the induced electromotive force is 1 
volt, when the current changes at the rate of 1 amp. per second. 

28. Capacity. — If two metal plates be separated by a good 
insulator and the two plates be connected to a source of electrical 
pressure, a momentary current will flow into the plates. The 
intensity of the current will depend upon the ability of the plates 
to hold a charge of electricity. This ability of a conductor or a 
system of conductors, to store electricity is called electrical 
capacity. The capacity of a system of conductors is determined 



22 ELECTRICAL METERS 

by their arrangement, number, and material separating them. 
The quantity of electricity that a condenser will hold is deter- 
mined by the capacity of the condenser and by the electrical 
pressure applied. Algebraically this is expressed by 

Q = EC 

Where Q is the quantity of electricity, E the pressure, and Cthe 
capacity. 

Farad. — ^The imit of capacity is called the farad and is that 
capacity which is charged to a difference of pressure of 1 volt 
by 1 coulomb. 

The effect of inductance and capacity in alternating-current 
circuits will be given later. 

29. Ohm's Law. — The relation between current and electro- 
motive force in a circuit was first enunciated by Dr. G. S. Ohm 
in 1827, and is known as Ohm's law. It may be stated as 
follows: 

The current strength in any circuit is directly proportional 
to the sum of all the electromotive forces in the circuit. This 
relation expressed algebraically is 

E = KI 

or 

E 

Y = K, a, constant. 

This holds for both direct- and alternating-current circuits so long 
as the physical conditions surrounding the circuit remain un- 
changed. For direct-current circuits K is equal to what is 
called the resistance of the circuit, and under these conditions 

^ = /?/ 
or 

Thus the ratio of the electromotive force to current is constant 
so long as physical conditions remain constant. If, for instance, 
the temperature changes, this ratio will change. This is ex- 
plained by saying that the resistance changes. 

In alternating-current circuits the total electromotive force 
must include the electromotive forces of mutual induction, 
self-induction, and capacity. When these are considered, Ohm's 



FUNDAMENTAL ELECTRICAL PRINCIPLES 23 

law, as stated, still holds. What quantities enter into the ex- 
pression 

when alternating currents are considered is explained in Chapter 
IV. 

30. Pressure Drop in Direct-ciirrent Circuits. — If a current I 
flows through a circuit, the electromotive force necessary to force 
it through a resistance R is, by Ohm's law, 

Ea = IR 

Thus the product of current by resistance is equal to the difference 
in electrical pressure between two points. This quantity IR is 
called pressure or voltage drop. 

31. Energy Loss. — The flow of electric current through a con- 
ductor is analogous to the flow of water through a pipe. The 
pressure forcing the water through the pipe is analogous to the 
electrical pressure which maintains the electrical current. Work 
is defined as force times distance through which it acts. Evi- 
dently, if the water pipe is closed and no water flows, considerable 
pressure can be exerted and still no work be done. If, however, 
the water is flowing under a given pressure a certain amount of 
work will be done which is proportional to the quantity of water 
times the pressure. This is seen to be true, if the pipe be vertical, 
in that case, the height of the pipe is proportional to the pressure 
and the height in feet times the weight of water delivered at the 
top equals foot-pounds of work. 

Similarly, the work done in transferring a certain quantity of 
electricity through a conductor is proportional to the pressure 
times the quantity of electricity. 

If we define our unit of work as the product of unit quantity 
times unit difference of pressure, the total amount of work will 
then be represented by the total difference of potential times 
the current times the time, or 
W = Elt, since It is the total quantity of electricity delivered. 

Power is the rate of doing work, or is the work done per second, 

hence, 

^ W Elt ^j 
Power, or P = y = — = EI 

If the difference in pressure between any two points, as A and B 



24 ELECTRICAL METERS 

of a conductor, is E and the current is 7, the energy spent per 
second in that portion of the circuit is IE. But, as has been 
shown, 

E = /«, 
Hence, P = IE = I X I X R = PR 

This is known as power loss or energy loss per second due to 
resistance. 

The effects of both the voltage drop and loss of energy due to 
resistance, are objectionable. The voltage drop produces a dif- 
ference of pressure between the generator and receiving circuit. 
The PR losses cause heating of the conductors, thus increasing 
the fire hazard. They also cause a deterioration of the insulation 
and lessen the efficiency of the distributing systems. 

SUMMARY 

The Ohm is the unit of resistance. It is the resistance offered 
by a column of mercury of uniform cross-section, 106.3 cm. in 
length, weighing 14.4521 grams at 0°C. 

The Ampere is the practical unit of current, and is that current 
which, when passing through a standard solution of silver nitrate, 
deposits silver at the rate of 1.118 mg. per second. 

The Volt is the practical unit of electrical pressure and is the 
electromotive force which will produce a current of 1 amp. 
through a resistance of 1 ohm. It may also be defined as 

1 J^Q«^ of the electromotive force of the Weston standard cell 

atWc. 

The Coulomb is the imit of quantity of electricity and is the 
quantity of electricity conveyed by 1 amp. in 1 sec. 

The Joule is the unit of work, and is represented by the work 
expended in 1 sec. by a current of 1 amp. under an electrical 
pressure of 1 volt. 

Joules = k X volts X amperes X time. 

The Walt is the unit of power and is equal to 1 joule per 
second. The watt is also equal to }/j4q hp. 

Watts = fc X volts X amperes. In direct-current circuits 
ifc = 1. 

The Kilowatt is the practical unit of power and is equal to 
1,000 watts. 



FUNDAMENTAL ELECTRICAL PRINCIPLES 25 

The Kilowattrhour is the practical unit of work and represents 
1,000 watts supplied for a period of 1 hr. It is equal to 3,600,000 
joules. 

The Henry is the unit of inductance and is defined as the 
inductance of a circuit in which the induced electromotive force 
is 1 volt when the inducing current changes at the rate of 1 amp. 
per second. 

The Farad is the unit of capacity and is that capacity which is 
charged to a difference of pressure of 1 volt by 1 coulomb. 
The farad is too large for practical use, hence, the microfarad 

farad j is commonly used. 



\1,000,000 



CHAPTER II 

CLASSIFICATION OF INSTRUMENTS 

32. Classes of Meters. — ^The discriminating characteristic of 
a classification of electrical measuring instruments may be the 
quantity to be measured, or the principle upon which the instru- 
ments operate. The plan here followed bases the main divi- 
sions of measuring instruments upon the quantities to be 
measured, while minor subdivisions are according to the principles 
of operation. The quantities measured by electrical instru- 
ments are: current, electromotive force, quantity'', power, energy, 
frequency, power-factor, and phase. Frequency, power-factor, 
and phase will be explained later. 

The instruments for measuring these quantities are anameters, 
voltmeters, coulometers or ampere-hour meters, wattmeters, 
watt-hour meters, frequency meters, power-factor meters, and 
synchroscopes. 

33. Groups of Instruments. — ^As already stated, the minor 
subdivisions of instruments wiU be based on the principles of 
their operations. Accordingly, we have electromagnetic, electro- 
dynamic, electrostatic, and thermal groups. 

34. Electromagnetic Instruments. — ^Any instrument that makes 
use of the interaction between the magnetic field surroxmding 
an electric conductor and the magnetic field around an iron 
core, belongs to the electromagnetic group. The application of 
the principle is made in various ways and accordingly we have 
the following types of electromagnetic instruments: 

1. The movable-core type. 

2. The movable-coil permanent-magnet type. 

3. The induction type. 

36. Electrod3mamic Instruments. — The force between two 
conductors carrying electric currents is called electrodynamic 
attraction or repulsion. Hence, electrodynamic instruments 
are those whose actuating forces are due to currents flowing 
through coils without iron cores. 

36. Electrostatic Instruments. — Electrostatic instruments are 
4 27 



28 ELECTRICAL METERS 

actuated by forces of attraction and repulsion between electne 
charges. Their action is independent of magnetic forces. 

37. Thermal Instruments. — The actuating forces of the thermal 
group are due to the expansion of a wire by the heat generated in 
it when an electric current is flowing. These are usually called 
hot-wire instruments. 

38. Controlling Forces.— Where any physical quantity is 
measured in terms of the force it exerts, provision must be made 
for the application of some countcrforce whose intensity will 
increase in proportion to the actuating force. Since the common 
methods of measuring electrical quantities are in terms of their 
force effects, the moving system of every meter must be counter- 
balanced in some way. This counterbalancing force must be 
BO adjusted that the deflection or speed of the moving part, as 
the case may be, is always proportional to the actuating force. 
If this were not done, the movable system would deflect to the 
extreme position, or would race, upon the application of a force 
sufficient to overcome the friction of the movable parts. The 
controlling forces employed for this purpose are: 

1. The resisting force of a spring. 

2. The torsion of some filament. 

3. The attraction of gravity. 

4. The attraction of permanent magnets. 

5. The attraction of induced and inducing currents. 

6. The mechanical friction of a rotating fan. 

The first four of these controlling forces are utilized in am- 
meters, voltmeters, and wattmeters of both the indicating and 
recording forms, while the fifth and sixth are applied in watt- 
hour meters of various types. \Vhen a spring is used it may be 
one of two forms, i.e., it may be helical in form, or in the form 
of a spiral. The helical form is used to control both in torsion 
and by axial extension. The fundamental law of the relation 
of the actuating force and distortion of spring within the limits 
of elasticity is: the actuating force is proportional to the dis- 
tortion produced. The strength of either form of spring will 
be increased by decreasing the number of turns, or by increasing 
the sectional area of the spring. Springs are usually made of 
some elastic nonmagnetic material. In most cases the material 
used is phosphor-bronze. 

The use of the torsion of a metal or silk fiber suspension is 
limited almost wholly to laboratory instruments. The same 



CLASSIFICATION OF INSTRUMENTS 



29 



relation between the actuating force and the resulting deflection 
holds as in the case of spring control. 

The third form of control is very satisfactory, when it can be 
applied. The application of this method of control permits the 
construction of comparatively cheap and relatively accurate 
instruments. In this method the law, mentioned above, con- 
necting the actuating force with the distortion does not hold. 
This will be made clear by referring to Figs. 12 and 13. Fig. 12 
shows a typical arrangement for gravity control. P, the pointer, 
is balanced by the weights B and C When the pointer moves 
to the right, C rises and B falls so that the moment of the two 





Fig. 12. 



Fia. 13. 



about the point of suspension is zero. The controlUng force is 
furnished by the weight A, which moves to the left and up as 
the pointer moves to the right. The moment of the force tend- 
ing to bring the weight back to its vertical position or the pointer 
to its zero position, will vary with the position of A. The 
moment of A around the point of suspension 0, Fig. 13, is equal to 

w X bV at b 
w X cc' at c 
w X dd' at df etc. 

If we call od = o6, etc. = r and if the angle through which the 
pointer has been deflected be represented by 6, then 66' = r sin 0; 
cc^ = r sin 6, etc., and thus the moment tending to bring pointer 
back to zero is in general, 

moment = wr sin 6. 

Since w and r are constants, the resisting moment varies as the 



30 ELECTRICAL METERS 

sine of the angle of deflection. The graduations of the scale on 
such an instrument are not uniform, being close together at the 
beginning and end of the scale, and relatively far apart in the 
middle. 

The fourth method of control is used only to a sUght extent. 
The objection to this method is that in the presence of a magnetic 
field the indications are Ukely to be in error without the knowledge 
of the user. This error in the readmg of the instrument is due to 
the influence of the outside field upon the permanent magnet 
of the instrument. 

39. Magnetic Shielding. — It is a well-known principle that the 
reluctance of iron is much less than that of air. Thus, when a 
piece of iron is introduced into a magnetic field, the magnetic lines 
will be concentrated in the iron. The lines will deviate from a 
straight hne and pass through the iron instead of through the 
air. 

The movable or working systems of some meters are quite 
readily afifected by a magnetic field and, to ehminate this in- 
fluence, they are enclosed in an iron case. When this is done, the 
external field does not penetrate the instrument, and thus the 
readings are unaffected unless the external field is very strong. 

40. Friction of Supports. — Several ways have been tried to 
support the moving system with varying degrees of success. 
The usual way of supporting the moving coil is to mount it upon 
two hardened steel pivots with sharpened points resting in 
sapphire, or diamond jewel bearings. Although the movable 
system is made as light as possible, the pressure per unit area is 
considerable on account of the small area of contact between 
pivot and bearing. Owing to this small contact, the wear and 
friction on the pivot increase with time, especially in portable 
instruments, unless some provision is made for relieving this 
pressure, when the instrument is not in use. 

One method of securing a resilient support for jewels is shown 
in Fig. 14. In this figure DD is a two-piece shaft fitted at top and 
bottom with cup-shaped jewels. In the middle or at the junction 
of the two halves of the shaft is a collar C which carries a small- 
diameter screw over which the halves of shaft DD are threaded. 
The distance between the jewels can thus be adjusted by screwing 
or imscrewing the collar C. Surrounding each half of the shaft 
is a spiral spring F, one extremity of which bears against the 
collar and the other against a cup-shaped guide bushing at the end 



CLASSIFICATION OF INSTRUMENTS 31 

of the shaft. This structure permits of longitudinal motion of the 
shaft against the tension of the spiral springs, and, consequently, 
in case of a sudden jar the coil G with its attached pointer will 




transmit the pressure of the pivot E, until the lower surface G 
comes into contact with the upper surface of the stationary core 
ff, thus preventing damage to jewels. 



CHAPTER III 



=0 



CURRENT AND PRESSURE-MEASURING INSTRUMENTS 

41. Ammeters and Voltmeters.- — These two classes of instru- 
ments will be discussed together since, with the exception of 
the electrostatic voltmeter, they are alike in most respects. 
The names ammeter and voltmeter are clearly derived from 
ampere and volt, the units of current and pressure respectively. 

42. Uses of Ammeters and Voltmeters. — The main difference 
between ammeters and voltmeters Hes in their use. Ammeters 
are connected in series with the circuit in which the current is 
to be measured. That is, they are connected in such a way 
that the total or proportional part of the total current passes 
through the instrument. Voltmeters, on the other hand, are 
connected in parallel. That is, the terminals of the voltmeter 

are connected to two points, between which 
the difference of pressure is to be measured. 
Fig. 15 shows a standard connection for a 
voltmeter and an ammeter. In so far as 
construction is concerned, ammeters and 

[ yM voltmeters are similar. With the exception 

V^ of the electrostatic voltmeters, all volt- 

meters are ammeters graduated in volts. 
Fm. 15. The moving system is actuated by the cur- 

rent passing through the instrument, and in 
each instrument the deflection depends upon the strength of this 
current. 

The pressure drop due to resistance between any two points 
of a conductor is JR, as already shown. Hence, if R is constant, 
the pressure drop varies with the current. 

In ammeters with shunts this pressure drop along a resistance 
is utilized for sending a current through the movable system. 
The resistance of the movable system being constant, the current 
through it is directly proportional to the pressure drop and thus 
to the main current. Since the current through the movable 
system is proportional to pressure drop, it is evident that the in- 



MEASURING INSTRUMENTS 33 

strument may indicate the voltage or current. Thus, if JB is the 
difference of pressure between the voltmeter terminals, Fig. 15, 

and if i2 is the resistance of voltmeter coils, the current through 

E 
the voltmeter is / = p- Since R is practically constant, I 

varies as E. The current which causes a deflection of the mov- 
able system thus varies as the pressure between voltmeter 
terminals. In place of graduating the instrument in terms of the 
current passing through it, it is graduated in terms of the dif- 
ference of pressure between terminals. The action in every 
respect is the same as that of an ammeter. The current through 
the ammeter is limited by the circuit to which the ammeter is 
connected. The current through the voltmeter is limited by the 
resistance of the instrument itself. 

In order that the energy lost in each instrument may be as 
small as possible, there is a great difference in the resistances of 
the two kinds of instruments. Since the load current or a certain 
per cent of it passes through the ammeter, its resistance must 
be very low in order that the PR loss may be small. 
Since the voltmeter is connected as a shunt to the main circuit, 
its resistance must be very large in order that the current may 
be small. Thus, voltmeters have coils of relatively high re- 
sistance — several thousand ohms — while ammeters have low 
resistance coils — only a few thousandths of an ohm. 

43. Range of Instruments. — The current intensity that an 
ammeter can indicate is mainly determined by the resistance 
of the movable coil. In practice two methods are used for 
increasing the range, viz., shunts for direct-current and trans- 
formers for alternating-current ammeters. 

44. Ammeter Shunts. — ^There are so many types of ammeters 
that it is practically impossible to make a general statement of 
principles. The following will be found to apply mainly to 
ammeters whose movable system is actuated by current passing 
through it. The movable coil carries only a small part of the 
current so that, when the instrument is made to be used as an 
ammeter, a shunt for the main current must be provided. This 
shunt is nothing more than a low resistance which bears a 
constant ratio to the resistance of the movable coil. For small 
currents the shunt is mounted within or as a part of the instru- 
ment. For measuring large currents, however, the shunt is 
moimted separately, and the instrument is connected to the 



34 



ELKCTRTCAL METERS 



terminala of the shunt as shown in Fig. 16. The instrument 
used in this way is in reahty a millivoltmeter which measures the 
voltage drop across the shunt. . The current strength is obtained 
in accordance with Ohm's law. This may be made clear by 
considering the following example: Assume that the shunt has 
a resistance of 0.001 ohm and that the instrument reads 40 milM- 
volts. According to Ohm's law the drop across the shunt is 

IR = E 
or i X 0.001 = 0.040 



If the shunt and instrument are to be used together constantly 
the shunt and millivoltmeter are calibrated together and the 
scale is graduated in amperes. 




FlQ. Ifl. 



Since the shunts carry the main current and become heated, 
they must be made of some material whose temperature coeffi- 
cient is very small. An alloy of copper, manganese, and nickel 
called manganin, fulfills this requirement more fully than any 
other, and for that reason is almost universally used for ammeter 
shunts. Fig. 17 shows some standard Weston shunts. 

45. Range of Voltmeters. — Two methods are also in general 
use for increasing the range of voltmeters. One is by means of 
resistance coils connected in series with the instrument and the 
other by what are called potential transformers. 

46. Voltmeter Multipliers, — It would be very inconvenient to 
make a movable coil of sufficient resistance to measure high 
differences of potential. To do this economically would necessi- 
tate large coils. The same thing can be accomplished in another 



MEASURING INSTRUMENTS 35 

way; that is, by mouuting in series with the movable coil of the 
instrument a resistance sufficiently large to reduce the current 
to the desired value. By providing different resistances, or 




multipliers as these are commonly called, the range of instrument, 
can be varied considerably. In some cases these multipliers 
are mounted inside of the instrument case, and the circuit is 



JUTWl 



connected to the proper multiplier by ii 
separate binding post, plug switches, 
device. 



i of a push button, 
some other simple 



36 ELECTRICAL METERS 

The current in the multipher is relatively small, so its resistance 
must be comparatively high. Mangaiiin, constantan, or somo 
other alloy of high specific resistance and low temperature 
coefficient, is used. Multipliers for Weston voltmeters are 
shown in Fig. 18. 

47. The Movable-core Type. — To this type of instruments 
belong all those in which a piece of soft iron is acted upon by 
an electromagnetic field. The electromagnetic field is formed 
by an electric current flowing in a stationary solenoid, while the 
soft iron is pivoted and attached to a pointer which moves 
over a graduated dial. 

One of the oldest and simplest instruments of this type is 
shown in Fig. 19. C is the stationary solenoid, P is the soft^ 
iron core pivoted at so that it can move freely up and down. 
^ To the arbor are also attached the 

pointer N and the counterweight Q. 
By referring to the discussion on 
controlling forces it will be seen that 
gravity is the controlling force in the 
plunger type of instrument, as that 
shown in Fig, 19 is usually called. 

In ammeters of this type the main 
current flows through the solenoid C, 
and the core F is drawn into the 
solenoid against the force of gravity 
on Q. The cod C, as shown, usually 
consists of a few turns of heavy wire. In voltmeters, however, 
the solenoid is made of many turns of fine wire. It is customary 
to place an additional resistance in series with the voltmeter coil 
of this type in order to reduce the current sufficiently when used 
to measure high voltage. By changing the resistance of the 
multiplier, the range of the instrument can be varied through 
wide limits. Fig. 20 shows the main features of a Westinghouse 
plunger- type ammeter. 

Another form of this type of instrument is the Thomson 
inclined-coil ammeter. The essential features of this instrument 
are shown in Fig. 21, and the complete instrument is shown in 
Fig. 22. As shown in the diagram of Fig, 21, the stationary coil 
makes approximately an angle of 45" with the shaft upon which 
is mounted a soft-iron vane, also making approximately an angle 
of 45°. 




Fig. 1 



MEASURING INSTRUMENTS 



The operation of the instrument is as followB: The current 
flowing through tho stationaiy coil, sets up a magnetic field, as 




Fig. 20. 



shown in Fig. 21. When the pointer is at zero of the scale the 
plane of the vane is nearly at right angles to the magnetic lines. 
When the magnetic field is set up, the vane moves so as to become 




parallel to the magnetic field. Opposing this motion is the 
Bpiral spring at the upper end of the shaft. Since the pointer is 



38 ELECTRICAL METERS 

also rigidly attached to the ahuft it moves over the scale, coming 
to rest when the torque due to the controlling spring is equal to 
the torque due to the action of the magnetic field on the vane. 
The counterweight balances the moving parts. 

The inclined-coil niovable-vane instrument is much more com- 
pact than the plunger type; the movable parts are lighter, 
reducing friction and mn.l<ing the instrument much more Gensitive. 




The gravity control of the plunger type ia replaced by the epiral- 
spring control. As has been already shown, the counterforce 
in the gravity-control method is proportional to the sine of the 
angle of deflection, while the counterforce of the spring is directly 
proportional to the deflection. This permits the use of a more 
uniform scale, although the graduations cannot be made exactly 
uniform on accoimt of the fact that the deflecting force acting 
on the vane is not directly proportional to the current. 



MEASURING INSTRUMENTS 39 

Another method of applying the principle of reaction between 
magnetic fields is utilized by the Weston Electrical Instrument 
Co. in their so-called "soft-iron" instruments. The essential 
parts of an instrument of this type are shown in Fig. 23. Refer- 
ring to the diagram, £ is a fixed piece of iron of nearly triangular 
shape, bent into cylindrical form. Concentric with this is a 
movable piece of similarly shaped iron D which is secured to the 
staff F, which carries the pointer P. The movable element is 
mounted on a support G and inserted in the field coil C, which 
for the voltmeter is connected in series with a noninductive 
resistance. Under the magnetizing action of the field coil the 
two iron pieces tend to separate and thus produce a torque 
which is opposed and controlled by the spring S, The torque 
for any deflection is approximately proportional to the square 
of the current in the field coil. The two iron pieces D and E are 
shaped so as to give a nearly uniform scale. 

The movable-core or soft-iron instruments may be used on 
both direct and alternating circuits. This is due to the fact that 
the iron core of the plunger type, and the vane of the inclined- 
coil type are attracted by a magnetic field no matter what its 
direction. When the instrument is to be used on alternating 
current, the core must be of laminated iron or of a bundle of 
soft-iron wire; this is done to prevent the flow of eddy currents 
and consequent alteration of the force. 

48. Approximate Equation for Pull on Iron Core. — The mag- 
netic field H within a solenoid is equal to H = 1.257 nl, where 
n is the number of turns per centimeter length, and I is current 
in amperes. When an iron core is introduced into the solenoid, 
the number of magnetic lines is greatly increased. 

Although the permeability of the iron core is not constant but 
varies with the intensity of magnetization, nevertheless it may 
be assumed that the flux density is approximately proportional 
to the current. This may be written 

B = KI 

The pull exerted by the solenoid upon the iron core is propor- 
tional to the product of the strength of magnetic flux and current, 
or 

Pull = K'BI 

But as has already been shown, B is proportional to /, so by 



40 ELECTRICAL METERS 

replacing S by / wc get pull = K'J*. That is, the puD on tte 

plunger is proportional to the square of the current flowing 
through the Holenoid, When the uiBtrument is used to nicasuro 
alternating current, the value D is at each instant proportional 
to the current. Since the current varies, B will vary, but at each 
instant the pull will be proportional to the square of the current 
at that instant. We may thus write instantaneous pull = fci', 
where i is the instantaneous current. The direction of the pull 
does not change, for as the current reverses the magnetic field 
due to the current reverses, or the field and current change their 
signs together. The inertia of the movable system does not per- 
mit it to follow the instuntancoua fluctuations of the pull; the 
plunger will assume a ]»ositioii determined by the average pull. 
By higher mathematics it can be shown that the average pull is 
pro|)ortional to the moan square of the instantaneous values of 
the current. The square root of the mean-square value is called 
the effcctivo value, and is the value given by all alternating- 
ourrent instruments. 

The movable-core type of instrument, when calibrated with 
direct current, should then give exact effective values of alternat- 
ing currents. In practice this is not quite true. The magnetic 
field does not increase uniformly with the current, and also the 
eflfeet of eddy currents and hysteresis is appreciable. The dif- 
ference, however, is not great; the readings differing only slightly. 

49. Movable-coil Permanent-magnet Type. — In this type of 
meter tho miigiietiu field remains constant and is due to a 
permanent magnet of the horseshoe form. Between the poles 
of tho magnet is mounted a rectangular coil in sueh a way that 
it can revolve through a considerable arc within a specially 
designed magnetic field. When in use, the current flowing 
through the coil tends to set up a magnetic field at an angle 
to the field of tho permanent magnet. The reaction between 
the two fields causes a deflection of the pointer which is rigidly 
attached to tho shaft of the moving coil. 

Tho general principles of this type of instrument are well 
shown in I''ig. 24. The permanent magnet is shown in the diagram 
by NS, N being the north and S the south pole. The rectangular 
coil C carries the current causing the deflection. Usually this is 
only a smalt per cent, of the total current to be measured. The 
controUing force ia furnished by two spiral springs, one at the 
upiier, the other at the lower end of the shaft. The springs are 



MEASURING INSTRUMENTS 



41 



coiled in opposite directions so that when the pointer is deflected, 
one of the springs is coiled up, while the other is uncoiled. This 
scheme compensates for any inequalities that may exist in the 
springs. In most cases the springs also serve to make connection 
between the coil C and the external circuit. 





A' 



Fia. 24. 



Fia. 25. 



In this type of instrument the direction of the main field 
remains constant. The deflection of the pointer will be in one 
direction when tte current flows from t to f and in the opposite 
direction when the current is reversed. This being the fact, it is 
evident that instnunents of this type cannot be used to measure 




♦^ 



Fia. 25o. 

alternating ciurent. They are, however, very eflSicient and con- 
venient direct-current instruments. The instruments of the 
Weston Electrical Instrument Co., made in accordance with the 
foregoing principles, have practically been the standard direct- 
current instruments for years. 



42 



ELECTRICAL METERS 



The cross-Bcction of the movable coil is usually rectangular 
and it usually surrounds a soft-iron cylindrical core. The 
function of the core is twofold; to concentrate the field and to 
secure a distribution of flux in the air gap such that uniform 
graduations are possible. 

A modified form of magnet core is employed by the Westing- 
house Co. in its movable-coil permanent-magnet type of meters. 
This is shown in Fig. 25, The two C-shaped magnets, A and 
A', are attached to two soft-iron pole pieces B and C. Instead of 
having a central core of soft iron, the pole piece B is shaped to 
conform to the semicircular cavity cut in the pole piece C. A 
small air gap G is left between thcni. The movable coil is wound 
upon a light aluminum frame to which is attached the pointer and 
hardened steel pivot, Fig, 25a. The coil Ie mounted eccentrically, 
that is, the staff is at one side of the coil. The advantage claimed 
for this form of construction is that the coil to a certain extent 
counterbalances the pointer, thus reducing the amount of 
additional counterweight required and making the weight carried 
by the pivots a miminum. 

50. Damping. — By damping is meant the checking or impeding 
the freedom of motion of the movable element. A properly 
damped instrument will deflect promptly, but not too quickly 
through the correct angle and no farther. The movement of an 
undamped instrument is Uablc to be oscillatory — the movable 
element will vibrate above and below the correct indication. 
Good damping is thus necessary, not only on account of the 
convenience and accuracy of making readings, but also because 
it reduces the wear on the pivots and lessens the danger of injury 
in case of overload. 

There are two general methods of damping in use in com- 
mercial electrical measuring instruments, mechanical and 
electro magnetic. 

In mechanical damping a vane or plunger is caused to move 
through a more or less resisting material such as oil or air. The 
use of oil for damping is restricted to instruments which remain in 
a fixed position such as on switchboards. In the Westinghouae 
plunger-type instrument. Fig. 20, the lower end of the plunger is 
immersed in oil which dampens any sudden movement of the 
pointer. 

In air damping a vane moves within a chamber which is con- 
structed with just the desired amount of air leakage. This 



44 



ELECTRICAL METERS 



leakage may be into or out of the chamber, or it may be from one 
side of the vane to the other. As the vane moves, it corapresBes 
the air in front and rarefies it behind. 

The amount of damping necessary depends upon the weight 
and moment of inertia of the moving element, and hence if air 
damping ia to be efficient the vane must be light and have a small 
moment of inertia. In this respect the beat made instruments 
meet all reasonable requirements. Fig. 23 shows one method of 
applying air damping. The vane B is attached to the movable 
element, and as this ia deflected the vane moves in the air damper 
, box A. 

The electromagnetic method of damping is employed in all 
f permanent-magnet movable-coil instruments. The movable 
/ coil of these instruments ia wound upon an aluminum or copper 
me which has eddy currents induced in it as it moves in the 
field of the permanent magnet. The reaction between these 
eddy currents and the magnetic field retards or dampens the mo- 
tion quite satisfactorily. The reaction between the movable 
coil and the magnetic field may also cause damping. In volt- 
meters this is not appreciable on account of the large resistance 
of the voltmeter circuit; but in ammeters it may be appreciable. 
The theory of electromagnetic damping is quite complicated, 
but a good discussion can be found in certain texts. ^ In Fig. 
26 are shown the movable elements of eight different makes of 
ammeters, while in Fig. 27 the same movable elements and 
magnets are assembled.^ The instruments represented in these 
figures are all of American make. 

61. Torque Exerted by a Magnetic Field upon a Rectangular 
Coil. — Let Fig. 28 represent both a side and a top view of a rec- 
tangular coil in a permanent magnetic field of uniform distribu- 
tion and strength H. Assume the plane of the coil to lie parallel 
to the field. When a current flows through the coil, a turning 
moment or torque will be manifest due to the interaction of 
current and magnetic field. This torque will tend to turn the 
coil in such a way that its plane will be at right angles to the 
permanent magnetic field. The force per unit length of con- 
ductor carrying a current / in a field of strength H, is HI. If 
a be the breadth and b the height of coil the force on one side 
per turn is bHI, and for N turns it is NbHI. For both aides of 

• Mprooch and Oschwald, "Electrical Insrunicnts." 

• Fitch and Hubbb, Bulletin Bureau of Standards, vol. 7, No. 3. 



46 



ELECTRICAL METERS 



the coil it will be twice this, or 2NbHL If the coil is pivoted at 
the middle point of a the torque is 

T = 2NbHI X a/2 
= NabHI 

T is the torque in dyne-centimeters tending to turn the coil when 
a and b are in centimeters and / in absolute units. 

When the coil is turned through an angle 6 about the axis of 
rotation, the component, or one may say, the intensity of the field 
producing torque, will be different. This component is equal to 
H cos 0. Hence, if the field is uniform as assumed, the torque 
becomes 

T = abNIH cos 6, 




■^ -J- -» 



N i:Ti 



N 



^-_>i.-iV 







^^^^2r 



Fkj. 28. 

In well-designed instruments the pole pieces of the permanent 
magnet are shaped so that H cos d is practically constant within 
the limits of motion of the coil. The quantities a, 6, and N are 
constant for any given coil, and if H cos 6 is constant, we may 
replace abNH cos ^ by a constant K, the expression for torque 
then becomes 

T = KL 

This shows that in well-designed instruments of the movable-coil, 
permanent-magnet type, the torque is proportional to the first 
power of current. Since the opposing torque of a spring is pro- 
portional to the angle of twist, the coiled-spring method of control 
is ideal, and is universally used upon this type of instruments. 
These principles make possible practically uniform graduations. 



CHAPTER IV 

FUNDAMENTAL PRINCIPLES OF ALTERNATING 

CURRENTS 

62. Introduction. — ^Before discussing induction-type instru- 
ments, some general principles of alternating currents will first 
be reviewed. 

In Chapter I were discussed some of the fundamental principles 
of power and work. It was there shown that the power in a 
direct-current circuit is given by IE watts, where / is the current 
in amperes and E the electromotive force in volts impressed upon 
the circuit. Similarly, the energy consumed or utilized by the 
circuit in t sec. is Elt joules. 

From this, and from the other considerations discussed in 
Chapter I, it is evident that the measurement of power in direct- 
current systems is comparatively a simple operation. All one 
needs to know is the current in amperes and voltage, when the 
power is readily obtained as the product of the two. Thus an 
ammeter and voltmeter suffice for power determination in direct- 
current circuits. 

When power is to be measured in a circuit in which alternating 
current is flowing, due to an alternating electromotive force, 
other considerations enter. These considerations we shall now 
briefly discuss. 

63. Alternating Current. — An alternating current or electro- 
motive force is one which begins at zero, increases to a maximum 
in one direction, then decreases to zero and again increases to a 
maximum in the other direction, finally decreasing back to zero 
again in one cycle. These cycles continue one after another so 
long as the current is flowing. Thus, in an alternating-current 
system the terminals of the circuit are alternately positive and 
negative and the current flows first in one direction and then in an 
opposite direction. 

61. Generation of an Alternating Pressure. — ^The simplest 
method of generating an alternating pressure is that indicated 
in Fig. 29 Here the rotating armature consists of two conduct- 

47 



48 



ELECTRICAL METERS 



Ofs A and B, connected so as to form a loop. The loop is 
supported on the shaft Z>, and centered between the two magnet 
poles .V and S. The ends of the loop are connected to two insul- 
ated metal slip rings, Cj and Ca. The circuit is completed 
through the external circuit R by means of metal contacts or 
brushes bearing on the riiiga. Assuming that the magnetic lines 
pass straight across the armature from the A'' polu to the S pole, 
when the loop is rotated the sides A and B of the loop have elec- 
tric pressures induced in them. Since the conductors arc moving 
across the field in opposite directions, the pressures in the conduct- 
ors will be oppositely directed with reference to the plane of the 
paper. But the two conductora are so connected that the two 
pressures act together around the loop; therefore, the pressure 




Fig. 29. 

between the brushes will be twice that developed in either 

conductor. 

Starting with the plane of the loop in a vertical position, the 
conductors ai'e moving parallel to the magnetic lines and, conse- 
quently, no lines are being cut and no pressure is induced in the 
loop. As the loop revolves from its vertical position, the angle 
at which the lines are cut approaches a right angle until the loop 
has turned through 90°, when the conductors A and B will be 
passing under the centers of the poles JV and S respectively. At 
this instant they are cutting the lines at right angles, and conse- 
quently the maximum pressure will be induced in each conductor. 
As the coil or loop rotates beyond this point, the number of lines 
cut by the conductor in unit time decreases. When the loop has 
advanced another 90° it will again be in a vertical position, but 



PRINCIPLES OF ALTERNATING CURRENTS 49 

A will be at the bottom and B at the top. At this instant the 
pressure is again zero. During this half rotation the current in 
external circuit will pass through exactly similar changes in 
strength. 

Duringthenext half revolution, conductorA will pass up in front 
of the S pole, and B down in front of the N pole; consequently, 
the pressure will go through the same changes that it went 
through the first half revolution, but the pressure will be directed 
in the opposite direction. The current through external circuit 
will flow in the opposite direction also, and its changes in value 
will follow those of the pressure. 

The pressure and current, therefore, pass through a complete 
cycle of changes; starting from zero they increase to a maximum, 
then decrease to zero; reverse in direc- * 

tion, increase to a negative maximum, ' 1 I i I iDj 
then again decrease to zero, after ^ t * + *j_P 
which the same cycle of changes is 
repeated. I 

56. Law of Fluctuation of Altemat- I 
ing Pressure and Current. — In Fig. -il-l 
30 let C and Ci represent the cross- 
sections of the two conductors of a 
loop, as in Fig. 29, revolving about 
an axis perpendicular to the plane of 
the paper at 0. Since the pressure 
induced in one conductor is equal to 
that induced in the other, it will be sufficient to consider the 
variation of pressure in one conductor only. Assume the con- 
ductor to be revolving counter-clockwise as indicated by the ar- 
row, and let ^ be the angle made by the plane of the coil with 
the line OA ; OA is taken as the reference hne. If the coil rotates 
with uniform speed, C will move around a circle with uniform 
speed, V, and ^ will be a uniformly increasing angle. Assume 
that the coil has turned through the angle and reached the 
position shown in the figure. 

By many experimeets it has been determined that whenever a 
wire is moved across a magnetic field an electromotive force is 
developed. The intensity of the electromotive force will depend 
upon three quantities: the strength of the magnetic field, the 
length of the wire within the field, and the speed with which it is 
moving. No electromotive force is induced when the wire 




Fio. 30. 



50 ELECTRICAL METERS 

moves along the direction of the field; hence, it is evident that 
the intensity of the pressure will also be influenced by the direc- 
tion of motion of the wire. Expressing these experimental facts 
in a mathematical equation we get e =^ HlVo in absolute units. 
If we wish to get e in volts, the above expression must be divided 
by 10«, or 100,000,000, since 10» absolute units equal 1 volt. The 
expression becomes 

^(voltH) = -j^j^- 

where 

H = strength of field in lincis per square centimeter. 

I = total cutting length in centimeters of all conductors in 
series. 

Vo = the velocity at right angles to the magnetic lines in centi- 
meters per second. 

Let CD, Fig. 30, perpendicular to OC represent graphically to 
scale the direction and magnitude of the constant velocity F, 
with which C is moving around the circle. 

Let DH be a line drawn through D parallel to the magnetic 
lines, and CH a line drawn through C perpendicular to the mag- 
netic lines. It is evident that at this instant the same number of 
magnetic lines would be cut if the conductor moved horizontally 
with a velocity 7p, equal to CH as whc^n it moves around the 
circle with the velocity V. Vo is the velocity at right angles to 
the lines and it is the velocity which must be used in the formula 
for e. 

From geometry, thcj angle mad(i by tluj lin(»8 DC and DH is 

equal to the angle <l>. The ratio of Vo to K, ( i/), is called the 

sine of the angle <t>; consequently, Vo = V sin <^. Substituting 
this value for Vo in the formula for e we get 

/// V sin 4> 

In this expression e is the instaiitan(;ous pressure. 

When <^ = 0, sin <^ = and the induced pressure is zero. 

When ^ = 90^, sin </> = 1 and the induced pressure is a maximum. 

HIV 
The expression -^^ represents thcj maximum vahui of the electro- 

HIV 
motive force. We can then write A « = ^^8 > ^^^ ^ ~ ^^ ®^^ ^» 

Em means maximum electromotive force. 



PRINCIPLES OF ALTERNATING CURRENTS 



51 



The instantaneouB value of the pressure is, therefore, propor- 
tional to the aiue of the angle which the plane of the coil makes 
with a plane at right angles to magnetic field. 

The successive values of the electromotive force, which are 
induced as the coil passes under the N and S poles, can be graph- 
ically represented, as in Fig. Si- 
Let the base line AB represent 360° and let it be divided into 
equal part^, each part representing 30". At points representing 
0", 30°, 60°, 90°, etc., draw vertical lines whose lengths represent 
the maximum value of the alternating quantity times the sin 0°, 
sin 30°, etc. Between 180° and 360° the sine is n^ative and the 




Fia. 31. 

values are drawn below the base line. This is in agreement with 
the fact already mentioned that the pressure changes in direction 
as the conductors pass from under one pole beneath another pole. 

A curve drawn through the extremities of the vertical lines is 
called a sine curve. If the maximum ordinate is Em, then the 
sine curve will be the sine curve of the pressure. If the maximum 
ordinate represents the maximum value of the current, the sine 
curve will be a sine wave of current, 

Another method of graphically constructing a sine curve is 
shown in Fig. 32. The radius of the circle, to the left, is made 
equal to the maximum value of the sine curve. Let OM be an 
extension of the line of reference AB and draw radial lines 
ON, OP, OQ, etc., making angles of 30°, 60°, etc., with the base 
line OM. From the extremities of these radii draw horizontal 
lines intersecting the vertical lines erected at points on AB repre- 



52 



ELECTRICAL METERS 



senting the corresponding angles. The points of intersection will 
be points on the sine curve. Between 0° and 180^ the ordinates 
are above the axis and from 180° to 360° they are below. A curve 
drawn through all the points of intersection will be a sine curve. 
At the point on AB representing 30°, the ordinate equals RN. 
But from trigonometry RN equals ON X sin 30°. If ON were 
drawn to represent Em then RN equals E^ sin 30°. In general 
the curve shows graphically the value of y in 



or 



y = A sin X 
e = Em sin <t>. 



Dcqrces or +imc 
oi Sec — * — >■ 02 Sec 

a40 270 300 330 360 




One cycle 
Fig. 32. 

If 0) represents the angle described by ON in unit time, 1 sec, 
in t sec. it will describe an angle equal to cot, and if < is the 
time required to describe angle </>, then <l> = (at. The expression 
for induced pressure then becomes 

e = Em sin wt. 

There is some advantage in considering AB, Fig. 31, as an axis of 
time, and plotting successive values of t horizontally rather than 
the angle </> or cot. For instance, if ON makes 50 complete 
revolutions per second, it will make one revolution in }4o or 
0.02 sec. The time required to describe an angle of 30° is one- 
twelfth of 0.02 sec. Thus the intervals A to 30°, etc., can just as 
readily be used to represent intervals of time. The significance 
of this will be seen when we consider phase difference. 

Although the positive and negative loops of an alternating 
current or pressure curve are nearly always alike, in general the 
fluctuations do not follow a simple law. Since any complex wave 
whose alternate loops are alike may be represented by the sum of 



PRINCIPLES OF ALTERNATING CURRENTS 53 

a series of sine and cosine curves having different amplitudes 
and frequencies, an alternating-current wave may be represented 
thus: 

i = Ii sin X + Iz sin 3x + Zs sin 5a; + etc. + /i cos x + Iz cos 
Sx + /s cos 5x +, etc. 

An analysis of such a representation of current or pressure is 
beyond the limits of this text. The following discussion is based 
on the assumption that the current or pressure curve may be 
represented by the first term on the right-hand side of the equa- 
tion; thus i = Im sin x = Im sin wt. 

56. Cycle, Frequency, Period, Alternation. — Referring to Fig. 
32, we may assume that the electromotive force induced within 
one coil of an armature, while under a north pole, is represented 
by the ordinates above the horizontal axis. Similarly, the ordi- 
nates under the horizontal axis represent the electromotive force 
induced in coil when under the south pole. These two sets of 
values are called a cycle. The number of cycles per second is 
called the frequency. The time required for the electromotive 
force to change through one cycle is called a period. 

Since the pressure and current pass through a complete cycle 
of values when the coil or conductor passes under a north and 
south pole, the number of cycles per revolution of an armature 
is equal to the number of pairs of poles. The frequency will then 
be equal to the number of cycles in one revolution multiplied by 
the number of revolutions per second, or 

/=|xn 

4 

where p is the number of poles and n the number of revolutions 
per second. If the revolutions per minute are given, as is 
usually the case, this number must first be divided by 60 to get 
the revolutions per second. 

There are always two alternations for each cycle, hence the 
number of alternations in any unit of time will be two times the 
number of cycles in the same unit of time. 

67. Instantaneous Value. — Representing the fluctuations of an 
electromotive force or current by a sine curve, the instantaneous 
value is represented by the distance from the horizontal axis to 
the curve at that particular instant. Thus in Fig. 32 the verti- 
cal lines y, yi, 2/2, etc., represent the instantaneous values at the 



ELECTRICAL METERS 



ends of the intervals of ; 



, etc., sec. aftflr the point 



600' 300' 200' 
-V has passed through M. 

68. Maximum Value.- — The instantaneous value at the point 

marked 90°, or at the end of — -- sec, is greater than that at 

any other point between 0° and 180°, and is consequently a 
maximum value. The numerical value at the point marked 
270° is equal to that at 90°; its direction, however, is downward 
and is, therefore, a negative maximum value. In alternating- 
current problems the term maximum has reference to only the 
numerical value and not to its direction. 

69. Average Value. — -The average value of an alternating 
electromotive force or current is the average of all the instan- 
taneous values for half a cycle, or the average of all the instan- 
taneous values for a complete cycle, irrespective of sign. The 
average or mean value of a series of quantities is, in general, 



■erage («) = 



ai + "a + q; + ■ 



where ai, Qi, oa . . . a„ represent the successive values and n 
is their number. 

Assuming that the instantaneous values of an alternating 
electromotive force vary according to a sine law, or that the 
alternating quantity is harmonic, the average value will be equal 
to the sum of the instantaneous values divided by their number. 
In olher words, it will be equal to the area between the curve and 
base line divided by the base line. It can be shown by calculus 

2 
that this is equal to - X maximum value = 0.636 X maximum 

value. The average value is used in some calculations. 

60. Effective Value or Root-mean-square Value. — The effect- 
ive value is very important in alternating-current problems. 

When a direct current is sent through a resistance, the energy 
converted into heat per second is 

Heat = I^R joules. 

An alternating current varies in intensity from instant to instant; 
its heating value is, however, at each instant equal to i^R, where 
(■ is the current at the instant considered. The heat developed per 
cycle will then be the average of i^R for the cycle. Since the 
resistance R remains constant, the heat developed per cycle 



PRINCIPLES OF ALTERNATING CURRENTS 65 

must be equal to R times the average of i^. Thus an alternating 
current, whose average square is /^, will develop the same amount 
of heat per second in a resistance ft as a direct current whose 
value is 7. 

If a direct current I be sent through an ammeter of the electro- 
dynamometer type, a torque proportional to P will be developed. 
If the same ammeter is used to measure an alternating current, 
the torque at each instant will be proportional to i^. This torque 
is always exerted in the same direction irrespective of the direc- 
tion of the current. The resulting torque will be proportional to 
the average of f^, and if the deflection with direct current is equal 
to that with alternating current, we may write 

KP = K average i^ 



and I = vaverage i^ 

That is, when the deflection is the same, the value of the direct 
current must be equal to the square root of the average of the 
squares of the instantaneous values of the alternating current. 
This square root of the mean-square value is called the eJBfective 
value, or "root-mean-square value," of an alternating current or 
pressure. It can easily be shown that for a harmonic current 
the ejffective value is M\^ times the maximum value; that is 



7= 0.707 7 
and E = 0.707 E, 



m 



m 



61. Effect of Inductance. — We learned in Article 10 that the 
wire along which an electric current is flowing is surrounded by a 
magnetic field. In a direct-current system this magnetic field 
remains constant, both in intensity and direction, so long as the 
current remains constant. The building up of the magnetic 
field requires energy which must be furnished by the initial cur- 
rent. Since no energy can be stored in any system unless that 
system reacts upon the source of energy or working substance, 
it follows that the magnetic field reacts upon the current to which 
it is due. This reaction prevents the sudden rise of current 
within a circuit to the maximum value, as indicated by Ohm's 
law. 

Again, when the circuit is opened and the current ceases, the 
energy that has been stored in the magnetic field is returned to 
the circuit and attempts to keep the current flowing. This 



56 



ELECTRICAL METERS 



energy manifests itself as a spark at the terminals of the circuit. 
Since the current cannot rise to a maximum value immediately 
upon closing the circuit, neither can it immediately fall to zero 
when the circuit is opened. This reaction of magnetic field upon 
the current is known as induction. 

The effect of induction may be considered as analogous to the 
action of a flywheel on a steam engine. When first the steam 
ia turned on, some of the energy of the steam is converted into 
energy of motion, or kinetic energy of the flywheel. The fly- 
wheel reacts upon the engine until steady speed is reached. 
When steady speed is reached, no more energy is given to the 
flywheel, but all of it goes toward running the . machinery. 
When the steam is shut off, the engine does not at once come to 
a dead stop; the flywheel keeps it in motion for some time until 
its kinetic energy has all been given back to the engine and 
machinery. 

62. Effect of Capacity.— In addition to inductance every 
circuit possesses some capacity, that is, the ability to become 
charged, or to store up electricity. One conductor alone has very 
little, but more than one, arranged in suitable ways, inay possess 
considerable capacity. When so arranged, the device is called a 
condenser. 

An electrical condenser may be considered analogous to an air 
tank. Suppose We have an air tank that under one atmospheric 
pressure holds a certain definite quantity of air, say 5 lb. We . 
can define the capacity of the vessel in terms of the number of 
pounds of air it holds, and call it a 5-lb. tank. 

If the pressure is doubled, the tank will hold 10 lb. of air. 
Since we have defined the capacity of the tank in terms of unit 
(one atmosphere) pressure, we cannot call it a 10-Ib. tank. A 
10-lb. tank under the same conditions will hold 20 lb. of air. 

Furthermore, suppose the tank to be exhausted, evidently no 
back pressure will be exerted when air is first admitted to the tank. 
As soon as some air is admitted to the tank, back pressure begins 
to manifest itself, and when the back pressure equals the applied 
pressure, no more air enters the tank. We thus see that the 
amount of air entering per imit time depends upon the back 
pressure, and this back pressure will depend upon the capacity 
of the tank. For instance, if we put 5 lb. of air in a 10-lb. tank, 
the back pressure will be one-half as great as when 5 lb. of air 
are put into a 5-lb. tank. We can then say that unit capacity of 



PRINCIPLES OF ALTERNATING CURRENTS 57 

a tank is such that when 1 lb. of air is forced into it the pressure 
will be equal to one atmosphere. Evidently, a certain amount of 
work will be done in forcing the air into the tank, and we could 
define unit capacity in terms of the work expended. 

The capacity of electrical conductors is analogous to the ca- 
pacity of the air tank discussed above. The capacity of a con- 
denser or system of conductors is usually defined in terms of the 
quantity of electricity required to raise the difference of pressure 
between the terminals by 1 volt. In accordance with this defi- 
nition the quantity of electricity that a condenser will contain is 
equal to the product of the capacity and pressure, or Q = EC, 
The flow of an alternating current within any circuit depends not 
only upon the resistance of the circuit, but also upon any induc- 
tance and capacity that may be contained in or connected with 
the circuit. 

The continual surging back and forth of the current in an 
alternating circuit gives rise to very important inductance and 
capacity effects in certain parts of the circuit, and the resulting 
peculiarities that distinguish the alternating from the direct- 
current circuit. The two factors mentioned above may be far 
more important than resistance, and in some cases may entirely 
control the flow of the current. 

63. Phase Difference. — It has been pointed out that the cur- 
rent wave is in form much the same as the electromotive-force 
wave in an alternating-current circuit. The constants of the 
circuit — ^that is, resistance, inductance, and capacity — will, 
however, influence the time at which the current will reach a 
maximum. 

This fact will probably be understood from the analogy of the 
flywheel as already given. If the pressure applied to the fly- 
wheel is constant it may be considered as analogous to the electro- 
motive force applied to a circuit possessing inductance. The 
speed of the flywheel may be considered as analogous to the 
current flowing. The pressure applied to the flywheel is maxi- 
mum at the start, while its speed does not reach a maximum 
until later. We can say that the speed lags behind the pressure. 
Similarly, the current in an inductive circuit does not reach a 
maximum until some time after the electromotive force. We 
thus say that the current lags behind the pressure. The time 
between the positive or negative maximum values of electro- 
motive force and current is the phase difference. This phase 



58 



EfjECTRICAL METERS 



difference depends upon the relative values of resistance and 
inductance of the circuit. 

When the circuit contains capacity, the analogy of the air 
tank serves to give an idea of the relations of these quantities. 
When the air is first admitted into the empty tank the current 
wiU be a maximum, and the counterpressure a minimum. The 
current of air thus leads the pressure. Similarly, when a source 
of electromotive force is connected to a circuit possessing capacity, 




l^'toOr-hQ 



Fig. 33. 



the current is a maximum ahead, in time, of the pressure; and 
we say the current leads. Again, the phase difference is repre- 
sented as the difference in time between the maximum values of 
current and electromotive force. 

The relative positions of the electromotive force and current 
curves are shown in Figs. 33 and 34. Fig. 33 shows the condi- 
tions in a circuit having resistance and inductance; and Fig. 
34, the conditions in a circuit having resistance and capacity. 
6 is the phase difference. 




Fig. 34. 

64. Power in Alternating-current Circuits. — Since in direct- 
current circuits the power is equal to the product of current and 
pressure, the instantaneous power in an alternating-current cir- 
cuit will be equal to the product of the instantaneous values of 
current and pressure. These, however, vary from time to time, 
so the average power per cycle will be the average of the instan- 
taneous values of the product of current and pressure. 



PRINCIPLES OF ALTERNATING CURRENTS 59 

When the current and pressure are in phase, that is, pass 
through their maximum and zero values at the same time, we 
have conditions as shown in Fig. 35. The power curve is ob- 
tained by multiplying together the instantaneous values of cur- 
rent and pressure, and, as the figure shows, the power reaches a 
maximum at the same time as current and pressure. The power 
curve is, however, always positive, for the product of two positive 

/A A 




time 
• -Currenr 

Fia. 35. 

quantities is positive, and likewise the product of two negative 
quantities is positive. 

In Fig. 36 we have conditions that are somewhat different. 
Here the current lags behind the electromotive force. The 
power curve has both positive and negative loops, that is, loops 
both above and below the horizontal axis. The average power 
supplied to the circuit will thus be the difference of the average 




7 time 
'>^' '"Current 

Fig. 36. 

of the positive and negative loops. It is thus evident that the 
average product of current and pressure in an alternating-current 
circuit does not give the average power unless the current and 
pressure are in phase as shown in Fig. 35. The power will 
depend not only upon the current and pressure, but also upon the 
phase difference between them. Ordinarily, the product of an 
anmieter reading and voltmeter reading will not give the true 

6 



60 ELECTRICAL METERS 

power in an alternating-current circuit. In general, the power is 
less than this product. 

As has already been shown, the phase difference will depend 
upon the inductance and capacity of the circuit, and hence the 
IKiwer will depend upon the inductance and capacity. 

66. Phase Angle. — We have defined phase difference as the 
interval of time that elapses between the maximum values of 
pressure and current. Physically this is exactly what the phase 
difference is. For purposes of computation, however, the phase 
difference is best expressed as an angle and, accordingly, the 
constant by which we multiply the product of the effective 
current and effective electromotive force to get the actual power 
in a circuit is usually written as the cosine of the phase angle, thus 

Power = IE cos 6 

where / and E are the effective values of current and pressure, 
or, in other words, are the values that alternating-current 
ammeters and voltmeters indicate. Cos 6 is the cosine of 
the phase angle and is called the power-factor. Another defi- 
nition of power-factor will be given later. When the current and 
pressure reach the maximum value at the same time, the difference 
in phase is zero and cos 6 = 1. When this is the case, the power 
is a maximum. 

This fact, that the alternating current and pressure causing 
the current may be out of phase, is fundamental in measuring 
alternating-current quantities, and should be mastered. As 
already stated, power computed from ammeter and voltmeter 
indications may be very much in error in some cases. Watt- 
meters, however, take account of the power-factor and their 
indications give correct values. 



CHAPTER V 

ALTERNATING-CURRENT CIRCUITS 

66. Single-phase Circuits. — A single-phase circuit consists of 
two line wires, and is fed by a single-phase generator. The 
armature of the single-phase genemtor contains a single wind- 
ing, the two ends of which are connected to two collector rings. 
In the revolving-field type of generator the single-phase genera- 
tor is provided with two terminals to which the external circuit 
may be connected. 

The electromotive force of a single-phase generator fluctuates 
between positive and negative values and is well represented in 
Figs. 33, 34, and 35. Similarly, the current in a single-phase cir- 
cuit fluctuates between positive and negative values, as indicated 
in the figures mentioned above. 

The single-phase circuit is thus similar to a two-wire, direct- 
current circuit. The flow of power in the circuit is, however, 
considerably different. It can be shown that the power in a 
single-phase circuit fluctuates with a frequency double that of 
the electromotive force or current. A curve showing the fluc- 
tuations of power in a single-phase circuit is shown in Fig. 36. 

67. Polyphase Circuits. — ^A polyphfise circuit may consist of 
either two, three, or more phases; th(e three-phase circuit being 
the most common. ) 

The winding of the armature of a quarter-phase, conunonly 
called two-phase, generator consists of two distinct sets of coils. 
This winding is so arranged that, when the coils of one set are 
under the field poles, the coils of the other set are midway be- 
tween the field poles. Thus, when the electromotive force in 
one set of coils is a maximum, that in the other set is zero. 
The electromotive-force curves of a quarter-phase generator are 
shown in Fig. 37. Calling the angular distance between two 
consecutive poles of an alternator equal to 180°, the difference 
in phase between the electromotive forces in the two sets of 
windings is 90®, as indicated in figure. 

A quarter-phase circuit usually contains four wires, each con- 

61 



62 



ELECTRICAL METERS 



nected to the terminals of one set of coils on the annattire. For 
simplicity, it may be looked upon as consisting of two single- 
phase circuits. In some cases two of the return wires are joined 
and the circuit consists of only three wires. This system is not 




very common. The quarter-phase generator is also being dis- 
placed by the three-phase machine, which is more efficient, every- 
thing considered. 

68. Three-phase Circuits.— The voltage relations in a three- 
phase system are represented in Fig. 38. The windings on the 




armature consist of three semi-distinct seta of coils so arranged 
that each occupies approximately one-third the distance between 
two field poles of the same polarity. The phase difference 
between the separate electromotive forces is then 120°, or one- 
tbird of 330°, since the distance between two like poles is 360 
electrical degrees. 



ALTERNATING-CURRENT CIRCUITS 



63 



The three-phase system may also be looked upon as three 
single-phase systems whose voltages are out of phase by 120*^. 
In practice, however, this would necessitate six line wires, which 
would make the system very complicated and expensive. The 
eflBiciency of the system lies in the fact that three ends of the 
armature coils may be joined together and the other three ends 
to the line wires, as shown in Figs. 39 and 40. The lamps, or 
other receiving circuits, are then connected between the line 
wires as shown by x, y, and z. The manner of connecting the 
armature coils, shown in Fig. 39, is known as the Y connection, 
and that shown in Fig. 40 as the delta connection. A, B, and C 
in each of these figures represent the separate phase windings. 




Fig. 39. 



FiQ. 40. 



69. Current and Voltage Relations in Three-phase Circuits. — 

Representing the maximum value of the pressure generated in 
each phase by a line whose length is proportional to the numerical 
value of the maximum pressure. Fig. 41, three equal lines, making 
angles of 120° with each other, will represent, both in magnitude 
and phase, the maximum three-phase pressures generated in a 
F-connected armature. The instantaneous values of the sep- 
arate pressures will then be equal to the projections of JSim, 
j&2m, and Ezm upon the vertical Une YY'. At the instant repre- 
sented by the figure these instantaneous values are for Eim Oei; 
for E2mf Oe2] and for Ezm, Oez- Representing Oei, Oe2 and Oes by 
ei, €2 and ez respectively the following relations hold: 



ei 

€2 

ez 



Elm sin d 

Earn sin {d + 120°) 

Ezm sin {e + 240°). 



By rotating Eim, E2m, and Ezm counter-clockwise, ei, 62, and ez 
will fluctuate as the sine of an angle, but differing in phase by 
120°. Hence, they may be properly represented by the sine 
curves of Fig. 38. 
The three lines Eim, E2m, and Ezm, Fig. 41, are called vectors. 



64 



KLECriilCAL METERS 



Vectors cannot be added algebraically, that is, the sum of E\m 
and Eim is not the algebraic sum of their numerical values. Vec- 
tors are combined geometrically. To get the sum of two vectors, 
form a parallelogram with the given vectors as sides; the diagonal 
will then represent the sum, both in magnitude and direction 




Fki. 41. 

The vector difference is obtained in much the same way. The 
direction of vector to be subtracted is reversed and the two 
vectors are then added. 
According to this method of addition and subtraction, the 

pressure across y. Fig. 39, is equal to the vec- 
tor difference between the pressures generated 
in windings A and B respectively. Represent- 
/ ^ \ ing the pressure developed in winding A by 
^ ^ vector Ea) and that in winding B by JSb, Fig. 

42, the vector difference is equal to -B, which 
is the pressure across y. Numerically 

E ^ Ea cos 30^ + Eb cos 30'' 
= iW'iEj, + y2V^EB 
= V^Ea = y/ZEa 

Fia. 42. 

when Ea = Eb, as is usual in practice. 
In the foregoing demonstration £, Ea, and i?B "represent either 
maximum or effective values. Hence, we may, in general, 
say that the pressure between the mains of a F-connected three- 
phase circuit is equal to V^ times the pressure developed in each 
armature winding. 




ALTERNATING-CURRENT CIRCUITS ()5 

The current in each main must be the same as the armature 
current, as is evident from the connections. 

In the delta-connected system the conditions are reversed. 
The connections plainly show that the pressure between mains 
is the same as that developed in one armature winding. The 
current in either main, however, is the vector difference between 
currents in two windings, and hence, according to what has just 
been said, the current in one main equals \/3 times the current in 
one armature winding. The power in any polyphase system is not 
pulsating as in a single-phase system, but is constant or steady. 



CHAPTER VI 

INDUCTION PRINCIPLE 

70. Introduction. — The fundamental principle of induction 
meters, as well as motors, was discovered by Arago in 1825. He 
found that if a copper disk is pivoted on the axis of a magnetic 
needle, its plane being horizontal, and rotated, the needle will be 
deflected. This principle is illustrated in Fig. 4& Above the 
copper disk C, but not touching, is a glass plate G. In the middle 
of the glass plate and directly above the center of the arbor is 
pivoted a magnetic needle. When the copper disk is rotated, the 
needle is deflected in the direction of rotation. If the position 




Fig. 43. 



of disk and needle be interchanged, and the needle rotated, the 
disk will rotate in the same direction as the needle. 

Faraday explained this phenomenon on the supposition that 
relative motion between needle and disk resulted in producing 
electric currents in the disk, and that the reaction between the 
magnetic field produced by these currents and the field due to 
the magnet caused the rotation of needle in the first case, and 
of the disk in the second case. This explanation has been veri- 
fied many times since. Whenever a conductor cuts across a mag- 
netic field an electromotive force is induced. If the conductor 
7 67 



68 



ELECTRICAL METERS 



forms a closed circuit, a current will flow through the circuit and 
a reaction is set up between the conductor and magnetic field. 

In the experiments of Arago and Faraday the magnetic field 
was caused to rotate by rotating the magnet to which the field 
was due. It is evident such a device is not suited for measuring 
instruments. What is needed is relative motion between the 
field and conductors, without the corresponding motion of 
magnets. 

71. Rotating and Revolving Magnetic Fields. — In practice 
there are two types of moving magnetic fields which may be 
designated by the two terms, rotating and revolving. In every- 
day language the two words, rotating and revolving, are used 
interchangeably, but there is a distinction in their meanings 
which should be kept in mind. 







Fig. 44. 

A body is said to rotate when it has a circular motion about 
its own center or axis; to revolve is said of a body that moves in 
a curved path, as a circle or ellipse, about a center outside of 
itself. According to this distinction a rotating magnetic field is 
one that turns about an axis passing through the field; and a 
revolving magnetic field is one that moves around an axis out- 
side of itself. 

72. Production . of Rotating Field. — To produce a rotating 
magnetic field of constant intensity, and rotating at a constant 
speed, necessitates polyphase currents. In Fig. 44 is shown a 
circular coil carrying a current which sets up a magnetic field at 
the center of the coil. The curved lines with arrow heads repre- 
sent magnetic lines in one position. When the current is alter- 
nating, the field is also alternating, increasing and decreasing 
with the current and reversing as the current reverses. Repre- 
senting the current by 

i = Im cos 0)t 



INDUCTION PItlNCJPLE 69 

we raay represent the instantaneous value of field strength by 

h = H„ cos <A 

A horizontal section of two such coils with their planes at 
right angles is shown in Fig. 45. The curved lines represent the 
magnetic lines of the two coils superposed when the intensities 
of the two fields are equal. When coil AA' is connected to one 
phase of a quarter-phase circuit, and BB' to the other phase, 
* the currents will produce alternating fields in the two coils. 
The direction of each field will always be at right angles to the 
plane of the coil producing it, but the intensities of the two fields 
will differ by one-quarter of a period. 




The instantaneous values of the field intensities can be repre- 
sented by 

hi = Him cos <d 
and hi = Hs» sin lA 

The resulting field will be the vector sum of fii and hi. Since 
fti and hi are at right angles to each other the instantaneous 
value of the resultant is 



h = VV + As' 



= VHiJ cos= <^t + HtJ sin <^t. 
= H jm, that is, when coils are exactly alike. 



70 



or 



ELECTRICAL METERS 

h = VHiJ^ (cos* (at + sin* cd) 
h = Him, a constant. 



The rectangular components are hi and A2, and when Him = Him 
= Hmj that is, when the maximum values of the component 
fields are equal, we have 



and 



or 



hi = Hm cos cot 
hi = Hm sin u)t 
hi^ + /i2* = Hm^ the equation of a circle 



Therefore, the resultant field rotates at a constant angular speed 
which is determined by the frequency. 




In practice the two component fields seldom have equal 
maximum values, consequently, the following is more important. 

73. Rotating Field Produced by Unequal Component Fields. — 
Two harmonically alternating fluxes at right angles to each other 
in space may be replaced by two rotating fluxes of different 
magnitudes rotating in opposite directions but having the same 
angular speeds. Thus in Fig. 46, let OA = 2Him and OB = 
2H2m represent two harmonic fluxes, produced by two circular 
coils having a common center but having planes at right angles 
to each other. OA and OB are fixed in direction but vary in 
magnitude according to the sine law. The flux OA may be con- 
sidered as being the projection of two equal vectors, each equal 



INDUCTION PRINCIPLE 71 

to }4 OA, rotating in opposite directions at a uniform speed so 
as to make one complete revolution while the values of OA pass 
through one cycle. 

Let OC and OCi represent the two component vectors at the 
instant they make an angle di with OA. Evidently, at this 
instant the intensity of the field along OA is given by 20C cos ^i 
= 20C cos (at 
where w = 27r X frequency. 

Similarly OB may be considered as the resultant of two vectors 
OD and ODi, each equal to }iOB. 

Combining the two components that rotate in the same 
direction we get the two components OF and OFi, which diflfer in 
magnitude, rotate in opposite directions, but have the same 
angular speeds. 

The numerical value of OF and OFi in terms of OC and OD, 
and thus in terms of OA and OB, can be obtained analytically as 
follows: 

Of 2 = OC^ + OD^ - 20C X OD cos ODF 

and OFi^ = OCi^ + ODi" - 20Ci X ODi cos ODxFi 
but OC = OCi = Him and OD = ODi = fl^2m. 
Then OF^ = Him^-\' if 2m' - 2if i^ifam cos ODF 
and Of i2 = HiJ + if 2^2 - 2Hi^fl2m cos OD,F,, 

ZODF is the supplement of ZCOD, 

But ZCOD = ZAOD + /.CO A = ^ - ^2 + ^i, and hence, 

ZODF = TT - (I - <?2 + ^1) = I + (^2 - <?l) 
Similarly ZODiFi can be shown to equals — (^2 — ^1). 

TT . 

Now 2 is the physical angle between the fluxes OA and OB, but 

62 — Ox is the time-phase diflference expressed as an angle between 
the alternating fluxes of which OA and OB represent the maxi- 
mum values. Representing this phase diflference by ^0 we finally 
get: 

OF^ = HiJ + Hirn" + 2HimH2m sin ^0 

OFi« = i?i„2 + H^J - 2Hi^H2m sin Oo. 

That is, in place of one resultant field rotating with a iiniform 



72 ELECTRICAL METERS 

Hpeed in one clirrction there are two fields with different ampli> 
tudes rotating in opposite directions. This principle has impor- 
tant application in induction-type instruments. 

74. I^odiictioa of a Revolving Magnetic Field. — Two quarter- 
phase currents may also be used for producing a revolving field. 
The manner in which the stator of a quarter-pbase motor b 
connected is indicated in the diagram of Fig. 47. The short 
heavy lines represent the conductors in the slots of the stator 
core, and the light lines represent the end connections. The 



Z^Z 




Fio. 47. 

curved lines outside may be considered as representing the front 
end connections, and, \mder this assumption, the curved lines 
witliin will represent the back connections. An examination of 
the diagram will show that the current in conductor 1 passes 
across the iron core from front to back while in conductor 11 it 
posses from back to front. The two groups of conductors, A and 
A', together with the connecting wires may thus be considered 
ns forming a. coil whiiOi surrounds a portion of the iron core. 
Similarly B and B', which surround another [wrtion of the core, 
will form another coil. Assuming a direct current to be flowing 
through phase A while pha^ B is open, it is evident that a north 



INDUCTION FKINCIPLE 



73 



pole will develop between A and A', and a south pole between 
A' and A", etc. In all there will be four poles. Such an arrange- 
ment of conductors is called a four-pole winding. 

A simplified diagram of an end view of a four-iwle two-phase 
induction motor is shown in Fig. 47a. In this diagram the con- 




■A 



ductors are represented by circles. For clearness the end con- 
nections are omitted. When current in winding A-A', etc., is 
maximum that in winding B-B', etc., is zero. The position of 
the magnetic lines at this instant is indicated by dotted lines with 
arrow beads. The current in group of conductors A is toward 




Fic. 47f<. 



the observer, and in group A' away from the observer. Under 
these conditions a south pole is formed at 5 under the stator core. 
One-eighth of a period later the current in winding A-A', etc., 
will have decreased to 0.707 of its maximum value and that in 
winding B-B', etc., will have increased to 0.707 of its maximum 
value. The currents will at this instant be equal and as they will 



74 



ELECTRICAL METERS 



be flowing in the eame direction, the position of the magnetic 6dd 
will be as indicated in Fig. 476. The magnetic fluxes due to the 
two currents will combine forming a resultant pole halfway 
between A and B". The same thing will hold tnie with reference 
to the other groups of conductors. Thus during one-ei^th of a 
period of the current, the magnetic poles have shifted one- 
sixteenth of the circumference of the stator. 

After another one-eighth of a period the conditions will be as 
represented in Fig. 47c. At this instant the current in winding 
A-A', etc., is zero and that in B-B", etc., is a maximum. The 
magnetic poles have again shifted one-sixteenth of the stator cir- 




cumference. The magnetic field which is confined to the outer 
periphery of the rotor and the inner periphery of the stator 
revolves independently of the iron core. A revolving magnetic 
field can be obtained from any polyphase circuit by means of 
appropriate windings. 

76. Speed of Revolving Field.— The speed with which the 
polarity will be transferred around the stator core will depend 
upon the frequency of the alternating current. The number 
of revolutions per minute will depend upon the number of pairs of 
poles per phase, and upon the frequency. If the frequency of the 
supply pressure be /, and if there be p pairs of poles per phase, 
then the field will make one complete revolution in ^ sec. It will, 
therefore, make n = 60- complete revolutions per minute. 



CHAPTER VII 

INDUCTION-TYPE AMMETERS AND VOLTMETERS 

76. Application of Induction Principles to Meters. — If a suitably 
mounted hollow conducting cylinder, or disk, be placed inside a 
rotating field, currents will be induced in it, due to the relative 
motion of the two, as in the experiment of Arago. The currents 
will react with the magnetic field in such a way as to cause 
rotation of the cylinder or disk. The reaction will be in such a 
direction as to oppose the motion of the magnetic field in ac- 
cordance with the general law of induction. The cylinder or 
disk will thus rotate in the same direction as the magnetic field. 

Induction meters operate in accordance with these principles. 
For single-phase instruments, the principle of rotating, or revolv- 
ing, field is obtained in a modified way. 

77. Induction Ammeters and Voltmeters. — One method of pro- 
ducing a revolving, or in this case what may be called shifting, 
magnetic field for single-phase instruments is shown in Fig. 48. 
The current circuit of the meter is represented by the winding 
ABC, The coil B surrounds the laminated iron core /. In the 
end of this iron core is a slot through which and around one-half 
of the core is wound a heavy band of copper as shown at E. The 
alternating current flowing through coil B induces a flux in the 
iron core. When the flux is increasing, a part of it will pass 
through the core of the short-circuited copper band, inducing a 
current in it. This current is in such a direction that it opposes 
the building up of the magnetic flux within the space surrounded 
by the band. While the current is increasing, the magnetic 
density of that part of the iron core which is not surrounded by 
the copper band will be greater. On decreasing current, the con- 
ditions are, however, reversed. The flux density of the unwound 
part of the core will decrease to zero before that in the other part. 
The flux thus shifts from the unwound portion to the wound part 
of the core. 

As this shifting flux penetrates the disk D, currents are induced 

76 



76 



ELECTRICAL METERS 



in it which react with the magnetic flux, causing the disk to 
rotate. The controlling force is supplied by a coiled spring as in 
other indicating instruments. 

It is plainly evident that the reaction between shifting field and 
induced currents in the disk is a function of both the intensity of 
the shifting field and frequency of current. If no provision were 
made for correcting the influence of frequency, changes in fre- 
quency would affect its indications. To compensate for fre- 
quency effects, the main coil B is made of low resistance and high 
inductance. The terminals of the coil B arc connected to a non- 
inductive shunt, S. The circuit is, therefore, divided into two 
branches, one containing resistance but no inductance and the 
other inductance but of negligible resistance. At normal fre- 




Fio. 48. 



quency the current will divide in a certain ratio between the two 
branches. An increase in frequency will cause more of the cur- 
rent to flow through the shunt, thereby decreasing the current 
in the meter coil. This reduced current, however, will be more 
effective in producing torque on account of its higher frequency. 
By properly adjusting the shunt, the two effects are made to 
neutralize each other so that the registration is not affected by 
considerable variation in frequency. 

The principles of the voltmeter are identical with those of the 
ammeter, with the difference that there is connected in series 
with coil B a high-resistance, non-inductive coil. This particular 
form of induction meter is no longer on the market, although it 
is still used. 



AMMETERS AND VOLTMETERS 



77 



78. Series-transformer Principle. — A most ingenious method 
of producing a rotating magnetic field was invented by Mr. 
Frank Conrad, and is used by the Westinghouse Electric and 
Manufacturing Co. in its induction instruments. 

In so far as principles of construction are concerned, a series 
transformer contains two independent windings the same as a 
shunt transformer. The difference between the two kinds of 
transformers lies mainly in their use. The primary winding of 
a series transformer is connected in series with the line, while the 




Fig. 49. 



other has its primary shunted across the line. Fig. 49 is a dia- 
gram of a series-transformer winding as applied to an induction 
meter. It is evident from the diagram that there are two dis- 
tinct windings; P, the primary winding, carries the line current, 
and S, the secondary, is short-circuited. The circle represents 
the cylindrical meter movement. The dotted lines marked <t) 
represent the magnetic fluxes set up by currents in the separate 
coils. 

The current to be metered develops magnetism in the core; 
this magnetism in turn induces a current in the secondary 
winding. This induced or secondary current, according to the 
principles of induction is nearly 180° out of phase with the 
primary current. If it were not for the losses and magne- 
tizing current it would be exactly 180° out of phase. If the 



78 



ELECTRICAL METERS 



magnetizing current were negligible, the ampere-tiims of the 
primary current would exactly equal the ampero-tums of the 
Becondary, or algebraically 

That is, the magnetizing effect of primary current would just 
balance the demagnetizing effect of secondary current. 




A vector diagram for primary and secondan,- ampere-turna is 
shown in Fig. 50. OP represents the product of primary current 
and primary turns, and OS represents the product of secondarj* 
current and turns. The magnetizing force, which sets up the 
flux in the core common to the two coils, is the resultant of the 
primary and secondary ampere-turns, and will, therefore, be 
represented by CM. OM may be 
considered as the resultant of two 
( components, OX in phase and OM' 
in quadrature with OP. ON will 
represent the ampere-turns necessary 
to supply energy' for the losses, and 
OM' will represent the true mag- 
netizing ampere- turns. This mag- 
netizing component is priniariiy re- 
sponsible for tile fact that the phase 
difference between the primary and 
secondary currente is not exactly 
180°. A vector diagram of the elec- 
tric and magnetic quantities is shown 
Fio. 51. in Fig. 51. 

The combined primary and sec- 
ondary ampere-turns produce a flux ^i whieli in time is nearly 
one-quarter of a period ahead of the flux 03 ilue to the auxiliary 
secondary winding- In space the two fluxes are at right angles 
to each other as shown in Fig, 49. These arc plainly the condi- 
tions necessary for producing a rotating magnetic field. 




AMMETERS AND VOLTMETERS 



Within the rotating magnetic field is placed the movable 
element, which consists of a light aluminum cylinder momited on 





1 



Fid. 62b. 

a shaft. The shaft is supported between jewels as in other types 
of meters. The rotating field induces eddy currents in the cup- 
shaped movable element, Fig. 52c, and thus 
creates a torque which is balanced by a coiled 
spring exactly as in other types of meters. The 
structural features of a portable ammeter are 
shown in Figs. 52o and 526, and of a switch 
I board voltmeter in Fig. 52d. The principles of 

construction of ammeters and 
voltmeters are exactly alike, with 
the exception that in the volt- 
nmter the primary coil is wound 
with fine instead of coarse wire, 
I and an external non-inductive 
seiies resistor of zero temperature 
cucfficient is used. 

79. Relation Between Current 
and Torque .-^Thcre are so many 
varying quantities involved that 
no exact expression for the torque 
or deflecting force with refer- 
ence to the current can be given. 
A general relation can be deter- 
mined as follows: 
The flux in the iron core is proportional to the current to be 
I measured and the induced currents in the rotating disk are pro- 



80 ELECTRICAL METERS 

portional to the flux. The deflecting or rotating force is propor- 
tional to the product of flux and eddy currents, hence, the de- 
flecting force is proportional to the square of the flux, which in 
turn is roughly proportional to the square of the current in the 
main coil. The motion is usually opposed by spiral springs and 
thus the angle of deflection is roughly proportional to the square 
of the current. 

According to the principles of Article 73, if fl^i = <f>iy Hi = 02i 
OFi = $1 and OF = *2 the two fields rotating in opposite direc- 
tions are given by 

*i^ = <t>i^ + <t>2^ - 2<t>i<t>2 sin e 

and f»2^ = <t>i^ + <t>2^ + 2<t>i<t>2 sin d 

6 is the time-phase difference between 4>i and <l>2 as represented 
in Fig. 61. 

Since the cylinder turns only until the driving torque equals 
the counter torque of spring, the speed of the drum is zero. The 
actuating torque is due to the cutting of the cylinder by the two 
fluxes *i and *2 in opposite directions. The deflection will be 
in the direction of the greater torque. 

The eddy currents in the drum due to ^i and *2 are propor- 
tional to $1 and $2 and to the speed of these which is 2vf. If the 
eddy currents lag y degrees behind the induced voltage the torque 
due to $1 is 

Ti = /Ki^i^ cos 7 

and that due to ^2 is likewise given by 

T2 = fKi^i^cosy 

The driving torque is equal to 

Ti - ^2 = fKi cos 7 (*i^ - *2^) = 4//Ci*,</>2 sin d cos 7 

K I 

but <f>i = —^ — t and <l>2 = Kzliy where 7i is the primary 

current. 
Then T = Ti — T2 = -^ > sm 6 cos 7 

= 4X1X2^3/1^ sin d cos 7 
Ki depends mainly upon the impedance of the drum and varies 
inversely with it. In place of Ki we may write Ki = ^> 



AMMETERS AND VOLTMETERS 



81 



where Z is the impedance of cylinder; then 

T = — ^ sin 6 cos 7. 

80. Influence of Frequency. — In the expression given above for 
torque, Z, 6, and 7 are quantities varying with frequency, and in 
order that the meter may be independent of frequency Z must 
vary as sin ^ cos 7. This can only be approximated, although 
the maximum error due to changes of frequency from 25 to 60 
cycles is not over ^ per cent. 

8L Influence of Temperature. — Variation in temperature will 
mainly affect the resistance of the movable cylinder. In order 
to correct for this variation, the secondary coil is arranged to 
have a temperature coefficient of resistance such as to exactly 
cancel the effect of the variations of resistance in the cylinder. 
To do this another series transformed principle is used. If in a 



I 



/ae 



/CO 



96 



96 




Tdnfue 



a/Zif/t Lcaef 









JOOOMt U/^nt/f> ^m9. 



9S, 



ao 30 40 

Fig. 53. 



90 



eo 



70 



Cycles, for curve No. 1 which shows the effect of changes in frequency. 
Minutes in circuit for curve No. 2 which shows the effect of self -heating at 
two-thirds load. Air temperature in °C. for curve No. 3 which shows the 
effect of variations in room temperature. 

series transformer the primary current be kept constant, the 
secondary current will remain nearly constant while the secondary 
resistance is varied over a considerable range. Thus, any in- 
crease in the secondary resistance causes a proportional increase 
in the flux of the core. This is made possible by working the 
core at a low flux density. 

The Westinghouse ammeter described has the secondary cir- 
cuit wound partly with copper and partly with a wire of low 
temperature coefficient, the resulting temperature coefficient 



82 ELECTRICAL METERS 

of the afiCODdary circuit being such as to increase the flux in the 
iron when the temperature rises, thus compensating for rise of 
temperature of the aluminum cylinder. Figs. 53 and 53a show 
the performance curves of ammeters and voltmeters respectively, 
82, Scale.^ — A direct reading scale of the induction type of 
instruments will ha\'e the same disadvantages as those whose 
defleetioQ is proportional to the square of the quantity to be 



«ie 



^ftpiw • a/fii /i-ooa 




ftti •3ta/K ■ 



Fk 



53a. 



Cycles, for (inrve No. 1 which ahowa the effect of changes in frequency. 
MtnulcB in circuit for curve No. 2 which shoivtt the effect of Bclf -healing at 
two-thirds load. Air t«inperature in °C. for curve No. 3 which shows the 
effect ot variations in room temperature. 

measured. In practice, this disadvantage is overcome in two 
ways. One method makes use of a cam-ehaped disk, which i9 
mounted so that less and less of it lies between the poles of the 
iron core as it rotates. A proper shaping of the disk permits the 
construction of a practically uniform scale for about 300° of 
arc. A second method, made use of by Siemens and Halske, con- 
sists in using an auxiliary weight so mounted that it reinforces 
the tendency of the moving element to rotate at the zero end of 
the scale, while at the upper end of the scale, it is vertically below 
the spindle. The iuatruraents marmfactured by the above- 
meiitioni;d firm have nearly a uniform scale extending over an 
arc of 90". 

82a. Damping.— The electromagnetic method of damping is 
employed in these instruments. In the earlier instruments an 
aluminum disk i.s mounted on the shaft, and as it moves between 
the poles of two permanent magnets effective damping is secured. 
The proper damping is now obtained by means of a "C" shaped 
permanent magnet located very close to the drum of the movable 
element. 




V ELECI 

^f 83. Introduction.— The principle upon which the operation 
of these instruments depends is, as its name implies, the mutual 
attraction and repulsion between adjacent circuits carrying 
electric currents. The principle that currents flowing in the 
same direction in parallel wires attract and when flowing in 



CHAPTER VIII 



ELECTRODYNAMIC AMMETERS AND VOLTMETERS 




opposite directions repel, 
instruments of this class. 



is the fundamental principle of the 
The repulsion and attraction is dui 



to the interaction of magnetic fields produced by the currents, 
hut as instruments possess no iron core, the interaction is called 
electrodynamic instead of electromagnetic. 

84. Electrodynamometer Type. — The essential features of an 
instrument of this type, which for a long time was extensively 
used for measuring alternating currents, are shown in Fig. 54. 
The completed inatrinnent is shown in Fig. 65. As shown in 
Fig. 54, the instrument contains two coils, one fixed, FF', and 
fl 83 



84 



ELECTRICAL METERS 



one movable, MM'. The movable coil is placed outside of the 
fixed coil and is supported by a fiber which offers \Gjy slight 
resistance to motion of the coil. The lower ends of the coil dipioto 
mercury cups which are connected to binding posts. 

The controlling force is furnished by a spiral spring, one end of 
which is attached to coU MM' and the other to the torsion head 
H. The index pin P is also rigidly connected to the torsion head, 
which passes through the fixed graduated plate A, and may be 
turned by the milled head at the top of the instrument. 

85. Operation of Electrodynamometer Ammeter.— The cir- 
cuit within which the current is to be measured is connected in 
series with T and T\., or T and T-i, depending upon the magnitude 
of the curj-ent. Assuming that direct current is to be measured 
and that the positive terminal is connected to T\, it will be 
noticed that the current flows up the side of the stationary coil 
marked F and down the side marked F'. After passing through 
the junction block Wand the connecting link flC the current enters 
the movable coil at C and flows up through the side M and down 
through the side marked M', finally leaving the instrument 
through binding post T. 

Keeping in mind the principle of parallel circuits stated in 
Chapter I, we see that the current flows in the same direction in 
Bides F, M', and F', M. Since the large coil FF' is fixed and can- 
not move, the coil MM' will be deflected in such a direction that 
the side M approaches F, and M' approaches F'. The motion of 
the coil is stopped when the pointer / strikes the pin N. By 
turning the torsion head G, the pointer / can be brought back to 
its original or zero position. The force tending to deflect the 
coil is then measured by the angle through which the torsion head 
has been turned, for within the limits of elasticity of the helical 
spring, the force causing a distortion or twist is strictly pro- 
portional to the angle through which it has been twisted. In 
order to measui'e the current, however, it is necessary to get an 
expression for the force in terms of the current in the coils. 
Both theory and experiment show that the force is proportional 
to the product of the current in M and F. In the case considered 
the same current flows through both coils, hence, the force of 
attraction must be proportional to the square of the current. 
Now, since the force is proportional to the angle of deflection, 
and likewise to the square of the current, it is evident that the 
square of the current must be proportional to the angle of deflec- 



AMMETERS AND VOLTMETERS 



85 



tion. Letting / equal current strength, K^ a proportionality 
factor, and 6 the angle of deflection, we may write the foregoing 
relation as follows: 



Whence 



/ = KVe, 



This is the fundamental equation for instruments of this type. 
It will be noticed that the current is proportional to the square 
root of the angle of deflection, and, hence, the scale of such an 
instrument, if it were to be direct reading, could not be uniform. 
In praiitice, the scale is graduated in degrees, and the current 
is determined from calibration curves or computed in accord- 
ance with the above formula after the constant K has been 
determined. 

It has been assumed that the current to be measured was 
direct, or continuous. One of the advantages of the electro- 



Non-inductive Resfstaaee 
AAAAAAA-^ 




/ a 



Shunt 



r 

O Movable Coil 

'^^'^Ffxed Coil 




R\l\ 



AAAAAAA-^ 



^o::>/o 





^Pixed Coil 




1 



Fia. 56a. 



FiQ. 666. 



dynamometer ammeter is that it can also be used on alternating- 
current circuits. That the deflection is in the same direction on 
alternating current as on direct current, will be evident on notic- 
ing that when the current reverses in the stationary coil it likewise 
reverses in the movable coil. The current will always be in the 
same direction in F as in Af , and in F' as in Af' , and consequently, 
the deflection on alternating current is the same as on dfrect 
current. Also, both by theory and experiment, it has been shown 
that the deflecting force on alternating current is proportional 
to the square of the effective current. Hence, the instrument 
gives true effective values of alternating currents. 

86, Shunted Electrodynamometer Ammeter. — ^To increase the 
range of an ammeter of this type the coils may be shunted in 
either one of two ways: A shunt may be connected across both 
coils as indicated in Fig. 56a, or only the movable coil may be 
shunted as shown in Fig. 566. 



r 



86 ELECTRICAL METERS 

When the connections of Fig. 56a are used, an additional non- 
inductive resistance of low temperature resistance coefficient 
must be connected in series with the coils of the instrument. As 
the coils of the instrument are usually made of copper, the instru- 
ment when so connected will be subject to two sources of error, 
namely, temperature and frequency. The temperature error 
will depend upon the ratio of the resistance of the instrument coils 
to that of the non-inductive resistance in series. If this is small, 
the temperature error will be small. 

The frequency error upon alternating-current circuits is due 
to the inductance of the instrument coils. The per cent error due 
to this cause may be calculated as follows: 
Let Ri = resistance of instrument circuit, 
Ro = resistance of shunt, 
X = reactance of instrument circuit, 
L = self-inductance of instrument circuit. 
Ii =. current in main. 
Jo = current in Rq. 
I = current in meter circuit. 
Then, if the ammeter be calibrated on direct current, the cur- 
rent flowing in the main to which the ammeter is connected is 
given by 

I (Ri + Ro) 



h = 



Ri 



When an alternating current gives the same deflection, the current 

I R 
through the instrument coils must also be 7: but I = — 7- = 

^ ' VRi^ + x^ 

I R 
= —y-. h and I will not be in phase; hence J2, the current in 

the main, is the vector sum of I and Jo, or 

h = V (/ cos 6 + 7o)2 + (7 sin 6)^ 
= V7 + 2 77o cos 6 + W 



But 



and 



io — p 



COS tf= Y 



Hence 



. = p-'V^ 



R 



0* + 2 BBi + Z* 



AMMETERS AND VOLTMETERS 87 



tt-'-'-n/^ 



X 



x^ 



and per cent error = 100 — 100 \ 1 + td i d n« 

X = 2TfL 



EXAMPLE 

A shunted electrodynamometer ammeter has a coil whose resistance is 
1 ohm. it is shunted by a resistance of ^9 ohm. If the inductance of 
the instrument coil is 0.3 millihenry, what will the error be when the fre- 
quency is 100 cycles per second? 

Solviion. — 

1 + (jg + fi )a 
Given L = 0.3 X lO"' henrys, 
/2i = 1 ohm, 
/ = 100. 
Then X = 2ir/L = 2ir X 100 X 3 X 10"* 

/2o + /2i = -gg ohms, 

A 4. inn .^^L . 4t^ X 10^ X 9 X 10-« X 99> 
and per cent error = 100 — 100 Vl H ttw 

= 100 - 100 X 1.0172. 

= 1.72 per cent low. 

The remedy for this would be to make the shunt inductive, which is difficult 
to carry out in practice. 

When the movable coil only is shunted as indicated in Fig. 
566, the frequency error will be much smaller. The algebraic 
expression for the per cent error in this case is given by 



Per cent error = 100 



2RARo^ I 



Where X = 2t/;/L, 

Ri = resistance of shunted coil, 

/?o = resistance of shunt, 

M = mutual inductance of the instrument coils, 

L = self-inductance of movable coil. 

In a particular instrmnent the per cent error at a frequency 
of 100 was found to be 0.01 per cent.^ 

87. Voltmeters. — The electrodynamic principle can be used to 
measure diflference of pressure as well as current. The arrange- 
ment of the coils for the dynamometer type voltmeter is shown in 

* RiSDALB, Journal I.E.E., vol. 48, p. 521. 



88 ELECTRICAL METERS 

Fig. 57. iSS are the fixed coils, which arc connected In series, and 
A is the movable coil to which the pointer P is rigidly attached. 
The movable and fixed coils are also connected in scries together 
with a non-inductive coil of high resistance and low temperature 
coefficient. The effect of this series resistance is to reduce the 
frequency and temperature errors to a negligible amount. 

The commercial instruments of this type are similar in mechan- 
ical construction to the permanent-magnet, moving-coil type of 
instniment. The electrical features differ in that the magnetic 
field in this type of instrument is due to the current flowing in the 
coils, which is proportional to the voltage to be measured. In the 
permanent^magnet type of instrument the magnetic field is due to 




the permanent magnets, and the current in the moving coil only 
is proportional to the difference of pressure. 

88. Effect of Inductance Upon Reading of Electrodynamometer 
Voltmeter,- — In well-designed voltmeters of this type the induc- 
tance is reduced to a minimum, and the inductance errors are 
practically negligible; nevertheless, the influence of this quantity 
may sometimes be appreciable. The relation between a direct 
electromotive force and an alternating electromotive force caus- 
ing the same deflection may be determined as follows: 

Let E = direct^current electromotive force causing a given 
deflection, 
E' = alternating-current harmonic electromotive force 
causing same deflection, 



AMMETERS AND VOLTMETERS 89 

L = inductance of coils, 

R = resistance of coils. 

E^ 
Then the deflecting force on direct current is proportional to p^» 

that is, to the square of current in coils. 

Since the deflection is assumed to be the same when alternating- 
current electromotive force is measured, the effective current 
must be equal to the direct current. The effective current 

7= ^' 



and 



whence, E' = 



E ^ E' 

R " V/2' + a)2L2 



R 



'^ 



Ex\l + "" 



ijj 



K 



When R is large in comparison with Lw, the second term under 
the radical sign has little effect; when this is not the case the 
difference between E and E' will be appreciable. 

89. Construction. — The dynamometer type of voltmeter con- 
tains no iron, and, as the three coils are all connected in series, it 
is well suited for alternating-current measurements. A phantom 
view of the essential features of a Weston dynamometer volt- 
meter is shown in Fig. 58. The Roller Smith Co. apply the 
same principle in their dynamometer type of voltmeters. In 
this case, however, the coil is mounted with its plane inclined at 
an angle to the arbor or shaft which supports it, Fig. 59. Such a 
construction makes it possible to fasten the coil to the shaft by 
small projecting lugs which are integral with and project from the 
sides of the coil frame. By clamping the lugs between appro- 
priate nuts, the coil is rigidly fastened to the arbor. The 
inclined-coil voltmeter of the General Electric Co. is also similar 
in construction. In these instruments both the fixed and mov- 
able coils are inclined with reference to the shaft carrying the 
movable coil, Fig. 60. The movement of a Westinghouse volt- 
meter of this type is shown in Fig. 61. 

The principles of operation are the same in all cases. In 
every case the force causing a deflection varies as the product 



90 ELECTRICAL METERS 

of curroits in fixed sjid movable coils. When these cuTTeote 
are the same, the deSecting force depends upon the square of 
the actuating current. On account of the change in relative 
poQtioa of coils when in use, exact proporti<Hiality does not 




eidst between the deflecting force and the square of cuirent. 
^oe in the instruments of the dj-namometer t\-pe the controlling 
foroe is due (o a Spiral or heljcal spring whose counterfowe 




varies diiectl; vitb the deSection, such instruments do not have 
uniform scales when direct reading. The graduations are 
oowded h^eth^ at the beginning and end of scale, especially at> 
the beginning, as is shown in Pig. 61a. 



AMMETERS AND VOLTMETERS 



91 



90. Ampere Balance. — ^A standard instrument for measuring 
current is known as Kelvin's balance, Lord Kelvin being the 
inventor and designer of the instrument. The operation of the 
instrument is based on the electrodynamic attraction between 
stationary and movable coils, in much the same way as the 
electrodynamometer discussed above. In Fig. 62 are shown the 





VOLTS 



Fig. 61a. 



essential features of the instrument. As shown in the figure, 
the instrument consists of four fixed and two movable coils. 
The fixed coils are designated by A, il', A'\ A'", and the 
movable coils by B, B'. • 

The coils are all connected in series by connections as shown in 
the diagram. The winding of the lower coil A is reversed with 



Suspension 
5trips:;-.s, 




Fig. 62. 



reference to the winding of the upper coil. The current thus 
flows in one direction in one coil and in the opposite direction in 
the other coil of the couple. In the same way the current flows 
in opposite directions in the stationary coils. Assuming that 
the current flows counter-clockwise in coil A, it will flow in a 
clockwise direction in coil A'. Thus, if coil A attracts coil B, 

9 



92 



ELECTRICAL METERS 



eoil A' will repel eoil B. On the other side the winding of B' 
being reversed, it will be repelled by A" and attracted by A'". 
As a result of this attraction and repulsion, the coils BB' will 
swing around the suspension C, which also serves for conducting 
the current int« the movable coils. 

The controlling force in this case is gravity acting on the rider 
which slides along a graduated beam fastened to BB'. When 
no current is flowing through the instrument, a weight is placed 
in a pan which balances the movable coils and the rider at its 
extreme left position, which corresponds to the zero position 
of the scale. When a current is flowing through the coils, the 
rider is moved to the right along the beam until the coils are 
again balanced. The value of the current is then indicated by 




I'lii. 63. 

the position of the rider. The balance arm is supported by two 
trunnions, each hung by an elastic ligament of fine wire, through 
which the current passes into and out of the movable coil at the 
end of the balance arm. The instrument as manufactured is 
shown in Fig. 63. 

With ampere balances four pairs of weights (sliding and coun- 
terpoise) are supplied with each instrument. The carriage and 
its counterpoise constitute the first pair. These weights are 
adjusted in the ratios 1, 4, 16, 64, so that each pair gives a whole 
number of amperes, or half amperes, or quarter amperes, or 
some decimal subdivisions or multiples of these magnitudes on 
the upper or inspectional scale. 

For the adjustment of the zero, a small metal flag is provided. 
The flag is operated by a fork, having a handle outside the case. 



AMMETERS AND VOLTMETERS 93 

To adjust the zero reading, the sliding weight is placed with its 

pointer at the zero end of the scale, and the flag is turned to one 

side or the other, until it is found that with no current passing, 

the balance rests in its zero position. 

When a current is passed through the instrument, the balance 

arm is displaced, and to measure the current the rider is slipped 

along the trough until the balance arm is again brought to its 

zero position. The strength of current is then indicated on the 

upper fixed scale by the pointer of the sliding weight. For 

greater accuracy the reading of the lower scale must be taken. 

Each number on the upper, or as it is called inspectional, scale 

is twice the square root of the corresponding number on the fine 

scale of equal divisions. Thus if the reading on the lower scale 

is 292, that on the fixed scale will be 34.18 = 2 X V292. A 

table of double square roots is furnished with the instrument. The 

reading, multiplied by the constant of weight used, gives the 

current. 

EXAMPLE 

A centiampere balance was used to calibrate a milliammeter. The 
milliammeter reading was 668 milliamp., and balance reading 326.8 on 
the lower scale. How much is the ammeter in error if the constant for 
weight used is 2? 

SoltUion. — 

2V326.8 = 36.14. 

/ = 2 X 36.14 centiamp. = 722.8 milliamp. 
Error = 722.8 - 668 = 54.8 milliamp. 

91. Uses of Kelvin Balance as a Voltmeter. — ^In order that the 
Kelvin balance may be used as a voltmeter it is necessary only 
to increase its resistance. When so used, the resistance of the 
operating coils is about 50 ohms, and special coils are provided 
to be connected in series. The resistance of these coils ranges 
from 400 to 2000 ohms, and the maximum voltage that can thus 
be measured is 500 volts. It is evident that the Kelvin balance 
operates upon the electrodynamometer principle, yet it is usually 
classed separately because the controlling force is gravity; the 
planes of the coils are horizontal instead of vertical; and the 
movable coils do hot rotate around a central axis, but revolve 
about an axis midway between them. 

The relation between the current strength and the force of 
attraction is the same as that of the electrodynamometer already 
discussed, i.e.. 



94 ELECTHWAL METERS 

but when the coil is balanced the force is proportional to the 
distance of the rider from the extreme left of the scale, hence 

7* = KH 
or 7 = K-\/T, wliich is of the same form as the equation for the 
electrodynamometer. 

From this equation we see that the scale which reads in am- 
peres cannot be uniform. On the other hand, in order to obtain 
the current from a reading on the uniform scale we must extract 
the square root of the reading and multiply this square root 
by the constant of the instrument. 

The commercial instruments are madfe in seven sizes ranging 
in. capacity from 0.01 to 2,500 amp. Detailed instruction for 
using the balance is always furnished with the instrument. 




Flo. 64. 

92. Westinghouse Dynamometer Ammeter and Voltmeter.— 
Fig. 64 shows how the Westinghouse Electric and Manufacturing 
Co. has adapted the Kelvin balance principle to one type of 
instrument. The figure shows the general arrangement of the 
measuring elements, the letters referring to the following parts: 

A, A', A', A\ fixed coils, 

C, C*, movable coils. 

B, non-inductive resistance. 

D, controlling spring. 

E, torsional head. 

F, pointer attached to niovalile element. 

G, pointer attached to torsion head. 



AMMETERS AND VOLTMETERS 95 

The four fixed coils and two movable coils are all connected in 
series, and in series with part or all of the resistance B, depending 
upon whether small or large electrical quantities are to be meas- 
ured. Precisely as in the Kelvin balance the meter depends for 
its operation upon the electrodynamic action between the fixed 
and movable coils. The controlling force is, however, a spiral 
spring instead of gravity. The influence of gravity is eliminated 
by mounting the coils with their planes vertical instead of hori- 
zontal. There is considerable similarity between the Westing- 
house dynamometer type of instrument and the electrodynamom- 
eter. In both cases the planes of the coils are vertical and the 
indications of the instruments are obtained in the same way. 
When a current is sent through either instrument, the movable 
coil is deflected and, by means of the torsion head, the movable 
element is brought back to its zero position. The deflection is 
indicated by the angle between the two pointers. The same 
law, viz., 

/ = K^/e holds. 

93. Influence of Earth's Magnetic Field. — Since the earth is 
surrounded by a magnetic field which has a definite direction 
and value, there is bound to be a reaction between this field and 
a coil carrjdng a current. In some of the types of instruments 
so far discussed, the influence of the earth's magnetic field must 
be considered, when measuring direct currents, if accurate results 
are expected. 

In instruments of the electromagnetic type, the strength of 
the operating field is usually so great in comparison with the 
strength of the earth's field that this influence is practically 
negligible. 

In some of the dynamometer type of instruments this influence 
may be appreciable. This is true with reference to those instru- 
ments having only one stationary coil. Instruments employing 
the Kelvin balance principle are astatic, that is, they are not 
influenced by the earth's field. This is due to the fact that the 
movable element of the Kelvin balance type of instrument con- 
tains two coils wound in opposite directions. The effect of the 
earth's field upon one coil is thus neutralized by its influence 
upon the other coil. 

To prevent undue influence of the earth's magnetic field upon 
the Siemens electrodynamometer, the plane of the movable 

10 



96 ELECTRICAL METERS 

coil should be placed at right angles to the magnetic meridian. 
The direction of the magnetic meridian is indicated by a compass 
needle when not influenced by iron or adjacent magnets. 

The mechanical method of damping is used in most of the com- 
mercial instruments of the dynamometer type. One of the most 
serious objections to the Siemens form of current meter is the lack 
of damping device, which necessitates considerable time and skill 
in making readings. The other forms of dynamometer instru- 
ments almost invariably make use of some form of air-damping 
device. In the Weston dynamometer-type instruments, which 
may be considered typical, damping is secured by two light 
symmetrical vanes enclosed in chambers made as nearly air- 
tight as possible. The Westinghouse meters of the type shown 
in Fig. 61 use the electromagnetic principle of damping. To the 
movable element is attached a sector which moves between the 
poles of permanent magnets. 

With the exception of the Siemens dynamometer and Kelvin 
balance forms, instruments of the types discussed are also made 
for switchboard use. 

94, Advantages. — Among the main advantages of the dyna- 
mometer type of instrument are its sensitiveness, accuracy, and 
adaptability to both direct- and alternating-current measure- 
ments. It may be calibrated on direct current and used on 
alternating current. 

96. Disadvantages. — ^The Siemens dynamometer and Kelvin 
balance are not direct-reading; they are not '^dead beat," and 
hence require considerable time and skill in making readings. 
The necessity for accurate leveling is also a disadvantage. 



CHAPTER IX 



MISCELLAMEODS AMMETERS AND VOLTMETERS 

96. Electrostatic Voltmeter. — The measuring instruments so 
far discussed require an electric current for their operation. 
Electrostatic instruments utilize the forces of attraction or 
repulsion between two electric charges. The gold leaf electro- 
scope is the simplest form of instrument of this type. 

When two plates are insulated and placed near each other, a 
force of attraction will exist between them if oppositely charged. 
If one of these plates is movable, but its motion is counteracted 
by some controlling force, the deviation of the movable plate 
from its normal position will be a measure of the force of attrac- 




Fia. 65. 



tion. Since the capacities of the two plates are practically 
constant, the deviation, or force required to prevent deviation, 
will be a measure of the difference of electrical pressure between 
the plates. Instruments which make use of this principle of 
attraction of charges are ordinarily called electrometers. When, 
however, they are provided with scales graduated in volts they 
are called electrostatic voltmeters. The adaptation of this 
principle to commercial instruments is due to Lord Kelvin. 
The essential elements of an electrostatic voltmeter are shown 
11 97 



ELECTRICAL METERS 



in Fig. 65. The stationary element consists of two parts or 
quadrants aa. The movable element hb is a very light figure- 
8-6haped aluminuni vane. The vane is suspended by a fine wire 
whose elasticity supplies the controlling force. The instrument 
is practically an air condenser with movable plates. When 
the connections are made as indicated, the quadrants and vane 
are oppositely charged and attract each other. If the vane 
remained stationary, the force of attraction would be propor- 
tional to the square of the potential difference between quadrants 
and vanea. Algebraically 

F = KE^. 



— * r~ 




This relation is not mathematically exact for the reason that a 
change in the relative position of vane and quadrants slightly 
changes the capacity. To measure low voltages the capacity of 
the instrument must be relatively large. To secure this large 
capacity, Lord Kelvin mounted several quadrants above each 
other and between them suspended the samo number of vanes. 
The principle of construction will be readily understood from 
Fig. 66, Such an instrument may be used for measuring voltages 
down to 50 volts. The suspending wire supplies the controlling 
force. For voltages ranging from 400 to 100,000 volts, only one 
8et of quadrants and one vane are used, Fig. 67. The vane is 



AMMETERS AND VOLTMETERS 99 

mounted to swing in a vertical plane and the controlling force ia 
due to the action of gravity upon weights which determine its 
eensibihty. In neither case is the scale uniform, A multi- 
cellular form voltmeter for low voltages ia shown in Pig. 68. 




97. Westinghouse Electrostatic Voltmeter. — The principle of 
mutual attraction between two electrostatic charges of opposite 




kind has been adapted by Mr. S. M. Kintner of the Westinghouse 
Electric and Manufacturing Co., in a novel maimer. The essen- 
tial features of this voltmeter are shown in Fig. 69. The measur- 



100 



KhKVTIill'AL MKTKHS 



ing elomontH conHiMt of a sories of fixed iind movable condenxem. 
Till! niovahle element to which a pointer ia attached i« HiiitAbly 
pivotud iind provided with spring control- 
As »)iowii in the diuKfUTniniilio sketch, tho movablo part 
Ml, Mi consiHtB of two hollow cylinders fixed to a pivoted arm. 
The curved plates Bi and Ba «ro mctftlllciilly eotmeelcd to the 
inner nondenBcr platcB of condennerH Ci and Cj, The operating 
elements of tho meti'r are immersed in a high grtulc of insulating 
oil contained in a metal-lined wooden cam provided with an 
tnBulating cover. 




I. 70. 



98. Operation. — When the terminals Ti and Ta are connected 
Id tho circuit whose voltage it is desired to measure, the con- 
t!oiiHer« C\ and d become oppositely charged. These charges 
induce other charges of opposite polarity on cylinders Mi and Mt. 
Tho con«equent attraction between the charges on B|, Bi and 
Mi, M-, causes a deflection of the movablo elements. This motion 
ia made possible by tho sliapc and relative position of plates Bi 
and Dt with reference to the axis of the cylinders. As the cylin- 



'(Fsir 



AMMETERS AND VOLTMETERS 



101 



dere revolve they approach the curved plates Bi and Bs, In this^ 
as in the Kelvin electrostatic voltmeter, the torque causing a 
deflection is proportional to the square of the applied pressure. 
The form and relative position of operating parts is shown in Fig. 
70. 

In the more recent instrument a condenser terminal is used in 
place of the plate condensers shown in Fig. 70. The range of the 
meter may be changed by short-circuiting layers of the terminal, 
Fig. 71. 




99. Insulation. — To secure proper insulation for measuring 
very high voltages is not only very important but extremely 
difficult. In the electrometer, or Kelvin form of instrument, the 
insulating properties of air are mainly relied upon. The high 
insulating properties of oil, together with its relatively high 
inductivity, makes its use advantageous in many respects. The 
most important advantages are; 

1. Possibility of more compact construction, as the oil permits 
the placing of the operating elements nearer together. 

2. The force of attraction between stationary and movable 
elements is greatly increased, both on account of the smaller 
distance between them and on account of the high inductivity of 
the oil. 

3. The buoyant effect of oil greatly diminishes the pressure 
and friction of bearings. 

100. Damping. — Both the Kelvin multicellular and Westing- 
house electrostatic voltmeter use liquid damping. The axis of 



ELECTRICAL MICTEHS 

the Kelvin instrument projects through the bottom of the eaBiiiR 
and is provided with a suitable vane, The cup in which the vane 
swings is narrow and deep and only about ono-third full of liquid. 

In the Westinghouae instrument, the resistance of the insulat- 
ing oil upon the movable element produces efficient damping. 

An electrostatic voltmeter of the electrometer type, manu- 
factured by Hartmann and Braun, employs electromagnetic 
damping. The moving vane moves between the poles of an 
electromagnet and as it moves the eddy currentiS induced effec- 
tively damp the movement of the pointer. 

101. Advaat^es. — Among the most important advantages of 
the electrostatic instruments may be mentioned the following: 

They do not consume any electrical current; may be used on 
either alternating- or direct-current circuits; are entirely un- 
affected by temperature, external magnetic fields, power-factor, 
or frequency. In addition to these they may be used on very 
high-potential circuits. 

102. Hot-wire Instruments. — When a current of electricity 
passes through a wire whose resistance is R, the energy trans- 
formed into heat is I^R joules per second, when I, the current in 
the circuit, is given in amperes. When a stationary condition 
in the temperature has been reached, the energy converted into 
heat must be equal to that radiated, and this quantity is propor- 
tional to the change in temperature. Hence, it follows that the 
square of the current, which is proportional to the heat developed, 
is proportional to the expansion of the wire through which the 
current flows. It must be remembered, however, that the resist- 
ance R is not independent of the temperature. The wire of moat 
instruments of this type is made of platinum silver whose tem- 
perature coefficient is about 0.00024. If Rq is the resistance of 
wire at room temperature to, its resistance at temperature d^C is 
given by 

R, = R«[l + 0.00024{(i- Ml 

Thus, a 100-ohm coil will undergo a change of 0.024 ohms per 
degree Centigrade. This change in resistance modifies, to some 
extent, the proportionality between square of current and expan- 
sion. From a practical point of view this is of no great impor- 
tance, for the scale can be determined by calibration, 

103. Hot-wire Voltmeter, — The principle mentioned above 
was first made use of in an instrument designed by Major Cardew. 



i 



AMMETERS AND VOLTMETERS 



103 



The wire in the Cardew voltmeter was made of platiuum silver 
and was of such a length that it could be connected across a 
110-volt circuit without any series resistance. The wire ran 
twice from end to end of a long brass and iron tube, passing over 
insulated rollers at each end. One extremity was fixed while the 
other, after passing over a pulley, was attached to a spring which 
kept it taut. The pointer was attached to the pulley which was 
rotated by the expansion and contraction of the wire. The 
tube consisted of brass and iron so proportional that its coeflScient 
of expansion was the same as that of the wire. Hence, so long 
as the temperature of both was the same, the tension of the wire 
was constant and the readings were independent of external 
temperature variations. 



SM 




zero adjustment 



Fig. 72. 



The arrangement of the wire was such that the instrument was 
bulky and very inconvenient to handle. It is no longer in use. 

In the more modern instruments of the hot-wire type, the work- 
ing length of wire is from 6 to 8 in. In voltmeters this wire is 
quite fine, and series resistances are provided. Fig. 72 shows 
the essential features of a Hartmann and Braun voltmeter. The 
terminals of the circuit, whose difference of potential is to be 
measured, are connected to A and B. The resulting current heats 
the platinum-silver wire causing it to expand. As the tension of 
AB is lessened, the point C is pulled downward by the tension of 
the spring HK, The silk thread HF being wrapped around the 
pulley rotates the pointer as the end H of the spring HK moves 
to the left. By means of the mechanism CD and FH, the pointer 



104 



ELECTRICAL METERS 



P is made to move many times the sag of AB, The tension of the 
current wire AB is adjusted by means of the screw S. 

When an instrument of this type has been in use for some time, 
the pointer seldom returns to its zero position, but by means of 
the screw S the zero adjustment of the pointer can be readily 
made. 

The instrument is made "dead beat" by means of the vane V 
rotating between the poles of the permanent magnet M. The 
vane V is mounted upon the shaft with the pulley G and pointer P. 
As these rotate, the vane cuts across the magnetic field of the 
permanent magnet, inducing eddy currents which effectually 
damp the vibrations of the needle. 

The mechanism, as shown in the diagram, is mounted upon a 
suitable base plate not shown in the figure. The base plate is 
divided near the point C, one portion 
^ ] ^ D consisting of iron and the other of brass. 
The relative lengths of the iron and 
brass parts are so designed that the ex- 
pansion of the base plate is the same as 
that of the wire itself. Even such an 
arrangement does not give correct in- 
stantaneous readings. This is due to 
the fact that the wire reaches its maxi- 
mum temperature almost instantly, 
whereas the base plate requires consider- 
able time to do so. 
"^' ■ Another arrangement of the working 

wire is found in the Holler and Smith hot-wire meter, the es- 
sential features of which are shown in the diagram of Fig. 73. 
The current-carrying wire in this type of instrument is looped 
around a pulley, and the two ends are fastened to the same plate 
C, as shown in the figure. One end of the wire is electrically con- 
nected to the plate, while the other end is insulated from it. The 
wire is kept in tension by the spring which may be adjusted by 
the screw S. 

In voltmeters a non-inductive resistance of very low tempera- 
ture coefficient is connected in series with the branch ^. 

The pulley D is rigidly attached to a shaft E to which is also 
attached the arm G. This arm is divided at one end and counter- 
balanced at the other. To the two branches of one end of the arm 




AMMETERS AND VOLTMETERS 105 

is attached a silk thread which is passed around a suitable pivoted 
small pulley H, to which is also attached the pointer /. 

The current to be measured passes only through the branch A 
of the working wire A-JS, thus heating A only. The resulting 
expansion diminished the tension of A, and equilibrium is re- 
stored by the spring F pulling B around the pulley D until the 
strain is equahzed. The motion of D carries G with it and the 
silk fiber rotates the pulley .H causing the pointer to move to the 
right over a properly graduated scale. 

In this type of instrument no special provision need be made 
for changes in the temperature of surrounding air. When the 
temperature changes, both branches of the working wire are 
affected alike, expanding alike. This expansion is taken up by 
the spring without the rotation of pulley D, 

Since the expansion of the wire A-B is independent of the 
direction of the current, it is evident that hot-wire meters are 
suitable for alternating as well as direct current. 

104, Hot-wire Ammeter. — The principle of the hot-wire am- 
meter is identical with that of the voltmeter. The construction 
is practically the same, the working wire being of larger diameter. 
In order to prevent sluggishness of action, a fairly fine wire is 
essential, and this introduces a diflBiculty in the case of ammeters. 
Messrs. Hartmann and Braun usually so arrange matters that 
the current is passed through the wire with several parallels, by 
means of thin silver strips making contact at various points 
along its length. Even by this means, however, it is found im- 
possible to pass more than a few amperes through the wire, and 
hence a shunt has to be employed. This entails a considerable 
loss of energy, since a fall of potential of 0.2 to 0.5 volts is required 
across the shunt. The large current taken, however, renders the 
instrument very susceptible to contact errors. In the more re- 
cent instruments the Hartmann and Braun Co. have substituted 
platinum-iridium for platinum-silver as the material of the work- 
ing wire. Platinum-iridium can be operated at a much higher 
temperature and its coeflBicient of expansion is considerably less 
than that of platinum-silver. As a result, the instruments are 
much less affected by changes of temperature and the zero shift 
is much smaller. The new instruments are made as ammeters 
and voltmeters in both switchboard and portable forms. 

106. Damping. — While the moving element is light and there 
is no great necessity for a damping device, nevertheless, one is 



100 



ELECTRICAL METERS 



added. This is practically the same aa that applied to the Hart- 
niann and Braun hot-wire instruments. The damper i3 an 
aluminum disk swinging between the poles of a stationary per- 
manent magnet. 

]n a bulletin of the Bureau of Standards on "Testing Electrical 
Measuring Instruments," we find the advantages and disadvan- 
tages of the hot-wire instrument stated as follows : 

"The hot-wire instrument is not used in this country to any 
great extent in practical work; its defects are relatively large 
consumption of energy, uncertainty of zero, errors due to change 
of surrounding temperature, and to heating when left in the cir- 
cuit. As the working wire must be run at a fairly elevated tem- 
perature, to give proper sensibility, it is easily 
damaged by sudden overloads, which would 
do little or no damage to other forms, except 
the possible bending of a pointer." 

The good points of the hot-wire instrument 
which cause it to be still used for certain 
classes of work, are its independence of ordi- 
nary frequencies, wave form, and stray mag- 
netic field; the fact that it may be calibrated 
on direct current, and that shunts may be 
used with the ammeter for alternating currents. 
106. Thermo-ammeter.— For the purpose 
of measuring very small currents, there has 
- ^-Heater recently been devised an instrument whose 
' r operation depends upon a combination of 

Fia. 74. the electro-magnetic and thermo-electric 

principles. 
It is well known that if two dissimilar metals, such as iron and 
copper, are connected so as to form a closed circuit, and if one of 
the junctions be heated, an electric current will flow through the 
circuit. The current flowing will be approximately proportional 
to the difference of temperature between the two junctions. 

The method of applying a combination of this principle with 
the other two is shown in the diagram of Fig. 74. 

A single loop of silver wire L is suspended by means of a quartz 
B[)er Q between the pole pieces JVS of a permanent magnet. The 
loop is surmounted by a glass stem which carries a mirror M, 
while its lower ends are connected to a bismuth-antimony thermo- 
couple (Bi, Sb). The heating resistance or "heater," consisting 




AMMETERS AND VOLTMETERS 



107 



of a fine filament of high specific resistance, is fixed Immediately 
under the thermocouple. One end of the heater is connected to 
the frame of the instrument to avoid electrostatic forces. The 
current to be measured, or a definite part of it, is seat through the 
heater. Part of the heat generated in the heater is radiated and 
carried by convection to the thermo-junction, raising its tempersr 




Fio. 75. 



ture. The resulting current Bowing through the loop L causes 
it to turn in the magnetic field. The resulting deflection can then 
be read oS by means of a lamp and scale. In the Duddell thermo- 
ammeter, however, the loop L is mounted in jewel bearings and a 
pointer is substituted for the mirror. In the usual pattern of this 
instrument the full scale deflection is produced by a current of 10 



108 ELECTRICAL METERS 

milliamp. either continuous or alternating, and by constructing 
heaters of higher or lower resistances the sensibility to current 
may be increased or reduced as required. The working elements 
of this ammeter are shown in Fig. 75. 

The instrument as at present constructed is not suited for 
central-station use. For measuring current in telephone lines, or 
for other high-frequency currents, it is of considerable importance. 



CHAPTER X 

POWER-MEASURING INSTRUMENTS 

107. Wattmeters. — The instrument most commonly used for 
measuring power is called a wattmeter. Wattmeters are of 
four classes, electrostatic, hot-wire, electrodynamic, and elec- 
tromagnetic. The electrostatic and hot-wire wattmeters are 
not in common commercial use, and, hence, will not be discussed. 



6 O 




. Stationary 
Series Coils 



Fig. 76. 



Wattmeters in common use are of the electrodynamometer and 
induction types. 

108. Electrodsmamometer Type. — The electrodynamometer 
type is very common and may be considered the standard 
indicating wattmeter. The essential features of such an instru- 
ment are shown in diagram. Fig. 76, and consist of two coils, one 
fixed and the other movable, as in the electrodynamometer 

109 



110 



ELECTRICAL METERS 



ammeter. In fact, the electrodynamometer ammeter can be 
used as a wattmeter, if suitable resistance is connected in aeries 
with one of the coils, preferably the moving one. 

In the diagram shown, the heav>' line connected in aeries with 
the Une is the stationary or current coil and counts of two 
part«, each of a few turns of heavy wire. The movable coil, 
which is mounted in the same manner as the movable coil of the 
electrodynamic voltmeter, consists of many turns of fine wire. 




Fic. 77. 

The manner of connecting such a wattmeter to a circuit is 
shown in Fig. 77. L represents the lamp, or receiving circuit, 
whose power consumption it is desired to measure. 

109. Theory of Eiectrodynamometer Wattmeter. — In discuss- 
ing the eiectrodynamometer ammeter, and Kelvin's balance, it 
was stated that the force of attraction between the fixed and 
movable coils is proportional to the product of the currents in 
the two coils. In that case, however, the same current flowed 
through the two coils. In the wattmeter under discussion the 
force of attraction is likewise proportional to the product of 
the currents in the fixed and movable coils, but the currents 
are not the same. The fixed coil carries the current supplied 



POWER'MEASURING INSTR UMENTS 1 1 1 

to the load, but the movable coil carries a current which is pro- 
portional to the electromotive force across the load. 

On direct-current circuits the deflecting force may be repre- 
sented by 

F = KI Xi 
where / is the load current, i the current in pressure coil, and K 
a proportionahty constant. 

If i2 is the resistance of the pressure coil, and E the pressure 

E 
across the receiving circuit terminals, i = ^- Substituting this 

value of i, we get 

F = §EI. 

Since R is also constant, the expression may be written 

F = KoEI. 

This expression shows that the deflecting force, and hence the 
torque, is proportional to the product of current and pressure, 
i.e., to power consumed in the load or receiving circuit. 

Assuming the inductance of the pressure and current coils to 
be negligible, the electrodynamometer wattmeter also gives the 
average power on alternating-current circuits. At any instant 
the torque is proportional to the product of current and pressure 
at that instant. The average deflecting torque will then be 
proportional to the average of the product of current and 
pressure. 

Representing the instantaneous pressure and current by 

e = Em sin w^ 
and i = I m sin {(d — d) 

the torque causing a deflection will be 

Torque = K average of e X i 
or T = K average Emim sin (at X sin ((d — ff) 

= KEmlm X av. [sin cat (sin (d cos ^ — cos w< sin 6)] 
= KEmlm av. (sin^ cat cos 6 — sin (at cos (at sin B) 
= KEmlm (av. sin^ cot cos 6 — a v. sin (at cos (at sin 6). 

The average of sin^ (at is }4i and the average of sin (at cos (at 
is 0. Hence 

T == K ^y^ cos d 

^ KEI cos 6 



112 



ELECTRICAL METERS 



where E and / are effective values. Thus the wattmeter auto- 
matically corrects for power-factor. The constant K, depends 
upon the windings of the instrument but, as instruments of this 
type are direct reading, it need not be considered. 

Since the reaction of a coiled spring furnishes the controlling 
force in instruments of this type, it would seem that such an 
instrument would have uniform scale. This may or may not 
be the case depending upon the operation of the meter. In one 
form of this type of wattmeter the movable coil is brought 
back to its zero po.siikjn by moans of a torsion head as in the 




l| 



Fig. 78. 

case of the dynamometer ammeter already discussed. Such an 
instrument will naturally have a uniform scale. 

In the other form, the pointer is attached to the shaft of the 
movable coil. Under these conditions the scale is no longer 
uniform. The graduations at the upper end of the scale are 
crowded together on account of the fact that when the deflection 
becomes great the deflecting force is not exactly proportional 
to the deflection, but more nearly to the sine of the angle of 
deflection. 

The essential parts of two makes of torsion head wattmeters 
are shown in Figs. 59 and 78. The principles used in the con- 
struction of the Roller-Smith wattmeter, Fig. 59, are evidently 



i 



POWER-MEASUJtING INSTRUMENTS 



113 



those of tho Siemens elect rodyn a mo meter, with the exception 
that the movable coil is mounted on a shaft, thus perntittiDg 
the omission of mercury cups. Meters constructed in thia way 
are subject to tho influence of external magnetic fields. Fig. 
69 is tho mechanism of a voltmeter, but tho same principles are 
applied in the construction of wattmeters. 

The Wcstinghouse preeision wattmeter, shown in Fig. 78, is 
also of the electrodynamomoter type but is constructed according 
to the principles of the Kelvin balance. The middle, movable 
coils are mounted on a light framework carrying suitable jewels 
mounted on ball bearings. 

As has already biien pointed out, such instruments are astatic, 
that is, not subject lo llie inftiieiicc of external niMrmni; flrlil.-. 




Fig. 79. I m. 

Both the General Electric and Weston portable wattmetera 
belong to the second form, i.e., the shaft of the movable coil 
carries the pointer. Tho deflection of the pointer is thus a 
measure of the angle through whi<:h the coil has been turned. 

The General Electric Co, uses the inclined-coil principle, as 
is ahown by Fig. 79. 

The Weston electrodynamometer wattmeter is shown in Fig. 
77, The principles of construction of this instrument are the 
same as those for the voltmeter, Fig. 58. Fig. 77 also shows tho 
manner of connecting sucli a meter to a circuit. Tho large termi- 
nals d-d are connected in series with the power line, and the 
amall terminals e-e are connected across the line to the terminals 
of the load. The button b, when pressed down, serves to close 



l\\ 



KLKCTKICAL METERS 



the proNHuro circuit. Thit) is iiocoHMtry to provoiit hontiriR of Uio 
prcHsure uuil whiin no roadiiiKS are boinK tukon. Tlie scalo in 
(Crnduiitod in watts or kilowiitltt, iluiKmiliiig upon tliu ruiiftu of 
tliQ instrumont. Tho instruiiicntH are normally made for a 
muxinium of liiO voltti, but tho rango can bo vitricd by tho uiw 
of Buitablo multiplicFH and f<hunt«. 

For switchboard ubo, iiiNlruniintsi .■iro manufactured upon 
pxaotly tho eamo principles. I'ljj^. sii :tn<l si nhow the principle-s 




of couBtruotiuii of WcHton MinKlc-phauu and polypboHC switch- 
board wattmeters. Although tlicMo am diroct-roading dufloction 
instrumonta, nevorthetew*, tho rcfinerDOiit of conBtniotion and 
adjustniunt niakcn positililu the uhc of uniform Hcak-H. 

110. Compensation for Power Consumed In Instrument.— 
Sinco both the current and pressure roilH of a wattmeter putwetw 
roHiHtiiiico, some power will be coii»umed in tho instrument Itself. 
Tho amount of this power is not larno, yot it would bo unfair to 
charRo it up to tlio roociving "f load yirciut. From tho diagram 
of Fig, 7(1 it is ovidont that tho current through tho series coil 
is tho sum of tho prcHSuro and load currents. On direct-current 
circuits this sum is equal to the algebraic sum of the eurrenta, 
but in nltornating-currcnt circuits, the in<hiGtanco of tho potential 
coil will never or seldom be the same as that of the receiving 
oirouit, U[id hence, the two currents will not bo in phase. In such 
a case, the current through the series coil will be equal to the 
vector sum of the prossuro and load currents. 



M 



POWER'MEASURING INSTRUMENTS 115 

The power consumption of the pressure coil is i^R = -^ , where 

i is the current in the movable coil and R the resistance of the 
voltage coil. If the load current is /, and the resistance of the . 
series coil r, the power consumption of the series coil will similarly 
be 7V. It is necessary to make correction for only one of these 
losses as can easily be shown. The relation between deflection 
and power, when current and pressure are in phase, is 

D ^ KXIXE. 

If the wattmeter is connected to the circuit as indicated in Figs. 
76 and 77, the current I is equal to the load current plus the 
pressure-circuit current. 

Let II = load-circuit current, 
and ie = pressure-circuit current. 

Then the line current is equal to the sum of h and ie or 

/ = /l + ie 

and the deflection is 

D = KE(h + ie) 
= KEh + KEi,. 

The deflection is thus due to two quantities, one KEIlj which 
is proportional to the power taken by the load, and the other 
KEiey which is proportional to the power spent in the pres- 
sure coil. The correction must then be made only for the power 
spent in the movable or pressure coil. On constant-voltage 
circuits this quantity is constant and corrections can easily be 
made by measuring the voltage, and movable-coil resistance. 

When the pressure coil is connected across the line side of the 
circuit, for accurate work correction must be made for the power 
used in the series coil. 

When such a connection is used, the current through series 
coils is only that demanded by the load. The pressure at the 
terminals of the voltage coil is, however, a trifle higher than that 
at the load terminals, due to the pressure drop, /r, across the 
series coil. The correction to be applied is then equal to /V. 
The power spent in the series coil is usually less than that spent 
in the pressure coil and, hence, the second method of connection 
is to be preferred when non-compensated wattmeters aroused 
and no corrections are made. When corrections are to be made, 
the usual method of connecting a wattmeter to a circuit is that 



116 



ELECTRICAL METERS 



indicated in Fig. 77, and corrections are made for the power 
consumed in the voltage coil. The reason for this is that the 
resistance of the voltage coil can be determined more easily than 
the resistance of the series coil. The resistance of the series coil 
is very small, and the resistance of the contacts d-d is an appreci- 
able part of this resistance. This, of course, is a variable quan- 
tity; it, therefore, would be extremely diflScult to make any 
correction if that were to be considered. 

The portable wattmeters manufactured by the Weston Electri- 
cal Instrument Co., are provided with a compensating coil as 
shown in Fig. 82. It will be observed that the compensating 




BlfiOY 



Fia. 82. 



coil is connected in series with the pressure coil, its winding, how- 
ever, being reversed with reference to the scries coil. The num- 
ber of turns in this compensating coil is carefully adjusted so 
that the counter torque, due to the pressure-circuit current, is 
just equal to the direct torque due to this same current when 
flowing through the scries coil. Such a compensation makes 
automatic correction at all voltages, since the current through 
the compensating coil is always the same as that through the series 
coil at no load and the same voltage. The complete pressure circuit 
thus consists of the voltage coil proper, the compensating coil, 
and the resistance -B, which, in some cases, may be separate from 
the instrument. Connection is made to the power circuit through 
binding posts C and B. 
The binding post D is connected to a resistance r of the same 



\ 

POWER-MEASURING INSTRUMENTS 117 

value as the resistance of the compensating coil, and is to be used 
in calibrating the instrument by means of two different sources 
of current. Also, in measuring power in high-potential circuits, 
when the series coils are connected to a series transformer and the 
voltage coil to a potential transformer, the independent ter- 
minal D is to be used. 

111. Influence of the Inductance of the Voltage Coil. — In the 
previous discussion, we assumed the inductance of the voltage 
coil to be negligible. While this is accurate enough for practical 
purposes and on circuits with large power-factors, on circuits 
of low power-factor the errors introduced may be appreciable, and 
the inductance of the voltage coil must be considered. 

When the receiving, or load, circuit has considerable induct- 
ance, the current through the series coil will lag behind the 
electromotive force. In such a case, the voltage current, when 




Fia. 83. 

the voltage coil is non-inductive, is in phase with the electromotive 
force, and the deflecting force is proportional to 

IE cos Of 

where 6 is the phase angle between electromotive force and load 
current. 

When, however, the voltage coil has inductance, the current 
in voltage coil will lag behind the load pressure and thus the 
angle between load current and voltage current will be less than 
between the load electromotive force and current. This is 
shown in the vector diagram. Fig 83, where a represents the 
difference in phase between the voltage current and load pressure. 

112. Correction Factor. — Electrodynamometer wattmeters are 
usually calibrated on direct current, and when so calibrated the 
inductance has no effect. If 72 is the resistance of the voltage 
ooil and i is the voltage current, the energy spent in the coil when 
used on alternating-current circuits is, 



118 ELECTRICAL METERS 

Ri^ = Ei cos a 
whence Ri = E cos a 

and ^ " p ^^® "• 

But W -= EI cos ^ 

and Torque = iCi/ cos 7. 

E 

Substituting ^ cos a for i, we get 

Torque, T = ,.» cos a cos 7 

J T K cos a cos 7 

^"^ w'^R—^^^rr 

R cos ^ 



whence TF = T X rr 

A cos a cos 7 

If the voltage and current are sine curves, 

y = e - a 
and cos 7 == cos (^ — a) = cos 6 cos a + sin ^ sin a. 

On direct current the watts are directly proportional to torque, 

R 
or to j^T, hence, the indication of a wattmeter, correct on direct 

current, must be multiplied by — to get the correct 

' * •^ cos a cos 7 * 

power on alternating current, and the correction factor becomes 

cos 6_ 

cos a (cos 6 cos a + sin ^ sin a) 
^ 1 

cos^ a (1 + tan $ tan a) 

Sec^ a 

"" 1 + tan 6 tan a 

^ _1 + tan^g 

~ 1 + tan d tan a 

2TfLi 
tan a = - ,y - 

, , 27r/L 
and tan 6 = — ~ 

R 

where Li and -Bi are the inductance and resistance respectively 
of the instrument coil, and L and R are the same quantities of the 
circuit whose energy consumption is being measured. Li and 
Ri are constant for any given instrument, hence tan a varies 
only with the frequency of the circuit while tan d depends upon 



POWER-MEASURING INSTRUMENTS 119 

the frequency and constants of the circuit. These constants are, 
of course, different in different circuits. 

When tan a is positive and less than tan 6, the correction 
factor is less than unity, and the wattmeter reads too high. 

When a = 0, or d, the correction factor is unity and the watt- 
meter indication gives the correct power. 

When tan a is positive and greater than tan d, the correction 
factor is greater than unity and the wattmeter reads too low. 

As tan 6 is likely to be unknown and may have any value, it 
is very evident that the correction factor is unknown and the 
wattmeter reading is uncertain. The relation between the true 
power and the wattmeter reading may be written in the form 

Wattmeter reading = true power X — i~T~i — i • 

When a is small, this reduces to an approximate expression 

Reading = power (1 + a tan 6), 

The error in the reading is evidently true power X a tan 6, and 
as tan 6 increases with 6, the error increases as the power factor, 
cos d, decreases. 

If the phase difference between pressure and load current is 
due to capacity, the current will lead the pressure in the main cir- 
cuit. The relation between the angles is then given by 

7 = a + ^ 

and the correction factor becomes 

1 + tan^ a 
1 — tan 6 tan a 

and the indication of the wattmeter is correct only when tan a 
= — tan Of that is, when a = 0, or — ^. For any other values 
of and a the wattmeter reading will be inaccurate and hence 
electrodynamometer wattmeters should be constructed so that 
a will be negligibly small. This can be done readily by connect- 
ing a high non-inductive resistance in series with the movable 
coil. The inductance of the current coils of standard commercial 
instruments is inappreciable. The effect of wave form upon the 
accuracy of the wattmeter will be taken up in Chapter XXIL 

113. Range of Wattmeters. — The range of the electrodyna- 
mometer type of wattmeter may be changed by connecting 
multipliers in series with the voltage coil, or shunts in parallel 
with the series coil on direct-current circuits and low-voltage, 



120 



ELECTRICAL METERS 



low-frequency, alternating-current circuits. When the wattmeter 
is to be used on high-voltage alternating-current circuits, trans- 
formers are used. It is not the practice of American manu- 
facturers to shunt wattmeters. 

114. Induction-type Wattmeters. — Induction-type wattmeters 
use in their operation the principles of the rotating and revolving 
magnetic fields. To imderstand the general apphcation of these 
principles, consider the case illustrated in Fig. 84 which is merely 
illustrative. 

The essential parts of an induction meter are a pivoted disk or 
drum Z), a pressure coil VC, and a current or series coil CC. 
The copper or aluminum disk, Z), is pivoted at its center and 



-qjOCW^ 



Vc 




D 



CC 



Fig. 84. 



carries a pointer not shown in the figure. The motion of the disk 
is counteracted by suitable spiral springs. The voltage coil is 
highly inductive so the current in the coil lags approximately 
90° or one-quarter of a period behind the pressure. The current 
in pressure coil produces a magnetic field which is in phase with 
it. The variation of this flux through the disk induces eddy 
currents which are one-quarter of a period out of phase with the 
flux. 

The current coil CC is non-inductive. The flux, due to this 
current through the disk, is in phase with it. Hence, the eddy 
currents, due to pressure current, and flux, due to load current, 
reach maximum values together and the reaction between them 



POWER-MEASURING INSTRUMENTS 121 

will be a maximum under these conditions. This reaction causes 
the disk to rotate. 

The eddy currents are proportional to pressure current, which 
in turn is proportional to the pressure at terminals of load, or 
algebraically 

i = KiE, 

where i represents the effective eddy currents, and E the effective 
pressure. Similarly 

* = KJ 

where ^ is the effective flux due to effective load current /. 
The torque is proportional to the product of i and f>, hence 

Torque = Kd^ = K1K2EL 

Or in other words, the torque is proportional to EI, the power. 

It can readily be shown, by the same process of reasoning, that 
when the current and pressure are not in phase, the torque is 
proportional to EI cos 6, where d is the difference in phase. 
Hence, the induction wattmeter, when properly adjusted, gives 
correct indication on circuits whose power-factor is other than 
unity. 

116. Westinghouse Induction Wattmeter. — A diagrammatic 
sketch of the magnetic circuit and windings of the Westinghouse 
induction wattmeter is shown in Fig. 85. It is evident that the 
magnetic circuit is of the same pattern as that of the induction 
ammeter manufactured by the same company. The winding is, 
however, modified to meet conditions of power measiurements. 

The windings consist of two principal coils V-C and C-C. 
The coils F-C are connected through a resistance across the line, 
and the coils C-C in series with the load. The coils V-C have 
relatively high inductance and consequently the flux due to the 
voltage ciurrent is nearly in quadrature with the pressure. 

Operation. — ^The pressure current makes (W-Z) and (X-Y) 
opposite in polarity. The load current through coils C-C 
makes (W-X) and {Z-Y) opposite in polarity, and as the flux 
due to load current is in phase with the current, the resulting 
field rotates. As already explained Ihis rotating field acting 
on the drum armature produces a torque which causes a deflec- 

13 



ELECTRICAL METEUS 





POWER-MEASURING INSTRUMENTS 123 

tion. The motion of armature is opposed by spiral springs as in 
the case of the ammeter. The auxiliary coils B-C are used to 
equalize any difference in the windings of the voltage coils V-C. 
A complete instrument of this type is shown in Fig. 86. 

In the foregoing discussion the assumption is made that the 
current in the voltage coil is exactly one-quarter of a period out 
of phase with the voltage at its terminals. In practice this 
relation cannot be secured with the arrangements of coils shown. 
This is due to the fact that the voltage coil possesses resistance 
as well as inductance, and also that eddy currents and hysteresis 
losses in the core are inevitable. Likewise, the current in 
current coil is not exactly in phase with the resulting flux. 
Hence, it follows that it is not easy to insm^e that the flux due to 
the jvoltagfi_^U .shall, iiififer by exactly one-quarter of a period 
from that due to the current coil. The effect of any such a dis- 
crepancy upon the indications of induction instruments is similar 
to the effect of inductance and capacity in the voltage coil of the 
electrodynamometer type of wattmeter; that is, the error is small 
when the power-factor of load is high; but it increases as the 
power-factor decreases. 

116. Lagging Induction Wattmeters. — The term lagging, as 
here used, means adjusting the meter so that it will read cor- 
rectly on inductive and non-inductive loads. This is accom- 
plished by means of auxiliary coils whose effect is to produce exact 
quarter phasing between fluxes due to voltage and current coils. 
Usually the coils for making this adjustment are connected in the 
voltage circuit. 

One method of securing exact quarter phasing is represented 
diagrammatically in Fig. 87. This represents the voltage circuit 
as consisting of three parts. A, B, and C. A is a, highly inductive 
coil, B also possesses some inductance but less than A, while C, 
which is connected in parallel with B, is a pure resistance. The 
current in the coil B produces the actuating flux. The principles 
involved are illustrated in Fig. 88. Representing the voltage 
across coil B, Fig. 87, by Eb, Fig. 88, it is evident that Ic, current 
in coil C, is in phase with Eb. Owing to the inductance of coil B, 
Is will lag behind Eb by an angle less than 90°. Ib may then be 
drawn in the direction of 07. I a, or current in coil A, is the 
vector sum of Ic and Ib> Vector I a represents this current. 
Since coil A is highly inductive Ea will lead I a by nearly 90° and, 
hence, may be represented by vector Ea» E, the resultant of- 



124 



ELECTRICAL METERS 



Ea and Eb, will under these conditions be represented by vector 
E or OX. The phase differences between E, Ea, Eb, I a, Ib and 
Ic depend upon the relative values of inductances and resist- 
ances of coils Af B, and C. It is thus evident that by a suitable 



^^^•> •»•«»••« 



Ic 

nAAAAi 

U A C 



Hi- — 



Ea — — ~">|<- 



Ej-M 




Fig. 87. 



Fig. 88. 



adjustment of the inductances and resistances of these three 
coils, Ib can be made to lag exactly 90° behind E. 
Perhaps the simplest and most commonly used method of 




Fig. 89. 



lagging a meter consists in winding the core of the voltage coil 
with, or interposing within the path of the voltage flux, a short- 
circuited coil whose resistance is adjustable. The short-circuited 
coil acts as the secondary of a transformer, of which the regular 
. voltage coil is the primary. This is the method used in the West- 



POWER-MEASURING INSTRUMENTS 125 

inghouse wattmeter shown in Fig. 85 in which L. C, represents the 
lagging coil. 

The influence of the lagging coil upon the phase relation 
between pressure coil and current coil fluxes, is much the same as 
that of the secondary of a transformer. The phase relation is 
shown in Fig. 89. f> represents the magnetic flux linking both the 
pressure and lag coils. It induces in the lag coil an electromotive 
force E'2 and in the voltage coil an electromotive force in the 
same direction, but of different magnitude, determined by the 
number of turns. Representing the exciting current in voltage 
coil by 7, the ampere-turns necessary to produce the flux f> is 
represented by Nil, and is made up of two components, NJi and 
iV2/2. The electromotive force applied to the voltage coil termi- 
nals may be separated into three components: the first E\ bal- 
ances the induced electromotive force due to the flux f>; the sec- 
ond, represented by ZiXi, balances the electromotive force pro- 
duced by any leakage flux which links with the voltage coil, but 
not with the lag coil; the remainder sends current through the 
voltage coil and is represented by liri. The terminal pressure Ei 
is the vector sum of these three components. If the lag coil be 
open-circuited, E2 becomes identical with E'2't Nili becomes 
identical with NJ; hri becomes smaller and farther from E\ in 
phase. As the current in the lag coil is increased due to a 
decrease in the resistance in series with it, 7i must increase to 
maintain /; angle ^ decreases, h becoming more nearly in phase 
with Eu hn increases, making Ex more nearly in phase with E\, 
the condition desired. An increase in hXi also aids in bringing 
about the desired relation. Since E'l is always in quarter-phase 
relation with $, adjusting the lag coil resistance secures the proper 
quarter-phase relation between $ and Ei. 

117. Scale. — Since the motion of the movable element is 
usually controlled by a spiral spring, the scale will be uniform 
when the torque is exactly proportional to the power in watts. 
This exact proportionality is not absolutely essential in indicating 
instruments as the whole scale can be calibrated. The scales 
of the best instruments are, however, practically uniform and 
extend over nearly 300°. It is evident that induction instru- 
ments can be used only on alternating-current circuits. 

118. Mercury Wattmeter. — The principle of operation of 
this meter, which will undoubtedly soon be placed on the market, 
is the same as that of the mercury watt-hour meter explained in 

14 



126 ELECTRICAL METERS 

Article 172, to which the student is referred. The difference in 
construction consists in the substitution of a torsion spring for 
the damping disk and damping magnets. 

The range of the instrument is varied by shunting the current 
coil, a method used only on this type of meter. The designers 
claim that the operation of the meter is entirely satisfactory. 



CHAPTER XI 

PHASE-RELATION AND FREQUENCY INSTRUMENTS 

119, Introduction. — The indications of two classes of instru- 
ments are determined by the phase difference between current 
and pressure in the same circuit, or the difference in phase 
between pressures in different circuits. 

Instruments of the first class are called power-factor meters, 
or indicators, and of the second class synchroscopes. 

120. Power-factor. — The term power-factor has been defined 
in two ways. According to one definition, power-factor is the 
cosine of the phase difference, the phase difference being the 
angle between the points at which the curves of current and vol- 
tage cut the axis in the same sense. Thus, in Fig. 32 the cosine 
of the angle represented by the distance between points where 
electromotive force and current waves cross axis in the same 
sense, is called the power-factor. The other definition has no 
relation to phase difference, but is based upon the relation. 

True power = volts X amperes X K 
whence, 

^ c j_ watts 

A, or power-factor, = — ,, ^^ 

' ^ ' volts X amperes 

If the current and pressure curves are true sine waves, the values 
of the power-factor obtained in accordance with either definition 
will be the same. When, however, this is not the case, and es- 
pecially when the current and voltage curves have different forms, 
the power-factor if, as determined in accordance with the second 
relation will not be equal to the cosine of the phase difference 
between the zero points of the electromotive force and current 
waves. For practical purposes, the power-factor is usually de- 
termined in accordance with the second relation given above, 
and is obtained from the indications of an ammeter, voltmeter, 
and wattmeter. The product of the ammeter and voltmeter 
readings gives the apparent power; the wattmeter gives the true 
power, and thus the wattmeter reading divided by the product 
of the ammeter and voltmeter readings will give the power- 
15 127 



128 



ELECTRICAL METERS 



factor. It is often advisable, however, to have a separate instru- 
ment for indicating the power-factor, so that no computations 
need be made. 

12L Power-factor Meter. — The essential features of one type 
of single-phase power-factor meter are shown in Fig. 90. The 
principle of this instrument is much the same as that of the 
dynamometer-type wattmeter. The instrument, however, is 
provided with two movable cofls in place of one. These cofls are 
mounted at right angles to each other, and the controlling spring 



L 




Fig. 90. 



is omitted. The current is led into the moving coils by means 
of two strips which exert practically no torque. The operation 
of the instrument is then as follows: 

The main or load current passes through the coils CC, while 
the voltage current is divided, one part passing through resistance 
R and coil B; and the other part through the inductance L and 
coil A. The current in resistance R and coil B will be in phase 
with the voltage across the load terminals, while that through L, 
which is highly inductive, will be about 90° out of phase with the 
current in R and B. 

When the load current and voltage are in phase, the reaction 
between the coils CC and coil B will be a maximum, and that 
between coils CC and A a minimum. As a consequence, the 
coil B will set itself in such a position that its plane will be parallel 
to the plane of the coil CC; or in other words the flux due to 
the current in coils CC will pass straight through coil B and in 
the same direction as the flux due to coil B. Under these con- 
ditions the pointer, which is attached to the shaft of coil B, will 
indicate unity power-factor. 

When, however, the load current and voltage are out of phase. 



FREQUENCY INSTRUMENTS 129 

the reaction between the coils CC and B will be less and there 
will be an added reaction between the coils CC and A. This 
added reaction will compel the coils A and B, which are mounted 
at right angles to each other, to take a new position. This new 
position is determined by the phase difference between load 
current and pressure. The deflection of the movable coils is 
independent of the magnitude of the main current, but it does 
depend partly upon the ratio of the currents in coils A and B as 
well as upon the phase difference between load current and 
pressure. The value of the current in L depends very largely 
upon the frequency and wave form of the applied voltage, and, 
consequently, the indications are also modified by the frequency. 
By carefully designing the coil L, it is possible to keep the ratio 




Fig. 91. 

of currents in coils A and B practically constant for moderate 
variations in the voltage and frequency. 

The instrument may be calibrated so as to indicate either phase 
difference in degrees, or power-factor. 

122. Analytical Proof of Principles. — That the foregoing 
explanation of principles is correct can readily be shown by 
mathematical analysis. In Fig. 91, let AA\ BB', and CC repre- 
sent the relative positions of the axes of coils A, B, and CC, 
respectively, at any instant. Furthermore, assume that the 
current in coils CC is in phase with the voltage. If the current 
in series coils is represented by 

ic = Im cos (*)t 

the currents in A and B may be represented by 

ia = la sin (jjt 

and 

ib = lb cos (jjL 

The coils A and B are designed so that their magnetic field 



130 ELECTRICAL METERS 

strengths are equal, and as the magnetic field will be in phase 
with the current producing it, we may represent the instantaneous 
field strengths of coils A and B by 

ha = Hm sin (f)t 
kb = Hm cos 0)t, 

Now the torque or reaction between either coil and coils CC is 
proportional to the product of this field strength by current in 
coil CC, and the sine of angle between the axes of the coils. Hence 
the average torque exerted on coil B is 

Tb = average of Khbic sin 

= av. KHnJm cos (at cos cot sin 
= av. KHmlm cos^ cot sin 0. 

But the average of cos^ cot is }4 7 hence the average torque on B is 

KHm r . , 

Tb = -y- Im sm <t>. 

This is zero when is and maximum when is 90°. That is 
torque is when the plane of coil B is at right angles to the plane 
of coil C Likewise the average of torque on coil A is 

Ta = av. haic sin (90° + <t>) 

— av. Hmlm sin (at cos w cos 0. 

But the average of sin cat cos (at is zero, hence the average torque 
on A is zero. The movable element will thus be deflected so 
that the reaction between coils CC and B is zero. This means 
that (t> is zero, or that the plane of coil B is parallel to the plane 
of coil C. 

When the current and voltage are out of phase, the same 
method of finding the torque can be used. Let the pressure lead 
the current by the angle 6) then the instantaneous currents in the 
several coils will be 

ia = la COS {(at - 90°) 

= la sin cot 
ib = lb cos cot 

ie = Im COS ((at — 6). 

The instantaneous values of field strengths due to coils A and B 
are again 

ha = Hm sin cot 
and hb = Hm cos cot. 



FREQUENCY INSTRUMENTS 

The average torque on coil A is 
Ta = av. Kicka cos * 

= av. KInHn sin ut cos (w( — 9) cos ^ 

= av. KI„H„ cos <^ (sin oit cos wt cos + sin* u 



tI^H„ 



s Bin 6, 



ranee the average of sin cui cos w( ia zero and of sin* wt is J^ 

Similarly the average torque on coil B ia 
Tt = av. Kicftt sin 6 

= av. KImH„ COS wi COB (w( — 6) sin ^ 

= av, KI„H„ sin * (cos* w( cos 8 + cos «( sin'wt sin fl) 

= -iyImH„ sin e< 




The total torque at any instant will be equal to the sum of Ta 
and Ti, or 

T = r, + n = -g /™H„ (cos * sin 9 + sin * cos fl) 

and y = 2 /„H„ sin (* + e). 

This torque must be zero when the movable system cornea to 
rest, or when ^ + 9 = 0. 

The scale may be graduated either in terms of the angle 6, or 
cos 0, the power-factor. An instrument in which these principles 
are practically applied is shown in Fig. 92. The movable coils 



132 



ELECTRICAL METERS 



are not visible in this figure but the manner in which they are 
mounted on the shaft is shown in Fig. 93. 

123. Polyphase Power-factor Meter. — The indications of the 
singlD-phase power-factor meter cannot be relied upon when the 




meter is used on circuits whose frequency is different from that 
for which the meter is designed. To obviate this objection to 
single-phase meters when used on polyphase circuits, a meter has 




been designed which utilizes the actual phase displacement ra 
polyphase system to obtain the voltage-coil magnetic field. A 
diagram showing the connections of a three-phase meter is shown 
in Fig. 94. The connections, as there shown, are intended for a 
balanced system. The three coils A, B, and C are mounted 



FREQUENCY INSTRUMENTS 



133 



on the same shaft in the same manner as the coils of a single- 
phase meter. The planes of the three coils are 120° apart, and 
one end of each is connected, through a suitable resistance, to one 
of the three mains, the other ends being connected together. 

The principles of operation are exactly the same as those of the 
single-phase instrument just described, but as there is no induct- 
ance in the voltage coils, the indications of the meter are inde- 
pendent of frequency, wave form, or voltage variations. 

For unbalanced three-phase cir- Q 

cuits, the instrument is made with 
three current coils, which may be 
connected to the separate circuits. 
The power-factor of each phase, or 
the average of the whole system, 
can thus be obtained. 

124. Westinghouse Power- 
factor Meter. — ^The operation of 
this meter is based on the interac- 
tion of a rotating and an alter- 
nating magnetic field. The oper- 
ating elements of the two-phase 
and single-phase meters consist of 
three coils and a pivoted iron vane 
or armature, Fig. 95. Two of 
these coils, M and N, are fixed in 
position at right angles to each 
other with their axes in the same 
plane. These coils of a two-phase 
meter are connected to each phase 
of the line so that the currents in them are in phase with the line 
currents. A resistance coil is connected in series with one of 
these coils, and a high inductance is connected in series with the 
other coil of the single-phase meter. The currents in the two 
coils M and N are thus in quadrature and produce a rotating 
magnetic field. 

The u-on vane is magnetized by a current in phase with the 
voltage and passing through a third coil. Fig. 96. This coil is 
mounted with its axis coinciding with the shaft of the vane, and 
at right angles to the plane of the axes of the coils M and N. 
As the iron vane will be attracted or repelled by the magnetic 
field of the coils M and N, it takes a position where the zero of 




Fig. 95. 



134 



ELECTRICAL METERS 



its alternating field occurs at the same instant as the zero of the 
rotating field. Thus, if the current magnetizing the vane is in 
phase with the current in coil N, it will assume a position parallel 
to or in the plane of the coil M. If the current in the coil C 
ia in quadrature with that in coil N, the vane will assume a posi- 
tion parallel to the plane of the coil TV. For any other phase 
relation between the currents in the coils C and N, the iron vane 
will assume a corresponding position. The iron vane thus shifts 
around to a position determined by the angle between the vol- 
tage and current in coil N, that is, the angle between the current 




and voltage of the circuit. The lanunated iron ring shown in 
Fig. 96 provides a return circuit for the flux of the pivoted 
armature. 

The three-phase meter is similar in construction with the 
exception that it has three current coils spaced 120° apart. 
These coils are then connected one to each phase of the three- 
phase circuit. 

An analytical proof almost exactly hke that given in Article 
122 may be applied to the foregoing principles. 

The motion of the pointer is damped by means of an alumi- 
num disk moving in the field of two permanent magnets. 

126. Frequency Meters. — Frequency of an alternating current 
has been defined as the number of cycles per second, where a cycle 
is considered as consisting of a complete set of positive and nega- 
If the magnetic field of an alternator consists of p 
s a speed of n revolutions per second, the frequency 



tive values, 
poles, and h 
is given by 



/- 



pn 



FREQUENCY INSTRUMENTS 



135 

An instrument designed to indicate the frequency is called a 
frequency indicator or meter. Frequency indicators are of two 
types, that is, they make use of two distinct principles in their 
construction. 

126. Resonance Frequency Indicator. — The resonance principle 
is of considerable importance, not only in its application to 
frequency indicators, but in many other ways. The principle 
can perhaps be understood from the following illustrations'. 
In ringing a lai^ church bell, the pull on the rope must come at 
regular intervals. A small impulse, if imparted at the right 
instant, and oft repeated may result in considerable motion. If 
two tuning forks of the same pitch be placed some distance apart, 
and one be caused to vibrate, in a short time the other will be 
sounding. The first fork sends out regular impulses of the 



^-Solder weight 




___ A.C.5upp^^ 



same frequency as that of the second fork. These impulses are 
transmitted through the, air, and, coming at regular intervals, 
cause the second fork to vibrate. The sounding board of a 
piano, and the column of air in the organ pipes arc also set 
into vibration by resonance, the former by the impulses from 
the wire, and the latter by air impulses from the Up of the 
pipe- 

The application of this principle for indicating the frequency is 
clearly shown by Fig. 97. Steel strips of different lengths are 
fastened at one end and free at the other end in much the same 
manner as the reeds of an organ. These strips have different peri- 
ods of free vibration, and can readily be caused to vibrate by 
outside impulses whose frequency is the same. The impulses are 
magnetic and are supplied by the alternating current in the 
electromagnet which is connected to the circuit whose frequency 
is to be determined. If the free period of vibration of the reed 
is equal to half, the period of the current, the magnetic impulses 



136 



ELECTRICAL METERS 



will Bet the reed into vibration as follows : As the current in t&e 
electromagnet increases, the reed is attracted toward the magnet, 
and springs away as the current falls to zero; as the current in- 
creases in the opposite direction the reed is again attracted. 
The amplitude is thus increased with each alternation of current 
until the energy dissipated in the reed by molecular and air 
friction just equals that imparted to it by the electromagnet. 
If the period of the alternating quantity differs but slightly from 
this critical value, the impulses due to the electromagnet will not 
occur at favorable moments. They will occur sometimes too 
early and sometimes too late, so that instead of reinforcing the 
motion of the reed, some of the impulses will oppose the motion 
and thus reduce the ampUtude. A very sUght difference between 
the frequency of the reed and that of the alternating current is 
very noticeable in a diminution of the amplitude of the reed. 
127. Campbell Frequency Meter. — One of the earliest instru- 




ments to make use of the foregoing principle was designed by Mr. 
.\ibert Campbell. The essential features of such an instrument 
are shown in Fig. 98. This meter was made with only one reed 
S, whose free length was variable. One end was fastened rigidly 
to a shding rack, while the other or free end projected in front 
of an electromagnet M. When in use, the rack is moved either 
to right or left until the maximum ampHtude of vibration is 
obtained. The corresponding frequency is then indicated by 
the pointer upon a suitable dial. 

128. Hartmann and Braun Frequency Meter. — The essential 
features of the Hartmann and Braun and Siemens and Halske 
indicators are the same as those shown in Fig. 97. Instead of one 
reed whose free length can be varied, these indicators are made 
with many reeds, one for each frequency. 

In another form the reeds are mounted on the outside of a 



FREQUENCY INSTRUMENTS 

cylinder, which can be rotated about a central axis. The electro- 
magnet is mounted on an arm pivoted at the axis of the cylinder, 
and projecting a httle beyond or outside of the cylinder. By 
rotating the cylinder, each reed may be successively brought 



eaiiB B 



within the influence of the electromagnet. Every reed is tuned 
to correspond to a different frequency, and, as stated above, its 
vibration will be reinforced by a current whose frequency is one- 




half that of the reed. Thus, when the electromagnet is brought 
up to a particular reed, it is set in vibration and emits a distinct 
sound only if the conditions are as stated. The frequency of Ihe 
current to which the reed responds can be read on a dial f 
above it. 



ELECTRICAL METERS 



In atill another form of meter, the electromagnet and reeds 
arc both fixed. The electromagnet is oblong in form and extends 
over several reeds. The reeda have their free ends whitened and 
their vibration is shown aa a white band, Fig. 99. These are 
suitable for switchboard use, Fig. 100. 

Yet another form is supplied with two pairs of electromagnets, 
one pair in front and the other back of the reeds. By this 
means, two frequencies from different sources can be determined 
at the same time. 

If alternating frequencies higher than those for which the 
instrument is made are to be measured, a magnetic superposition 
arrangement is required. This is accomplished by adding a few 
turns of a second winding upon the electromagnet core. Through 
this second winding is sent a direct current which, to a certain 
extent, polarizes the magnetic field due to the alternating current. 
By this means tlic scale readings have double values. The 
explanation of this is as follows: The electromagnet is alternately 
positive and negative with the fluctuations or alternations of the 
current in the coil. A non-polarized reed is attracted by both 
positive and negative magnetism and, hence, the reed will 
vibrate twice as fast as the frequency of the current. When, 
however, the reed is polarized, that is, made a permanent magnet, 
it will be attracted by only one of the magnetic impulses. For 
instance, if the north pole of the reed ia near the electromagnet, 
it will be attracted when the electromagnet is negative, and 
repelled when the electromagnet is positive. Since the alter- 
nating magnetization is superposed upon a permanent magnetiza- 
tion, the latter is merely increased and decreased, but not 
reversed. Under these circumstances the frequency of the reed 
will be the same as that of the current. The same reed may thus 
be used to measure two frequencies, the lower frequency will be 
indicated when the reed is unpolarizcd, and the higher frequency 
when it is polaiized. 

Instruments of this type are very permanent and accurate in 
their indications. 

129. laduction^type Frequency Meter. — An instrument of this 
type is manufactured by the Westinghouse Electric and Manu- 
facturing Co. The essential features of such an instrument 
are shown in Fig. 101. The instrument may be described 
as consisting of two induction voltmeters, the electromagnets of 
which tend to cause the disk to rotate in opposite directions. 



FREQUENCY INSTRUMENTS 



139 



The electromagnet B of one of the voltmeter elements is con- 
nected in series with a non-inductive resistance H, and the 
electromagnet A of the other voltmeter element is connected in 
series with a relatively high inductance or a condenser. The 
current through B is thus independent of frequency while that 
through A will vary with the frequency, other conditions re- 
maining constant. The coils are so adjusted that any change 
in voltage causes the torque due to the two electromagnets to vary 
in the same ratio. The indications of the instrument are thus 
independent of voltage variations, but depend solely upon varia- 




FiQ. 101. 

tions in frequency. The aluminum disk G consists of two halves 
of eccentric circles. If the disk were a true circle any change 
in frequency would produce continuous rotation. The left-hand 
edge of the disk which moves under A is practically the arc of a 
circle whose center coincides with the shaft. The right-hand 
edge, which moves under B is practically the arc of a circle 
whose center is slightly above the shaft. With this arrangement 
the amount of metal in the air gap of electromagnet A is prac- 
tically constant, while the amount of metal in the air gap of - 
electromagnet B varies with the position of the disk. When 
the frequency decreases, electromagnet B becomes stronger than 
A and the disk turns counter-clockwise. The part of the disk 
in the air gap of B decreases until the torques of the two 
electromagnetB balance, when the disk stops ; when frequency 



140 



ELECTRICAL METERS 



inoreaseB, the torque of B is decreased and the disk rotates clock- 
wise; a greater part of the disk gradually enters the air gap until 
the two torques arc again balanced. For every frequency, there 
is a definite point at whicli the meter comes to rest. The exact 
shape of disk is obtained by experiment; such an arrangement 
avoids the necessity of controlling springs. The mechanism of 
this meter is shown in Fig. 102. 




Fio. 102. 

130. Weston Frequency Meter. — The frequency meter of the 
Weston Electrical InBtrument Co. operates on somewhat the 
same principle as the movable-core type of ammeter and volt- 
meter. There is, however, this difference; in the ammeter 
and voltmeter the magnetic field varies in intenaity but not in 
direction, while in the frequency meter the field remains constant 
BO long as pressure is constant, but its direction varies with the 
frequency. The direction of the field is determined by the ratio 
of the currents in two coils which are mounted at right angles to 
each Other. The relative intensities of the currents are deter- 
mined by an ingenious arrangement of inductance and resistance 
coils. 

Fig. 103 is a diagram of the internal connections of the instru- 
ment. The two fixed coils are marked (1-1) and (2-2) respec- 
tively. As is plainly evident from the diagram, coil (1-1) ia 
connected in series with reactance coil Xi and in parallel with 
resistance coil Ri; and coil (2-2) is connected in scries with re- 



142 



ELECTRICAL METERS 



same as that through (2-2) and in phase with it. The resultant 
magnetic field in this case will be parallel to CB in the diagram. 
This position of the magnetic field will remain fixed bo long as 
the frequency remains constant. This is shown in Fig. 105, 
where Hi represents the position and maximum value of field 
due to coil (1-1), and Ih represents the maximum field due to 
coil (2-2). Since the intensities of the two fields change to- 
gether, the resultant field will be represented by H, both in mag- 
nitude and direction. The resultant magnetic field will thus 
coincide in direction with OB, and only its intensity will change 
when voltage alone changes. The position of the soft-iron core is 
determined by the position of the resultant magnetic field. 




Any change in frequency will change the ratio of the currents 
in the two fixed coils. For instance a higher frequency will 
decrease the current through Xi and also through X,. Part of 
the current through Rj under this condition passes through A 
and through coil ('2-2) in addition to that which passes through 
coil (1-1). The magnetic field of coil (2-2) is thus stronger than 
that of coil (1-1) and the resultant magnetic field is shifted in the 
direction of //j, Fig. 105. Thus every change in frequency is 
accompanied by a shitting of the space position of the resultant 
field, and this shifting causes a deflection of the pointer. 

131. Synchronizing Devices. — Although instruments that 
indicate whether two generators are in synchronism are not prop- 
erly meters, nevertheless their practical importance justifies a 
discussion of them in this text. 

When two alternators, or two synchronous motors, are to be 
operated in parallel, some device is necessary to show whether 
the two machines are in synchronism, that is, whether at the 



FREQUENCY INSTRUMENTS 143 

same frequency, and whether the terminals of the separate 
machines are positive and negative together. The simplest forni 
of a device for this pm*pose is an incandescent lamp connected 
across the contacts of a single pole switch as shown in Fig. 106. 
When the points A and B are at the same potential, no current 
will flow through the lamp L and, consequently, it will not 
light up. In order that this condition be fulfilled the electro- 
motive force of one generator must equal the electromotive force 
of the other generator and the two electromotive forces must be 
in phase. Owing to the fact that it requires an appreciable differ- 
ence of potential to cause an incandescent lamp to light up, 
there is considerable indefiniteness in the use of such an indicator. 
In well-appointed central stations the synchronizing lamps are 
rapidly being displaced by special devices called synchroscopes or 
synchronism indicators. An indicator of this type should per- 
form three distinct functions, as follows: 

1. It should indicate the difference in speed between the two 
generators to be synchronized. 

2. It should indicate which machine is running the faster, and 
finally, the time of exact synchronism. 

3. It should indicate phase difference when frequencies are 
equal. Modern synchronism indicators perform these functions 
well. 

The principles of operation of synchronism indicators are 
practically the same as those of the power-factor meters already 
discussed. Thus, in Fig. 90, if the coils CC are wound with fine 
wire and connected to the terminals of one alternator while the 
two ends marked a and b are connected to the terminals of the 
other alternator, the pointer will indicate the phase difference 
between the electromotive forces of the two machines. 

In practice, the stationary coils CC are connected to the line, 
or terminals of machine running, while the moving coil is con- 
nected to the generator to be synchronized. The resistance R 
is usually an incandescent lamp. The inductance L and resist- 
ance R are used for "splitting" the phase of the current through 
the rotating element so as to produce a revolving field. 

The field through the stationary coils pulsates with a frequency 
equal to that of the "running" generator while the field in rotat- 
ing coils, due to the incoming generator, revolves. If the fre- 
quencies of both machines are the same, there is a certain position 
of the armature where no torque will be exerted upon it. If, 

16 



144 



ELECTRICAL METERS 



however, the frequencies are dififerent, the field of one set of coils 

is constantly changing its phase with reference to the other, and, 
consequently, there is a torque exerted upon the armature caus- 
ing it to rotate. The speed of the armature is equal to the dif- 
ference of the frequencies, the armature making one revolution 
for each complete cycle gained by one generator over the other. 
The direction of rotation will also depend upon the relative speeds 
of the two generators. 

132. Weston Synchroscope. — A synchroscope, working on the 
foregoing principles, would evidently rotate in one direction if the 
incoming generator were too fast and in the opposite direction if 
too slow, and the rotation would be continuous unless some 
retarding force were used. The Weston synchroscope uses 
spiral springs to counteract this motion. The movement of 
the pointer is thus limited. The connections of the various 




operating parts of this synchroscope are shown in the diagram of 
Fig. 107. The incoming machine is connected to terminals A 
and B, while the machine with which it is to be synchronized is 
connected to busbars at C and D. If the two machines are not 
running at the same frequency, the phase displacement will con- 
tinuously shift and with it the torque on the movable coil will 
vary from zero to maximum in one direction back to zero and 
to maximum in the other direction. Thia variation in torque 
will cause the pointer to move back and forth over the dial. If 
the machines have the same frequency, but are not in phase, 
the pointer will come to rest at one side or the other of the 
middle point of the scale, the position being determined by the 
average of the torque. 

Remembering that the average torque is zero when the current 



FREQUENCY INSTRUMENTS 



145 



in the movable coil is 90° out of phase with the current in the 
stationary coil, it is evident that the pointer will stand in verti- 
cal position when the two machines are in synchronism; for at 
that time the current in the movable coil leads the other current 
by one-quarter of a period. This phase displacement is brought 
about by the condenser in the movable-coil circuit. 

When the two generator currents are not in phase, the currents 
in the movable and stationary coils will no longer be in quad- 
rature. When this is the case, a torque will be exerted upon the 
movable coil causing a deflection. The direction of the deflection 
will be to the left when the incoming machine is slow and to the 
right when it is running too fast. 

Pointer -B 




..-Shaft- S 




40 



Fig. 108. 



The synchronizing lamp which illuminates the dial is con- 
nected to the low-voltage secondary of the transformer. An 
examination of the winding on the transformer will show that 
when A and C are of the same polarity, the flux through the 
secondary winding is a maximum and the lamp is brightest. 
That is, the lamp is brightest when the pointer indicates exact 
synchronism. 

133. Westinghouse Synchroscope. — The essential principles 
of another form of soft-iron movable-core synchroscope are shown 
in Fig. 108. As shown, the winding consists of three fixed coils 
M, N, and C. 

The axis of the coil C coincides with the shaft .to which the 
pointer is attached. Upon this shaft is mounted a cylindiical 



146 



ELECTRICAL METERS 



iron core which carries two projections A-A. Tlie other two coils 
have their axes 90" apart, but in the same plane; this plane, how- 
ever, is at right angles to the shaft. The axea of the three coils 
thua correspond to the three rectangular axes of coordinate 
geometry. 

In series with coil M is connected an inductive reactance, 
while in series with N is connected a non-inductive reaiatance. 
The two coils are connected in parallel across the busbars. The 
coil C is connected through a non- 
inductive resistance ffi across the 
mains of the generator to be syn- 
chronized. 

Analysis of the principles in- 
volved will show that the principles 
of operation are nearly identical 
with those explained in Article 72. 
There it was shown that a movable 
core would rotate when subjected 
to the influence of two coils which 
arc mounted at right angles to 
each other and through which cur- 
rents in quadrature flow. When 
an alternating current flows through 
C the projections A~A are alter- 
nately positive and negative. If 
at the aame time a current be flow- 
ing through coil N, the movable 
iron core will be deflected so that 
the projections A~A are parallel to the field of the coil N. It 
the frequenciea of the two currents are equal, the current in 
coil C will reverse with that in N, and hence the movable core 
will remain stationary. If, now, a current in quadrature with 
that in C be passed through coil M, its average torque on the 
armature will be zero, according to the explanation of Article 
122. When, however, the frequency or phase of the current 
in coil C is not the same as that of the current in coil N, the 
magnetic field in coil M will have some effect in causing a de- 
flection. The demonstration for this is identical with that given 
in Article 122 concerning the electrodynamometer type of power- 
factor meter. That is, the pointer will come to rest when ^ -|- 
fl = 0, where is the deflection and 6 the phase difference. 




Fio. 109. 



FREQUENCY INSTRUMENTS 147 

This expression also shows that <{> is constant so long as ^ remains 
constant, and (t> varies as 6 varies. Thus, when the frequencies 
of the two machines are different, 6 will be a varying quantity, 
and the pointer will rotate. 

134. Lincoln-type Synchroscope. — The Westinghouse Electric 
and Manufacturing Co. makes still another form of synchro- 
scope known as the Lincoln type. A diagram of the internal 
connections of this type is given in Fig. 109. The essential parts 
of the Lincoln type of synchroscope are a bipolar laminated field 
M, the winding of which is connected to the busbars, and thence 
to the machine in operation. On iron core D, which is mounted 
on a shaft in such a way that it can rotate freely, are wound two 
coils, B and C, at right angles to each other. These two coils 
are connected in a "split-phase" relation through a non-inductive 
resistance R, and an inductive reactance X to the incoming 
machine terminals. 

The theory of the operating principles of this form of synchro- 
scope is identical with that of the power-factor meter. Article 
122, and hence need not be repeated. Since the relation between 
the deflection of the pointer arid phase difference is given by <^ + 
^ = 0, it can easily be shown that the angular speed of the pointer 
is proportional to the difference in the frequencies of the two 
machines. If the two currents start in phase but have fre- 
quencies /i and /2 after an interval of time t, they will be out of 
phase by 

e = 2Tfit - 2TrU 

Hence <^ = — 2ir^(fi — /2) 
or - = CO = — 2t(/i — /2) ; -. or w is the speed of rotation of 

the poinL. 



CHAPTER XII 



RECORDING OR GRAPHIC METERS 

136. Introduction.^By recording meter is meant an instru- 
ment which makes a continuous record, on a properly ruled chart, 
showing the instantaneous values as well as fluctuations of a 
quantity whose magnitude changes with time. Quantities 
whose instantaneous values as well as fluctuations lend them- 
selves to such a record are current, voltage, power, power-factor, 
and frequency, or in fact, any quantity whose instantaneous value 
may be given by an indicating instrument. 

Nearly all electricaUy operated apparatus and machinery 
requires, for eSicient operation, either constant potential or 
constant current. Thus the ordinary carbon filament lamp will 
change about 25 per cent in candlepower with a 5 per cent 
fluctuation of voltage. A knowledge of the fluctuations in elec- 
trical quantities is thus of great importance. This information is 
most readily obtained by the aid of recording, or graphic meters. 
These meters may be roughly divided into two general classes — 
direct-acting, and relay. 

136. Direct-acting. — It is very evident that from purely 
theoretical considerations a recording meter can be made by 
attaching a pencil or pen to the pointer of most of the indicating 
instruments so far discussed, and also attaching a properly 
graduated chart, moved by clockwork, upon which the pen or 
pencil can trace a line. 

Simple as such an arrangement appears, it is by no means 
easily carried out in practice. The chief practical difficulty is 
the elimination of pen friction. The friction of the pen is con- 
siderable and, to overcome this, considerable force must be 
exerted by the movement. This necessitates an expenditure of 
additional energy, else the accuracy of the instrument is decreased. 
The pen must also contain a large quantity of ink, enough at 
least for several days' use. As the ink is used up, the weight at 
the end of the pen varies. The pen must be so designed as to be 
filled easily and the ink must not be spilled in the event of sudden 
movements of the pointer. 



RECORDING OR GRAPHIC METERS 



149 



The main difficulties or drawbacks to most of these meters may 
be classed as follows: 

1. The attention required in winding the clock, changing the 
paper, and filling the pen. 

2. The inaccuracy in readings occasioned by the friction of 
the pen. 





3. The increased conauniption of energy to overcome the ef- 
fect of friction. 

4. On account of the friction and weight of pen, the instrument 
is liable to lack sensitiveness. 

137. Bristol Recording Instruments. — One of the oldeet and 
simplest forma of direct-acting grapliic meters is that of the 
Bristol Co. The ammeters of this company make use of the 
electromagnetic principle for their operation, while the voltmetere 



150 ELECTRICAL METERS 

and wattmeters operate on the Kelvin balance or eiectrodyna- 
mo meter principle. Fig. 110 shows the construction of a high- 
current capacity ammeter. The current coil is stationary, being 
attached to the back of the instrument. The moving element 
consists of a combination of disk armature mounted on a non- 




magnetic shaft extending through the current solenoid. Both 
ends of the shaft are supported upon vertical steel springs. 

When current flows through the current coil the armature is 
attracted toward the stationary coil. The motion of the arma- 
ture, which is proportional to the current) is opposed by the 
vertical knife-edge springa. The pen arm is attached directly 
to one of these springs. It is clear that the motion of the pen 



RECORDING OR GRAPHIC METERS 151 

is many times that of the disk armature. In another form tho 
pen is mounted on a knife edge below the axis of the coil. The 
pen is actuated by tho iron core as shown in Fig. 111. By 
means of such a device the motion of the pen is multiplied. 
There are no jewels, permanent magnets, make-and-break 
contacts, or spiral control springs. Tho sensitiveness of the 
meter is mainly determined by the friction of the pen on the 
paper. 




Where current rapidly fluctuates it is advisable to have some 
damping device. In this particular case this is secured by 
attaching one end of an arm to the disk armature shown at the 
left of the coil and the other end to a vane which is submerged in 
oil in the box above the coil. 

Since the voltmeter and wattmeter both operate on the same 
principle an explanation of one will be sufficient. 



152 



ELECTRICAL METERS 



Fig, 111 shows the construction of a wattmeter. The current 
coil ia stationary, while the voltage coil is mounted upon a shaft 
the ends of which rest upon the knife edges of the spring supports. 
The terminals of the voltage coil are connected to the positive 
and negative conductors, ant! the magnetic effect of the current 
through this coil of high resistance will be dependent upon the 
voltage, while the magnetic effect of the main current through the 
current coil which ia of low roaiatance, will depend upon the 




number of amperes passing. The mutual attraction of the coila 
will be the product of these magnetic forces and proportional to 
the number of watts. The marking arm is attached directly to 
the knife-edge supports of the movable coil and partakes of its 
motion. One of the knife-edge supports is made with a double 
bearing. By this means the motion of the movable coil ia 
multiplied, permitting the location of the voltage coil near the 
current coil. Such a construction makes it possible to use an 
evenly divided scale on alternating-current instruments aa the 



RECORDING OR GRAPHIC METERS 



153 



magnetic field is quite constant over the short distance that the 
coil moves. 

The construction of the voltmeter is in principle the same as 
that of the wattmeter. The voltage coil is divided, one part being 
rigidly attached to the meter frame, and the other part is mounted 
in the same way as the voltage coil of the wattmeter. The 
graduations on the dial are, of course, in volts instead of watts. 
Fig. 112 shows a Bristol recording voltmeter. 

In the beginning of this article it was stated that a recording 
meter could be made by attaching a pencil or pen to the pointer 
of an indicating instrument. The serious difficulty encountered 




Pig. 114. 



in making a graphic meter in this way lay in the excessive friction 
introduced. This difhculty has, however, been overcome by 
the simple process of having the pointer moved in front of a chart 
against which it is momentarily pressed by a lever arm actuated 
by a clock. Between contacts the pointer is free to awing just 
as in any indicating instrument. The intervals between successive 
impressions can bo made as short or long as desired. 

The instruments of this type as manufactured by the Bristol 
Co, employ two types of recording mechanism. In one typo 
the record is made on a smoked surface. Every time the pointer 
is pressed against the chart a white dot is left. If the intervals 



154 



ELECTRICAL METERS 



between the impressions are brief, and if tlie quantity being re- 
corded does not fluctuate too rapidly, tlie dots make a continuous 
line. To make the record permanent, the charts after use are 
dipped into a solution of shellac which quickly dries and prevents 
the rubbing off of the smoke. 

In the other type of recording mechanism, to the end of the 
pointer is attached a small capillary tube, and the lever arm is a 
curved ink pad which is supported in front of the chart in a plane 
parallel to its surface. At regular intervals the ink pad is auto- 
matically pressed against the capillary tube which is thus forced 




FiQ. 115. 

against the chart making an ink mark. The capillary tube is 
supplied with ink every time it comes into contact with the ink 
pad. Figs. 113 and 114 show the miUiammeter of this type. 
138. General Electric Recording Meters. — Another form of 
the direct-acting type of recording meters is that made by the 
General Electric Co. The appearance of a polyphase watt- 
meter with cover removed, is shown in Fig. 115. The movable 
element of an ammeter ia shown in Fig. 116, by the aid of which 
the operation of the instrument will be most readily understood. 



RECORDING OR GRAPHIC METERS 



155 



The two fixed coila AA are connected in series with each other 
and with the line. The current in these coils sets up a magnetic 
field which acting on the iron armature B produces a turning 
moment on the shaft D. The consequent movement, which is 
opposed by the spiral springs E, is transmitted through the 
pen-arm supporting frame G to pen arm H. The resulting mo- 
tion of the pen K traces on the chart L a curve whose distances 
from a zero line are proportional to the current. As shown in 
Fig. 115, the motion of the pen is restricted to a straight line, 




Via. 116. 

and hence the chart may be ruled in rectangular coordinates, 
which is an advantage in many respects. 

The movable element is suspended from the top support by 
means of a steel piano wire. The lower end of the shaft D is 
accurately centered by a small steel pivot passing through a 
sapphire jewel. The friction due to supports is thus nearly 
eliminated. 

The comparatively heavy, weight of the movable element, 
including the pen, necessitates a strong torque to give sufficient 
sensitiveness. 

The pen, a cut of which is shown in Fig. 117, holds enough ink 
to operate one week without refilling. The pen depends for 
its operation upon capillary action. The point coiuiBtB ot an 



156 



ELECTRICAL METERS 



iridium tube of very small bore, hard, durable, non-corroaive, 
and capable of receiving a high polish. This point is sealed 
into the end of a very small glass tube which in turn is placed 
inside a larger glass tube. The lower end of the small capillary 
tube is submerged in ink, which is carried to the point by capillary 
attraction. 

The record is made on a band of specially ruled paper which 
is fed at the rate of 3 in. per hour by 
means of clockwork. 

Damping. — To prevent undue swinging 
of the pen, its motion is damped by 
means of an aluminum disk rotating be- 
tween the poles of permanent magnets. 
140. General Electric Recording Volt- 
meters and Wattmeters. — In so far as 
^"'- '!"■ the recording device is concerned, the 

voltmeters and wattmeters of the General 
Electric Co. are practically identical with the ammeter. 

The voltmeters and wattmeters operate on the dynamometer 
principle, employing fixed and movable coils. This principle has 
already been fully explained. 

141. Esterline Graphic Meters. — Direct-acting graphic meters 
are also manufactured by the Esterline Co. The direct-current 
t are of the permanent-magnet movable-coil, or as it is 





Fig, lis. 



commonly called, D'Arsonval type. The alternating meters are 
of the dynamometer type. 

The movement of a direct-current ammeter is shown in Fig. 
118. The large permanent magnet ensures a strong magnetic 
field with a consequent heavy torque. 

The writing mechanism consists of a stationary ink reservoii 



RECORDING OR GRAPHIC METERS 

attached to the meter element near the upper bearing, and a 
metal tube fitted with a capillary glass pen at the outer end. One 
end of the pen is bent down aud dips into the ink reservoir. The 
intake is flexibly supported on pivots carried by another arm 
attached to the shaft. An adjustable counterweight is fitted 
to the back end of the tube by means of which the pen can be 
balanced so as to give a light uniform pressure on the paper. 

Damjring. — The movable coil is wound on a metal frame in 
which eddy currents are induced as it moves in the magnetic 

i 



■i^fr 



Fig. 119. 

field. The reaction between these eddy currents and the 
magnetic field effectively damps the motion of the pen. 

The motion of the pen of the alternating-current meters ia 
damped by a vane which is attached to the lower end of the 
movable element, Fig. 119, and which moves in a cup of oil. 
The meter element used in wattmeters and alternating-current 
ammeters and voltmeters is shown in Fig. 120. 



158 



ELECTRICAL METERS 



142. Relay Type of Recording Meters. — Theobjectionaenumer 

ated at the beginning of this cliapter against recording meters 
are, to some extent, ehminated in meters operated on the relay 
principle. 

In this type of meter, the moving element of the meter proper 
operates merely a set of contacts, which close an auxiliary circuit. 
This auxiliary circuit energizes the solenoids which operate the 
pen. A comparatively large amount of energy is not objection- 
able in this case nor does friction in any way impair the accuracy 
and sensitiveness of the instrument. 

The clock mechanism which moves the paper is made electric- 
ally self-winding and does not require attention. The recording 
pen is made to move across the paper in a straight line, and the 
record is obtained on a continuous sheet of paper ruled with 
rectangular coordinates. 

143. Principles of Operation.^ — A complete set of recording 
instruments embodying these features is built by the Westing- 
house Electric and Manufacturing Co. The voltmeters, alter- 
nating-current ammeters, wattmeters, and frequency meters, 
operate on the electro dynamo meter or Kelvin balance principle. 
The operating principle of the power-factor meter is that of the 
magnetic vane or movable iron core. The measuring elements 
of the direct-current ammeters operate on the principle of the 
permanent-magnet moving-coil type. In order to diminish the 
influence of the earth's or other external magnetic field, two coils, 
astatically arranged, are pivoted within the magnetic fields of 
two permanent magnets. 

144. Construction, — The "Westinghouse recording voltmeter, 
with cover removed, is shown in Fig. 121. The electrically 
operated measuring clement is shown in the upper part of the 
cut. The similarity between the Kelvin balance and this is at 
once evident. 

A schematic diagram of the connections is shown in Fig. 122, 
which shows quite clearly the manner in which the meter oper- 
ates. The fixed coils A, B, C, D, and the two movable coils E 
and F are connected in series in the same manner as those of the 
Kelvin balance. The movable coil E is provided with a relay 
contact /, located between the stationary relay contacts H and 
/ of the solenoid circuits of the recording element. 

The recording element comprises the pen-actuating solenoids 
K and L, their iron plungers K' and L', which are supported by 



RECORDING OR GRAPHIC METERS 



159 



the T-shaped lever arm M, pivoted at N; the pen arm ia con- 
nected to M by pin bearing P and provided at the upper end with 
a pin R, which moves in the stationary guide slot V; and the 
recording pen S, arranged to pass across a suitable record paper 
T moved by clockwork not shown in the diagram. 

The control .spring consists of the helical spring U, mechan- 
ically connecting the movable-coO system of the meter element 
with the movable pivoted supporting arm M of the recording 
element. 




The solenoid coils K and L are connected to the stationary 
relay contacts H and /, respectively, as shown, with their junc- 
tion brought out to binding post No, 2. The contact J of the 
movable-coil system of the meter element is connected to binding 
post No. 1. 

Leads from the control circuit are brought to binding posts 
Nos. 1 and 2, and leads from the circuit to be metered are brought 
to binding posts Noa. 3 and 4. 

lis. Operatioa. — The measuring coils are wound in such a 
direction that when the current in them increases, coils E and 
F are attracted by coils B and C and repelled by coils A and D 



160 



ELECTRICAL METERS 



respectively. This attraction will close the relay contact J 
on the solenoid terminal /, thus closing the recording circuit 
through solenoid L, energizing it and causing it to pull the 
plunger L' downward. The downward motion of V rotates 
the T-arm M about the pivot A''. This movement of M moves 
the pen toward the right across the chart. 

The downward motion of U will continue until the tension of 
spring U is just sufficient to counteract the attraction and repul- 
sion between fixed and movable coils. When the torque of the 




movable-coil Bysteni is balanced by the controlling spring, the 
contacts / and J are pulled apart, opening the solenoid circuit. 
The dimensions and weights of the various parts of the meter 
and the control spring are so porportioned that the entire moving 
system, including solenoids, pen-actuating arms, and measuring 
coils, remains stationary in the position occupied when the sole- 
noid circuit is broken. In the meantime, the clock continues 
to move the record paper forward, thereby causing the stationary 
pen to draw a line lengthwise on the chart. This line represents 
the quantity which is being metered. 



RECORDING OR GRAPHIC METERS 161 

If the quantity being metered rises, the contact J is again 
forced down against the contact /, and the entire operation 
abeady described is repeated until the increased tension of the 
control spring U again balances the increased torque of the mov- 
ing coils and opens the solenoid circuit. The recording system 
will then remain stationary until another change takes place in 
the current in the measuring coils. 

Where the quantity measured decreases in value, the electro- 
dynamic torque decreases and control spring U depresses the 
coil spring F, bringing contact J against contact H. The diagram 
clearly shows that this operation opens the circuit of solenoid L, 
but closes the control circuit through K. The electromagnetic 
effect of the current in K pulls K^ downward, thus turning the sup- 
porting arm M to the left and causing the pen arm to move the 
pen toward zero or minimum scale value. This movement con- 
tinues until the arm M has been suflSciently tilted to relieve the 
tension in the spring U, thus restoring the balance between the 
actuating forces of the meter element and the spring, causing the 
contact J to leave the contact H and breaking the circuit through 
the solenoid K. Thus any variations in the quantity measured 
cause the contact J to move up or down, making or breaking the 
circuit through either one or the other of the pen-actuating sole- 
noids. The corresponding oscillating motion of the pen, com- 
bined with the uniform motion of the clock-driven record paper, 
results in the drawing of a line, the distances of which from the 
zero line represent the magnitude of the quantity in the metered 
circuit. 

Damping. — The motions of all the moving parts of the meter 
and recording elements are rendered dead beat by means of 
suitably arranged pistons working in glycerine dashpots. The 
movements of the solenoid plungers are damped by the action 
of pistons attached to their lower ends and working in dashpots 
located below and partly within the solenoid coils. One of these 
is shown at B, Fig. 121. The action of the pistons relieves the 
plungers of excess momentum, thus preventing them from over- 
shooting and hunting. The magnitude of this control can be 
readily varied by changing an adjustable opening in the washers 
located just below the pistons. Quick pen action is readily 
obtained by increasing the size of the opening, or by using a light 
grade of oil, while the use of a heavy grade of oil will give extreme 
slowness of action on badly fluctuating loads. 



162 



ELKCTRICAL METERS 



will be found most aatisfautorj' to have tlie pen travel across the 
paper in from 15 to 20 sec. 

In all meterH except iKiwer-factor meters, a piston working in 
the daahpot shown at C, Fig. 121, damps the motion of the mov- 
able coils of the meter element, thereby preventing the movable 
contact from vibrating against the stationary relay contacts. 

146. Sensibility. — The sensibility of the meter may be readily 
controlled by varying the distance between the stationary relay 
contacts. With the contacts adjusted close together, the line 
drawn on a rapidly fluctuating load will be very irregular, A 
more regular curve can be obtained, however, by increasing the 
distance between the stationary contacts. 

147. Westinghouse Recording Ammeters, Voltmeters, and 
Wattmeters, — The foregoing principles are applied to both 
alternating-current and direct-current voltmeters and wattmeters 
and to alternating-current ammeters. The only difference 
being in the character of the windings. The fixed and movable 
windings of the voltmeters and ammeters are connected in series. 
The voltmeter windings are of fine wire and those of the ammeters 
are of wire large enough to carry 5 amp. The range of the instru- 
ments may be changed by the use of multipliers and shunts on 
direct-current circuits, and voltage and current transformers on 
alternating- current circuits. The single-phase wattmeters have 
fixed coils identical with those of alternating-current ammeters, 
and are operated from current transformers. The movable, or 
voltage coils, are wound with fine wire and connected in series 
with each other and in series with an external resistance. The 
direct-current wattmeters are similar to alternating-current 
wattmeters, except that the current coils are designed to carry the 
total current. The direct-current ammeters differ in that no 
fixed coils are used. In place of fixed coils two permanent mag- 
nets are used. The movable coils and permanent magnets are 
arranged astatically. 

148. Westinghouse Recording Frequency Meters. — These 
meters are of the same type of construction as voltmeters, except 
that the coils are wound differentially in two circuits, one circuit 
being connected in series with a non-inductive resistance and the 
other with an inductive reactance. The two circuits are then 
connected in parallel across the line, so that any variation in the 
frequency will change the current in the inductive circuit, and 
hence the torque on the movable coil will change with the fre- 



RECORDING OR GRAPHIC METERS 



163 



queiicy. The recording element operates iti the same manner aa 
that of the other meters. 

149. Westingbouse Recording Power -factor Meter. — The con- 
struction of the relay type of graphic power-factor meter is 
shown in Fig. 123, It is plain that the recording element is 
identical with that of the other meters. The meter element is 
the same aa that of the Weatinghouse indicating power-factor 
meter, explained in the previous chapter. The only novel feature 
is the manner in which the circuit through the controlling sole- 




FiG. 123. 



noids is closed and opened. This feature can readily be explained 
by reference to Fig. 124. To the shaft of the iron armature G is 
connected a light arm which plays between contacts H and I on 
the slotted arm. The contact arm takes the place of the pointer 
on the indicating power-factor, meter. No controlling springs 
are employed. 

150. Operation. — The direction in which the light arm moves 
is determined by the power-factor. If the phase difference 
between the voltage in coils A-B and current in coil C is such 
that the light arm makes contact with I the recording circuit is 
closed through solenoid L. The resultant pull on plunger L' 
will move pen, pen arm, and arm U to the right. This motion 



164 



ELECTRICAL METERS 



will continue until the arm has moved a distance which on the 
indicating meter would represent the phase difference. The 
final position of pen S will then be determined by the power- 
factor, and any change in the power-factor will cause the posi- 
tion of the pen to change. The line traced will thus represent 
the power-factor. 




161. Sangamo Graphic Meters. — The operating element of 
the Sangamo graphic meter consists of two motor movements 
whose principles of operation are the same as those of the mercury 
watt-hour meter to be explained in later. As shown in Pigs. 
125 and 126 the movable elements are placed at the back of the 
instrument and insulated from each other. 

The actuating force is obtained by the reaction of the current 
flowing through the mercury, chamber and the copper-disk 



RECORDING OR GRAPHIC METERS 



165 



armature, and the magnetic field produced by a current flowing 
through the coils oa the magnet yokes, Fig, 126. In the 
direct-current meter, the yokes carry shunt coils, while in the 
alternating-current wattmeter, series coils are carried on these 
yokes. The armature current for the operation of the alternating- 
current meter is obtained from a suitable transformer whose pri- 
mary is connected across the line at 100 or 220 volts, and whose 
secondary, of one or two turns, supplies a comparatively large 
current to the armature. 

The direct-current meters may be used on either the two- or 
three-wire circuits without change; while the alternating-current 




instruments may be used on either the two-wire or three-wire 
single-phase, or polyphase circuits. 

While Figs. 125 and 128 are of the wattmeter, the same gen- 
eral principles of construction and operation are applied to 
directrcurrent and alternating-current ammeters, and to alternat- 
ing-current voltmeters. The direct-current voltmeter movement 
consists of two d'Arsonval elements operating on mercury 
bearings, so that an identical mechanical structure and the same 
general arrangement of the motor elements are preserved. 

The two movable arms are connected by a cross link aa shown 
in Fig. 125, moving on jewel bearings in each of the arms. On 
this cross link are mounted the pen and the ink reservoir. The 
pen is very light and terminates in a capillary tip. As the mov- 



16« 



ELECTRICAL METERS 



able eystem passes across the chart, the position of the capillary 
tube, with respect to the ink well, changes, so that the position 
of the pen with reference to the chart remains constant. By this 
construction the pen maintains constant pressure against the 
chart, irrespective of the amount of ink in the reservoir. The 
construction also permits the use of rectangularly ruled charts. 

162. Rigbt-line Pen Movement. — To obtain accurate records 
on charts having rectangular ruling, the pen must move in a 
straight line at right angles to the motion of the paper. This 
right-line, or parallel motion, is obtained by making PN = 
PS = PR, Fig. 122. fl is a pin rigidly attached to the arm 
and sliding in slot V. With such an arrangement, the pen S 




moves in a straight line perpendicular to a line through R and 
N, In the older form of these instruments the pin R was fixed 
and the slot was in the pen arm 0. The arm PR thus varied 
in length and the motion of the pen was only approximately a 
straight line. 

162a. Advantages and Disadvantage. The chief advantage of 
a recording meter lies in the fact that it makes a continuous 
record of the value of and variations in the electrical quantity. 
An examination of the record may thus be made at any time. 
This examination may be the means of detecting faults or dis- 
closing characteristics which need improvement, and which would 
otherwise be overlooked. 

The disadvantage in their use is lack of sensitiveness, which 



RECORDING OR GRAPHIC METERS 167 

defect is due mainly to the weight and friction of the pen. The 
objections to the form of pen used on the Bristol meter are the 
evaporation of the ink due to the exposure of a large surface, and 
the small capacity of the V-shaped trough. The effect of the pen 
friction, which is a variable quantity, impairs the accuracy of 
the record. The weight of the pens on the General Electric and 
Westinghouse meters makes accurate record impossible when 
the quantity fluctuates rapidly. Then, since the ink is fed by 
capillary action, the capillary tube will, sooner or later, become 
clogged, and it is cleaned with considerable diflSculty. 

Recording voltmeters are always more difficult to employ 
satisfactorily than the other instruments, because they are of 
very little use imless they are both sensitive to small changes of 
voltage and also remain in accurate calibration to within 1 volt 
or less. 

The records of such instruments are often useful not merely 
for indicating the range of fluctuation of voltage in a distributing 
system, but also for indicating the nature of the fluctuations, as 
to suddenness, protractedness, and frequency. The cause of 
the fluctuations can often be determined from an examination of 
the charts with reference to these points of behavior, with reason- 
able expectation either of removing or of minimizing such as may 
be serious. The degree of damping is an important considera- 
tion in the operation of the recording instruments. They 
should be strictly aperiodic as far as possible, neither overshooting 
the mark on the one hand, nor undershooting and lacking in 
promptitude on the other. 



18 



CHAPTER XIII 

INTEGRATING METERS, WATT-HOUR METERS 

163. Introduction. — Integrating meters are instruments that 
register the sum of the electric quantity measiu'ed over a period 
of time. Thus if the intensity or strength of a quantity varies 
with time, the registration of an integrating meter will be pro- 
portional to the sum of the several products formed by multi- 
plying together the quantity at a given time by the time during 
which it remained constalit. For instance, if 2i, /2, and 1 3 are 
currents in a circuit for times Ti, 2^2, and Tz respectively, the 
integrating meter will register a quantity which is proportional 
to IiTi + I2T2 + IsTs. It is thus clear that the element of time, 
as well as the electrical quantity determines the registration of 
the meter. In practice it is necessary to know the electrical 
energy and quantity of electricity that has been utilized, and 
accordingly we have watt-hour meters and ampere-hour meters. 

154. Watt-hour Meters. — The definition of the unit of energy, 
the watt-hour, is given in Article 25. An instrument whose 
registration is proportional to the energy impressed or utilized, 
is called a watt-hour meter, often incorrectly called ''recording 
wattmeter" or simply ''wattmeter." It is gratifying to note 
that makers have recognized this confusion in names and all 
of them now call the meter by its true name. 

The distinction between a watt-hour meter and other meters 
such as wattmeters, both indicating and recording, is very clear, 
and the reader should keep this distinction in mind. The indi- 
cation or registration of a watt-hour meter is determined by 
the energy that has passed in a given time, while the indication 
of a wattmeter is determined by the rate at which that energy is 
passing. 

An analysis of the principles of operation of watt-hour meters 
will show that they may be classed as electrodynamometer and 
induction types. The former type is usually used only on direct- 
current circuits, although instruments of this type may be used 
on alternating-current circuits. The induction type can be used 
on alternating-current circuits only. 
19 169 



170 



ELECTRICAL METERS 



165. Electrodjmamometer Type (without iron). — The diagram 
of Fig. 127 shows the essential features of this type of meter. 
The similarity between the essential parts of this type of meter 
and those of an electrodynamo meter is very evident. The 
electrodynamometer contains fixed and movable coila. The 
watt-hour meter likewise contains fixed and movable coils. 
The stationary, or scries winding, consists of two coils FF 
through which all or a proportional part of the line current 
passes. The movable coil, or armature A, consists of several 




coils of fine wire and is connected in shunt with the load through 
the resistance R, and compensating coil C, whose function will 
be explained later. The main difference between the electro- 
dynamometer and this type of watt-hour meter consists in the 
permissible rotation of the movable coil. The motion of the 
movable coil of an electrodynamometer is opposed by a spiral 
spring, and the coil is thus restricted in its rotation. On the 
other hand, the movable coils of the watt-hour meter are free 
to rotate continuously. This is accomplished by mounting 
upon the shaft a commutator to which the ends of the several 



WATT-HOUR METERS 171 

coils are connected. Current is led into the armature coils by 
means of brushes which rest upon the commutator. For this 
reason this type of meter is usually called the commutating type 
to distinguish it from another form which does not require a 
commutator. The movable system is then mounted between 
supports, the ends of the shaft resting on jewels. On account 
of the manner in which it is connected to the circuit, this type of 
watt-hour meter is sometimes compared with the shunt motor. 
This similarity is very evident. There, is one distinction, how- 
ever, and that is the fact that neither the field nor armature of 
the watt-hoiu* meter contains iron. It has been shown that the 
attraction between the stationary and movable coils of the 
electrodynamometer is proportional to the product of the cur- 
rents in the two coils. The torque causing the deflection is thus 
proportional to the product of these currents. The torque on 
the armature of a watt-hour meter is likewise proportional to the 
product of currents in armature and field coils. The current in 
the armature is proportional to the voltage across load terminals, 
and the current through field coils is equal, or proportional, to 
the load current; hence, the torque on the armature is propor- 
tional to the product of the load voltage and current. That is, 
the torque is proportional to the power. 

166, Counter-torque. — In order that the driving torque may re- 
main proportional to the power, there must be present a counter- 
torque whose value increases and decreases with the load. Such 
a counter-torque is obtained by mounting upon the armature 
shaft a d isk of aluminum which rotates between the poles of two 
permane nt magnets. These magnets and the disk are shown in 
Pig. 128, which is a view of the Westinghouse direct-current watt- 
hour meter. The development of the retarding torque and its 
relation to the driving torque is as follows: The magnetic flux be- 
tween the poles of the permanent magnets is constant, and 
hence the eddy currents induced in the disk, as it rotates, are 
proportional to the speed of the disk. The counter-torque is 
proportional to the product of the eddy ciu'rents and magnetic 
flux between the magnet poles. Since the currents are propor- 
tional to the speed, the counter-torque must be proportional to 
the speed. The counter-torque thus increases and decreases 
with the speed, that is, with the direct torque on the armatiu'e. 
When the load increases, the speed increases until the counter- 
torque just balances the torque on the armatm-e. When the 



172 



ELECTRICAL METERS 



load decreases, the speed decreases until the two torques are 
again equal. Thus, neglecting friction, the speed of the arma- 
ture is proportional to the load, and the meter should repster 
' ooirectly at all loads. 




Fia. 123. 

157. Summation of Power. — The torque acting upon the rotat- 
ing element at each instant is proportional to the power being 
consumed by the load at that instant. For simplicity, assume 
the load to consist of a fixed number of incandescent lamps, 
and that the voltage E is constant. Under these conditions, the 
power will be constant and equal to IE. The driving torque is 
likewise constant and equal to KIE. Since the counter-torque 
increases with the speed, the driving torque will increase the 
speed until the two torques just balance each other. When 



WATT-HOUR METERS 



thiB condition is reached, the speed remains constant, that is, 
the disk makes the same number of rotations each minute. 



Under these 
given time i 
write 

but 



conditions the number of rotations of the disk in a 
j strictly proportional to the time. We may thus 



Torque X time = 
Torque X time = 



work 
KIE X tim 



It has already been shown that IE X time is electrical energy, 
hence the torque X time is proportional to electrical energy pass- 
ing through the meter. The 
product of the torque by the 
time evidently determines the 
total number of rotiitioiis of 
the disk, hence 

Kn — electrical energy. 
The total number of rotations 
n of the disk is then a measure 
of the energy transmitted to 
the metered circuit. The num- 
ber of rotations of the disk or 
armature is transmitted 
through a suitable train of 
gears to the dials. The 
operation of the registering 
mechanism is quite simple 
and needs little explanation. ., .^o 

The upper end of the shaft is 

finished with a worm, or small gear wheel, the teeth of which 
mesh with the first of a train of gears. The number of teeth 
on the gears is such that when the one operating the pointer 
on the first dial has made ten revolutions, the one operating the 
second has made only one revolution, etc. The dials are 
graduated in units of electrical energy such as the watt-hour or 
the kilowatt-hour. 

The speed of the meter is usually adjusted so as to make the 
meter direct-reading. This is taken care of in the design of the 
instrument and by adjusting the position of the permanent 
magnets. 

The general principles here explained are applied in the West- 
inghouse, General Electric and Duncan, Columbia, and other 




174 



ELECTRICAL METERS 



(iirect-curient meters, in- 
terior views of which are 
shown in Figs. 128, 129, 
KiO and 131. 

157a. Large Current 
Capacity Watt-hoxir Me- 
ters. — A large-capacity 
series-type watt-hour me- 
ter for switchboard 
mounting is manufactured 
by the General Electric 
Co. The movable ele- 
ment of this meter con- 
sists of two spherically 
wound armatures 
mounted on the same 
132 and 133. The field winding 
consists of four circular coils placed as near each other 
as possible, one on either side of each armature. The 
armatures and field coils are so connected that the cuirentB 




shaft 




WATT-HOUR METERS 175 

in one set flow in a direction opposite to that in the other set; 
that is, they arc connected astatically. By such an arrange- 
ment the effect of a stray magnetic field upon one armature or 



element is neutralized by its effect upon the other element. 

The damping magnets are also arranged astatically and for 
further protection are enclosed in a laminated soft-steel case. 




An interesting feature of the construction shown in Fig. 132 
IS the gravity control for brush tension. A counterweight 
C composed of two knurled nuts is mounted on a lever to 
the other end of which the brushes are attached. The lise of 



176 



ELECTRICAL METERS 



two nuts permits the locking of the couiifcorweight in any de- 
sired position, obviating any danger of change in tension due to 
vibration. 

Two types or models of those meters are manufactured. The 
difference between them consists in the construction of the field 
coils. In one the field coils are circular and in the other they ' 
are of busbar type. The former is made in oapacitiea ranging 
from 50 to 1,500 amp., white the latter is made in capacities 
ranging from 2,000 to 10,000 amp. Both are made tor two- 




FlG, 134, 

or three-wire circuits and for potentials ranging from 100 to 
600 volts. A 2,000-amp. 500-volt meter is shown in Fig. 133. 
The series watt-hour meter is not well adapted for measuring 
energy on circuits carrying heavy currents. The main difficulty 
lies in the construction of the series coila. To meet these diffi- 
culties, several watt-hour meters of the shunted type have been 
placed on the market within the past few years. One of the 
latest forms of the shunted type is shown in Figs. 134 and 135, 
The construction of the meter is in general very similar to the 
series form, The field consists of four comparatively large 



WATT-HOUR METERS 



177 



coila of large conductors surrounding a rather elongated arma- 
ture. The conductors have to be very large in order that their 
resistance may be low enough to permit sufficient current to flow 
with only a small voltage drop across the shunt. Furthermore, 
in order that the magnetic field may be strong enough to give a 
relatively high torque, the field coils must contain many turns. 
The use of shunts introduces compUcations which result in 
variable errors. 




168. EUctrodyuamoineter Type (with iron).^ — There has lately 

been placed on the market a watt-hour meter which differs in 
Bome respects from those already discussed. This ia made by 
the Columbia Meter Co. 

The main difference between this form of Columbia direct- 
current watt-hour meter and other direct-current watt-hour 
meters lies in the design of armature or rotating clement. This 
difierence will be brought out more clearly by reference to Fig. 
136, which shows the rotating element of the Columbia instrument. 

The armature windings, as shown, are a group of six cylindrical 
coila arranged between two aluminum disks, close to the central 
shaft and parallel to it. 

Within each coil is a thin strip of sihcon steel whose ends are 
bent at right angles to the axis of the coil, and extend radially 



178 



KLECTRICAL METERS 



along the lower surfatie of the upper, and upper surface of the 
lower disk, These radial extensions are split so as to distribute 
the flux more uniformly around the circumference of the disk. 
The series winding consists of four coils arranged astatically. 
That is, the coils are connected in such a way as to cause the 
magnetic flux to flow through each element of a pair in opposite 
directions. By such an arrangement, the influence of a stray 
field on one coil is neutralized by its influence on the other coil of 
the pair. The |>ositions of the 
\:iL-i(iu3 parts of the meter are 
iiMwii in Fig. 137. 

Another characteristic diflference 
between the Columbia and other 
direct-current watt^hour meters is 
the use- of shunts, which use ia 
made jxissible by employing iron 
in the armature. The use of iron 
in the armature makes it possible 
to secure sufficient torque to 
operate the meter with a much 
smaller field current. Accordingly, 
they adjust all their meters so as 
to take exactly 5 amp. in the cur- 
rent coils at full load. 

169. Friction Compensation.— 
Fio. 130. rjo matter how carefully the 

meter is constructed, all friction 
cannot be eliminated. Some energy is thus always required 
for the operation of the meter. In a well-designed meter 
this amount of energy is very small, yet if some means 
are not provided for overcoming this frictional toi'que, the 
meter will not register on a very light load. With the 
introduction of high-efficiency incandescent lamps, the neces- 
sity for accurate compensation is much greater than previously. 
Nevertheless, the compensating torque should not be so great as 
to overcome excessive or unnecessary friction. It is usual to 
design the coil so that on about 5 per cent of full load the maxi- 
mum possible compensating torque will give an excessive speed 
of about 10 per cent. If the frictional torque is greater than this, 
the cause should be discovered and removed. 

The compensating torque is obtained by connecting a coil in 




WATT-HOUR METERS 



179 



seriee with the armature or voltage coil, the plane of the coil 
being parallel to the current, or series coil. Such a coil is shown 
at C, Fig. 127. The strength of the compensating torque can be 
adjusted in either one of two ways. In the General Electric, 
Westinghouse and new Duncan watt-hoitr meters the position of 
the compensating coi! with reference to the armature is changed 
until the proper degree of compensation is secured. The arrange- 
ment of the compensating coil of the Westinghouse meter ia shown 




Fi,), 137, 

in Fig. 128, where it is called friction compensation. By releasing 
the clamping screw B, the arm supporting the coil is released and 
may be moved up or down, nearer to or farther from the arma- 
ture, thus changing the torque it exerts. In the more recent 
Duncan model E Y^ watt-hour meter the fixed compensating 
coil has been replaced by a coil whose position is adjustable. 
This ia shown in Fig, 130. 

The Duncan Electric Manufacturing Co. formerly used a some- 
what different method of varying the torque. In the older Dun- 
can meters the compensating coil is firmly fixed within the front 



180 



ELECTRICAL METERS 



series coil, and the intensity of the compensating field is varied by 
changing the number of active turns on the coil. This is accom- 
plished by moving a amall contact lever either to the right or 
left, as the case demandsj over multipoint contacts. Fig. 138 
shows this compensating coil with the lever at its middle position. 
The Columbia Meter Co. uses in principle a hke method. 
The only difference is that the proper adjustment is obtained 
by changing the position of the hard-rubber plug with its enclosed 
brass spring bushing along the projecting terminals of a series of 
small-resistance coils visible to the right of the dial plate, Fig. 131. 
Changing the position of the plug changes the number of active 
turns and, hence, the compensating torque. 




Fig, 138. 

160. Creeping. — The armature circuit, when the meter is in 
service, is connected to the mains all the time. Thus, there is a 
current at all times through the armature. When the field due 
to the compensating coil is such as to furnish torque just sufficient 
to overcome the friction when the meter is installed where there is 
no vibration, it may creep when installed in a place subject to 
jar. The jarring reduces the friction of the bearings, and at the 
same time the armature is partially reheved of its weight while 
the vibration lasts. Under these circumstances the initial torque 
may be sufficient to cause the meter to revolve slowly. 

Another cause of a meter's creeping may be due to a higher 
voltage than that for which the meter was adjusted. If the com- 
pensating torque on a certain voltage is nearly great enough to 



WATT-HOUR METERS 181 

cause the meter to register on no load, an increase in voltage will 
increase the armature current and, since the compensating coil 
is in series with the armature, the compensating current will 
increase. The compensating torque, which is proportional to 
the product of the armature current and compensating current, 
will also increase. The two currents being the same, the com- 
pensating torque is then proportional to the square of the 
armature current. We may write this 

T = KP 

but 7=1 

where E is the electromotive force between mains and R the 

resistance of armature circuit, including compensating coil. 

Then 

E^ 
/^ = ^ and substituting for P, we get 

T =^,XE^ 

K and R both being constant, the expression shows that the 
compensating torque is proportional to the square of the voltage 
between mains. It is thus evident that a compensated meter cor- 
rect on light loads will register on no load when the voltage is 
raised. The average conditions in practice are met by adjusting 
the meter so that on light load it is from 1 to 2 per cent slow. 

161. Brushes. — Some of the chief objections to the commutator 
watt-hour meter are friction of brushes, sparking at the brushes 
when the commutator becomes oily or dirty, a change in speed 
due to improper position of brushes, and additional weight of 
moving parts due to commutator. The use of a commutator 
thus introduces difficulties which cannot be wholly eliminated, 
but their effects can only be minimized by careful design and 
construction. Brushes must therefore be made out of material 
whose elastic properties do not change with time. To meet this 
and other requirements, it is common practice to make the 
stems of the brushes out of phosphor-bronze wire or strips, and 
to provide the contact ends with silver tips. It has been found 
that brush friction is considerably reduced by making the tips 
round instead of flat. 

The pressure of the brushes upon the commutator is governed 



182 



ELECTRICAL METERS 



by either the tension of a spring or the force of gravity. Where 
spring control is used, the elasticity of the stem of the brush 
suppUea the necessary tension. Two typical devices of this kind 
are shown in Fig. 139 and 140, an examination of which will 
give an understanding of its operation. 

In the gravity method of control, uniform pressure is secured by 

attaching the brushes to one end of an arm which is pivoted 

and carries a counterweight at the other end. The distance of 

the counterweight from the fulcrum 

may be changed, thus changing the 

It'iision. 

162. The Commutator. — In order 
that the frictional torque may be 
reduced to a minimum, the commu- 
t ritor must be of very small diameter. 
The smallest diameter that can be 





successfully used on a 110- to 220-volt meter is about J/fo in. 
Por higher voltages the diameter of the commutator must be 
greater to permit of proper insulation. 

The commutator is usually made by forcmg a piece of silver 
tubing over a fiber bushing on the shaft. The tube is then sawed 
into the proper number of segments which are held in place by 
fiber or metal rings. The metal rings are, of course, insulated 
from the segments. It is customary to use silver for both the 
commutator segments and brush tips, because it is the cheapest 
metal that can be used which does not readily oxidize. The com- 
mutator of the Duncan shunted type is made of gold. Some 
makers use fiber to insulate the segments from each other, while 
others leave merely an air space. 



WATT-HOUR METERS 



183 



163. Aimature. — The distinctive characteristics of some meter 
armatures have already been briefly pointed out. The armatures 
of watt-hour meters without iron in their magnetic circuits are 
mainly of two forma, spherical and cylindrical. The spherical 
form permits of a more compact construction, thus minimizing 
the magnetic leakage and correspondingly increasing the torque; 
or, what amounts to the same thing, securing maximum torque 
with a given weight of armature and given energy consumption 
in armature and field. For the cylindrical form, the advantage 




is claimed that it can lie repaired m\ich more readily. The 
cylindrical form is shown in Fig, 141. 

The windings of both forms of armature are of the drum type. 
The coils of the spherical armature are usually wound upon a 
light fiber shell which is moimted directly upon the shaft, the 
coils being held in place by grooves pressed in the shell. The 
supports for the cylindrical armature are two light hardwood 
Bpiders firmly fastened to the shaft. This permits of a light and 
open construction which is conducive to good ventilation. 

The coils of the armature are wound with wire of pure copper 
and of smallest gage consistent with mechaaiccd strength, 



184 



ELECTRICAL METERS 



usually not larger than No. 40 B. & S. gage. Armatures wound 
for 110 to 220 volts have as a rule eight coils of 1,000 turns each 
connected to the eight segments of the commutator. The 
Columbia meter, howf^vcr, has only three coils which are con- 
nected to a three-segment commutator, Fig. 142. For voltages 
above 220 it is common practice to wind the armature with 16 
coils, and the commutator has a corresponding number of seg- 
ments. The main reason for this is to reduce the voltage between 
adjacent coils and commutator segments. 

The resistance of the armature coils and auxiliary resistance is 
so adjusted that practically the same current flows in the arma- 
ture of meters for different voltages. The armature resistance 
is practically the same in each case, but for the higher voltages 
additional resistance is placed in series. 



Busn ng 




riu 141 



FiQ. 114. 



164, Bearmgs.^Tho necessity for a very small frictional 
torque makes the proper design of the bearings of great impor- 
tance. The function of the top bearing is merely to hold the 
movable element centered, and ia therefore subject to very little 
pressure, and, consequently, very little friction. One form of top 
bearing is shown in Fig. 143. It consists of a steel pin fastened 
to a removable screw and projecting down into a bushing in a 
recess drilled in the shaft. The bottom of this recess is filled 
with billiard cloth, saturated with watch oil. A film of oil is 
maintained around the pin by capillary action. In another form 
of bearing the conditions are reversed. The pin is a part of the 
shaft and the recessed bushing projects from above downward. 
This form is shown in Fig. 144. 

Owing to its importance, by far the most attention has been 
devoted to the design of the lower bearing, which has now reached 



WATT-HOUR METERS 185 

a high degree of perfection. There are, in general, two forms of 
lower bearing. One form may be called pivot bearing and the 



A 




FiQ. 145. 

other ball bearing. Details of a typical pivot bearing are shown 
in Fig. 145. The pivot is not an integral part of the shaft, but 
is made separately and screwed 
into the lower end of the shaft or 
spindle. It will be observed that 
the bearing consists of a hollow 
screw with a heUcal spring. Sur- 
mounting the spring is a plug 
within the upper face of which is 
embedded the cupped jewel. 

The ball bearing is shown in 
Fig. 146. The lower end of the 
shaft, instead of ending in a con- 
icaJ pivot, has a cup-shaped jewel 
fixed in it. Another cup-shaped 
jewel is fixed in the upper face 
of the plug, and between these I 
jewels is a hardened steel ball. 
It is claimed that the ball bear- 
ing has the longer life. In so 
far as friction is concerned there 
is perhaps not much choice.^ 

166, Jewels. — Until recently it has been almost universal 
practice to use sapphire for the jewels. £Ixperience has demon- 




186 ELECTRICAL AfETERS 

stratod the inability of sapphire to withstand, for more than a 
comparatively short time, the grinding and hammering action 
of the pivot. The only material that is able to show permanently 
satisfactory performance is the diamond. The earliest diamond 
jewels were flat and required a stone ring to maintain the pivot 
in place, an arrangement which did not give complete satisfaction. 
Later experiments showed that it was possible to grind the dia- 
monds in the form of a cup, and jewels of this form require no 
guiding ring. The cupped diamond jewels are now used exten- 
sively for meter bearings. Experiments performed on meters 
with sapphire and diamond jewels show that a higher accuracy 
on light load was maintained by the meters with diamond 
bearings. 

166. Magnets. — A most important feature of the watt-hour 
meter is the permanent magnets, for upon their permanency 
depends to a great extent the performance of the meter. The 
necessity for magnets whose strength will remain constant can 
easily be appreciated when it is remembered that the retarding 
torque is proportional to the product of eddy currents in the disk 
by magnetic flux. The eddy currents at any given speed of disk 
are, however, proportional to magnetic flux, hence the retarding 
torque is proportional to the square of the magnetic flux, or in 
algebraic symbols, 

T = A'*=. 

It is thus very evident that a small change in * will have an 
important effect in changing the counter-torque and, indirectly, 
the registration of the meter. In this respect the manufacturers 
of first-class instruments take special precautions, and strive 
to produce magnets that will retain their strength indefinitely. 

167. Registering Mechanism. — A typical registering mechan- 
ism is shown in Fig. 147, This consists of dials, dial train, and 
reducing train. The dial and dial train of gears are not clearly 
shown; the reducing train, however, is. Great care is necessary 
in the manufacture of the various parts in order to eliminate all 
imperfections. The wheels are usually made of hard brass and 
gold-plated to prevent corrosion. The entire mechanism is 
ahgned by dowel pins and attached to the frame by screws. 

168. Electro dynamo meter Type on Alternating-current Cir- 
cuits. — Since the principles of operation of the commutator form 
of watt-hour meter without iron are the same as those of the olec- 



WATT-HOUR METERS 



187 



trodynamometer-tyj)e wattmeter, most of the theory of the latter 
instrument as given in Chapter X will hold with reference to 
the watt-hour meter. In the diacussion referred to, it was shown 
that the deflecting torque is proportional to the power when the 
voltage coil is non-inductive. This, however, is 3eldom the case 
and, hence, adjustments, termed lagging, must be made before 
the meter wiU register accurately on alternating-current clrcuita. 
It was shown in Chapter X that a wattmeter with an inductive- 
voltage circuit gave too high indications on circuits of low power- 
factor, and that on circuits where the current leads the pressure. 




the deflection under certain conditions would be negative. An 
clectrodynamoraeter wattmeter which has not been lagged is 
subject to exactly the same inaccuracies, viz., on inductive load 
the registration will be too high, and on a load such as an over- 
excited synchronous motor, it may run backward. This will be 
the case where a is greater than cos 0, a and 6 having the same 
significance as in Article 112. 

169. Lagging. — In order to avoid the foregoing errors it is 
necessary to adjust or modify the series circuit of the meter in 
such a way that the angle between the series current vector and 
the voltage vector shall be exactly the same as that between the 
armature current vector and the voltage vector on non-inductive 
load. This is accomplished by shunting a part of the series 
current through a non-inductive resistance. Under these condi- 
tions, the main current will divide inversely as the impedances of 
the two parallel circuits. Since the series winding is to some ex- 



188 



ELECTRICAL METERS 



tent inductive, the current in this will lag behind the current 
through the non-inductive shunt. The main current will then be 
the vector sum of these two components, and its angle of lag will 
be determined by the ratio of these components. Thus in Fig. 
148, let /i bo the current through the scries winding. Then if Bj 
and Xi are the aeries-coil resistance and inductance respectively, 
RiIl will be the resistance drop, and X,Il the reactance drop. 
The series current will be in phase with Rili; and the applied 
voltage and current through non-inductive shunt are in phase 
with OE. If Oil represents the series-current vector, and OI3 
the shunt-current vector; then 01 is the resultant, or main- 
current vector. The angle /J by which the aeries-circuit current 
lags behind 01 can evidently be changed by changing the ratio 
of Oil and Oh. These in turn depend upon the resistance of the 



Fig. 148. 



PiQ. 149. 



shunt circuit. In a properly lagged meter this angle ^ is made 
equal to the angle of lag between applied voltage and voltage- 
circuit current. 

170. Value of Shunt-circuit Resistance. — The value of the 
shunt-circuit resistance can be calculated if the resistances and 
inductances of the voltage and series circuits are known. Thus 
in Fig. 149 let 7i be the series current, and /j the shunted current, 
R, Ri and R-t are the resistances of the voltage, series, and shunt 
circuits respectively, and if X and A'l are the reactances of the 
voltage and series circuits, we may find R^ in terms of R, Ri, 
X, and Xi, as follows: 



taniS = 



but 
and 



I, + 1, erne 




K. 


(ft, 


' + X,')» 




X, 


'Ri 


■+Zi")>' 



WATT-HOUR METERS 189 

Then 

UXy. 



tan|3 = -(^+^^^)" 



J , I2R1 



/2X1 



The relation between 7i and Jj is given by 

Ii:I,::R» : (i2i« + X,«)^ 

whence 7» = fr (J?i' + -X:)**- 

Substituting for J2, we get 

iV2 



tan /3 = - 



/i (Bi^ + Xi^)^^ + ^ (iJi2 +Xi2)' 



This reduces to 



tan j8 = 



i2i -h 722 



But the angle of lag of current in the voltage circuit is given by 
the relation 

tan a = p- and if a is to equal P 
X Xi 



Whence R2 = 



B Bi -{" B2 
RX\ — XBi 



X 



In practice, R is large, being about 1,200 ohms, while fii, X, and 
Xi are comparatively small. Hence, it is evident that JB2 will 
be large and that only a small per cent, of the line current will 
pass through the shunt. No account is taken of the capacity 
of the armature, since the inductance usually predominates. 
Likewise, the efiFect of mutual inductance of the coils, is so small 
that in practice it is negligible. 

171. Three-wire Direct-current Meters. — For measuring 
energy on three-wire direct-current circuits, one three-wire, or 
two two-wire meters may be used. A three-wire meter differs 
very little from a two-wire meter in construction, and in principle 



190 



ELECTRICAL METERS 



of operation not at all. In meters intended for three-wire cir- 
cuits the two series coils are distinct; the ends of each being 
brought out to terminals which, when in service, are connected 
to the load circuits as indicated in Fig, 150, The voltage coil 
may be connected across mains 1 and 3, or between either 1 or 3 
and neutral 2. 

When the connection is as indicated in Fig. 150, the torque 
exerted upon the armature is equal to the aura of the torques 
exerted by coils A and B separately. When the voltage between 
mains 1 and 2 equals that between mains 2 and 3, the torque 
exerted by coil A ia 

T, = KJiE 




and the torque exerted by coil B is 

Ti = KJiE. 

Since the two current coils for accurate registration should exert 
the same torque under like conditions, Ki = Kg and the total 
torque equals 

T = Tt+ Ti = K(h + h)E 

which ia evidently proportional to the load. 

If, however, the load is unbalanced to such an extent that the 
voltages are no longer equal, then the torques cease to have the 



WATT'HOUR METERS 191 

same ratio to the load. Let Ei, E2, Ii and I2 represent the vol- 
tages and currents on the two sides. The total load is then 

W = EJi + E2I2 

The pressure current is, however, due to E2 only, hence the meter 
registration is equal to 

TFi = (7i + l2)E2 
The difference between W and TTi is the error. This is 

W - Wi = EJi + E2I2 - E2I1 - E2I2 

= Ii{Ei — E2) 

This is zero only when Ei = E2. When Ei is greater than E2, the 
meter is slow, and when E2 is greater than Ei, the meter is fast. 
This error may or may not be appreciable, depending upon the 
degree of unbalancing. 

When the voltage coil is connected across outside mains, that 
is, 1 and 3, Fig. 150, the error on unbalanced load will always 
be of the same sign. Under the previously assumed condition 
the load is again 

W = EJi + E2I2 

but the registration of metQr is 

W = }iE{Ii + 72) 

where E is the voltage between mains 1 and 3. 

But E = Ei + E2 

hence Wi = }4(Ei + E2)(Ii + 1 2) 

and error is 

TT - TTi = EJi + E2I2 - }4EiIi - }iEil2 - ^^2/1 - ^^2/2 

= M(^i - E2)(Ii - 72) 

which is zero only when Ei = E2 or 7i = 72. In general, on un- 
balanced load the meter will register too high, for when 7i is 
greater than 72, Ei is less than E2 and TT — TTi is negative; also 
when 72 is greater than 7i, E2 is less than Ei and again W — Wi 
is negative, that is, the registration is higher than the energy 
supplied. 

It must also be noted that on unbalanced load the error is in 
general greater when the voltage coil is connected between neutral 



192 ELECTRICAL METERS 

and one outside wire than when it is connected between the two 
outside wires. 

On circuits that are subject to considerable unbalancing it is 
preferable to use two-wire meters, 

172. Mercury Watt-hoar Meter. — ^The source, or cause of 
many commutating type watt-hour meter troubles is the com- 
mutator. The chief objections to the commutator are: friction 
of brushes, sparking at brushes when commutator becomes oily 
ur dirty, change in speed due to an improper position of the 
brushes and additional weight of moving element. Many 
attempts have been made to lessen the influence of these troubles, 
but the most radical procedure has been the development of a 
watt-hour meter which eliminates the commutator entirely. 

The principle of operation of the mercury integrating meter 
was discovered in 1823 by Barlow, Fig. 151 is a diagram of the 




Fia. 151. 

operating parts of Barlow's invention. As the reader will 
observe, this consisted of a copper diak D mounted on a horizontal 
axis so as to rotate freely between the poles of a permanent 
magnet. When current is passed into the disk through the axle 
and out at the circumference, the reaction between the current 
in disk and the permanent-magnet field develops a torque, which 
causes the disk to rotate in the direction of the arrow head. The 
rotation is in such a direction as to carry the current out of the 
magnetic field. This torque will vary with the current strength, 
for, as has already been shown, the torque is proportional to prod- 
uct of current strength and field. The field being constant, 
the torque must vary with the current. 

The adaptation of this principle to integrating meters will be 
readily understood by reference to Figs. 152, 153 and 154 which 
ebow the essential characteristics of the Sangamo direct-current 



WA TT-HOVR ' METERS 




194 



ELECTRICAL METERS 



watt-hour meter. Fig. 152 shows a crosa-setition of the motor ele- 
ment with the principal parts designated. The rotating element, 
or armature, is the copper disk submerged in the mercury. Sur- 
mounting the disk is a hardwood float whose weight is adjusted 
so that the buoyant effect of the mercury will relieve the lower 
bearing of the weight of the entire moving system. By careful 
adjustment the downward pressure has been entirely eliminated 
and a small upward thrust has been produced. 

The mercury chamber of the meter is made of insulating 
material into which have been imbedded two nickel-plated 
copper terminals and a laminated steel ring. The copper termi- 
nals serve to lead current into and out of the mercury chamber, 
and the stoel ring reduces the reluctance of the magnetic circuit, 
thus competUng the magnetic lines to pass through the armature 
disk. 

173. Operation.^A simplified diagram of the connections and 
wiring of the meter is shown in Figs. 153 and 154. The current 
enters the meter at the terminal Ti, passes through the hea\'y 
conductor and through copper lug i?i into the mercury and arma- 
ture disk A ; it leaves the armature disk through the mercury to 
lug El, thonce through heavy copper conductor to terminal Tj 
and back to line. The voltage circuit consists of the fine winding 
surrounding the magnet core Y, and a resistance coil R'. The 
current in this circuit develops a magnetic field between the ends 
of core Y and the return stoel plate. Fig. 152. The intensity of 
this field is proportional to the current in coil SC and hence, to 
the voltage across the main Une. The torque on the armature 
is proportional to the product of armature current and magnetic 
field, and hence to power, which is the condition necessary for 
watt-hour meters. This torque is, however, very low, being only 
about 2 cm. -grams when 5 amp. are flowing through the disk. 
This low torque is due to the fact that the armature may be con- 
sidered as consisting of only one turn. Since the pressure of the 
movable element has been relieved, and the friction reduced to a 
minimum, a very high torque is not absolutely necessary. It ia 
not practicable to pass more than 10 amp. through the mercury 
and disk, and hence shunts are used on all meters above 10 amp. 
capacity. 

The counter- torque is obtained by the aluminum disk D rotat- 
ing between poles of permanent magnets M exactly as in all 
motor watt-hour meters. 



WATT 'HOUR METERS 195 

174. Compensation for Friction. — ^Light-load compensation is 
secured by sending, in the proper direction, through the mercury 
chamber a current from a thermocouple. The thermocouple 
consists of two strips of dissimilar metal terminating in slotted 
ends held by screws B and C, Fig. 155. The couple is energized 
by the coil A which is connected in series with the voltage coil 
as shown by H in Figs. 153 and 154. The thermocouple is 
shunted by a variable resistance G, Fig. 155, and the degree of 
compensation can be varied by changing the position of the sUd- 
ing clamp E. Recently an improvement has been made so that 
either positive or negative compensation may be obtained. This 
reversal of compensation is secured by changing the thermocouple 
connections from under screws B and C to screws C and D. 
Another modification in construction allows a compensation so 
that the meter has a range from about 5 per cent slow to 10 
per cent fast on 10 per cent of full load. This is secured by 
connecting one end of the thermocouple to a point somewhat 
remote from the left-end bracket. This, point of connection 
becomes the zero point of adjustment, so that when the clamp 
is moved to this position there is no compensating ejBfect. When 
the clamp is moved to the right the desired starting effect may be 
obtained, but if the meter shows a tendency to creep on light load 
with the clamp at the zero position, this tendency can be 
eliminated by moving the clamp slightly to the left. 

The load current through the mercury chamber has a tendency 
to demagnetize the field magnet. To overcome this, but primarily 
to compensate for fluid friction on the movable element which 
increases with load, the load current is passed around the magnet 
core. As the load increases the demagnetizing and compensating 
actions increase together. 

These meters are now made for both two- and three-wire 
circuits. Fig. 154 shows the connections for the three-wire 
instrument. 

176. Full-load Adjustment — One other dijBference between the 
Sangamo mercury watt-hour meter and the other makes of watt- 
hour meters is worthy of mention. The retarding ejBfect of the 
permanent magnets is varied by shunting some of the magnetism 
through the soft-iron disk, instead of moving the magnets nearer 
to, or farther from the axis of the disk. The soft-iron disk is 
threaded and may be screwed up or down, thus changing the 
reluctance of the magnetic circuit. If the disk is screwed down, 



196 



ELECTRICAL METERS 



some of the magnetism passes from one magnet through t 
magnetic shunt to the other, thus weakening that which passes 
through the copper disk. Under these conditions the meter 
will run faster. 

176. Induction-type Watt-hour Meters. — Some of the dis- 
advantages of the electrodynamo meter type of watt-hour meter 
for use on alternating-current circuits have already been men- 
tioned. The advantages of the induction type of watt-hour 
meter have relegated the clectrodynamometer type to direct- 
current circuits almost exclusively, and hence, the two types arc 
sometimes classified as direct-current and alternating-current 
watt-hour meters. 

The fundamental advantage of the induction-type watt-hour 
meter is the absence of commutator, and in fact of all sliding 




electrical contacts. The electrical circuits are all stationary, 
heuce the movable element consists merely of a shaft and disk. 
The disk performs the functions of both the armature and retard- 
ing disk in the other type. This great reduction of the number 
of parts greatly decreases the weight of the movable element, 
and consequently diminishes the bearing friction and jewel wear. 
The fact that all windings are stationary permits a much more 
rugged and cheaper construction, eliminates commutator troubles, 
decreases the friction, and greatly improves the accuracy of the 
meter over long periods of time. The induction-type meter 
can, however, be used on alternating-current circuits only. Fig. 
156 shows the parts of a General Electric induction-type single- 
phase watt-hour meter. The essential operating parts are a 
stationary element comprising the electric and magnetic oir- 



WATT-HOUR METERS 



197 



cults, the Fotatitblu disk, the registering inct^hanisni, and retarding 
magnets. 

177. Operation. — These meters operate upon the principle of 

the revolving ma,gnetio fic!d already (>\|il:iiTK:d in connection 




with the induction -type wattmeters. Although exactly the 
same general principles apply in the two cases, nevertheless they 
are applied in a somewhat modified way and hence a more ex- 
tended discussion is justified. To make clear these principles 
there is given in Fig, 157 a simplified diagram of the driving and 



198 ELECTRICAL METERS 

revolviDg parts. The element consists of two magnetic circuits, 
M and M', which are built up of laminated steel punchings. 
Core M carries the voltage coil P and lag coil L. The series 
coils CC are wound upon the two projections of M'. Imme- 




diately below the central prong of M is a copper stamping F 
known aa the bgbt load clip The disk is shown m position 
between the central prong of W and upward projecting parts of 
M'; mm are the retarding magnets 




Fig. 158 shows the distribution of the magnetic hnes around 
the two cores of the series coils. It is very evident that the end 
of one of these cores is a north pole wbiie the other is a south 



WATT-HOUR METERS 190 

pole. The distribution of the magnetic lines due to voltage coil 
is shown in Fig. 159. It will be seen that these lines radiate in 
all directions, chiefly to the right and left, some, however, 
passing downward. 




These figures were obtained by sprinkling iron filings upon 
sensitized paper, which was laid flat upon the stationary element 
of the meter, while direct current was passed successively through 

Magnetic lines.. 




Fia. ICO. 

the series and voltage coils. The figures thus do not accurately 
show the field within the air gaps, but outside of the cores as the 
iron filings shunt the magnetic lines. Illustrative diagrams of the 
distribution a' 'o^netic lines between the cores correspond- 



ELECTRICAL METERS 



ing to Figs. 158 and 159 are shown in Figa. 160, 161, and 164. 
Fig, 162 shows the relative position of voltage coil core, B, 




¥}ii. 161. 

series coil cores, A-A, and the disk. It is thus clear that when 
direct current is used for excitation the lines due to the series 
coil leave the end of one core and 
enter the other while those due 
to the voltage coil divide and pass 
upward through the adjacent iron. 
When alternating currents are 
used for excitation, the resultant 
fields are similar to those pro- 
duced by direct currents, but, 
owing to the fact that they are 
due to alternating currents, they 
shift either in one direction or the 
other. 

The coil P, Fig. 157, consists of 
many turns of fine wire, the coil is highly inductive, and^thg. 
current flowing in it is almost one-quarter of a period behind 
the voltage across its terminals. On the other hand, the coilB 




Fig. 1C3. 



WATT-HOUR METERS 



201 



CC are nearly non-inductive and the current in tliem is in 
phaae with the voltage, when the load power-factor is unity. 
The phase relation of these quantities is shown in Fig. 163. 
This figure is a tracing of an oscillogram, and curve / represents 
the series current, E the applied voltage, and i the voltage coil 
current. It is very evident that although the line voltage and 
current are in phase, the voltage coil current lags only about 
72° behind the voltage. The im po rtant t hing is_that. the vol- 
tage-coil flux and series-coU flux should be in quadrature, and 
not that the currents should be. How this is secured will be 
shown later. 

178. Shtftmg Magnetic Field. — Giving attention to the char- 
acter and distribution of the magnetic fields only when at their 






Pig. 164. 

maximum values, it can be shown that the resultant field shifts 
with reference to the disk, as the currents in the pressure and 
series circuits fluctuate. 

For the time being, assuming a phase difference of one-quarter 
of a period between series and voltage currents, at the instant 
the series current has reached a positive maximum value, the 
voltage current is zero. At this instant the polarities of the iron 
cores will be as indicated at A, Fig. 164. 

Considering a north pole + and a south pole — , the polarity 
of 1 is 0; of 2 it is +; of 3 it is zero; of 4 it is — ; and of 6 it ia 0. 



202 ELECTRICAL METERS 

A quarter of a period later, the current in the Beries coils has 
fallen to zero and that in the voltage coil ia a maximum. The 
polarity of the cores at this instant is indicated in B, Fig. 164. 
In the same way C shows the direction of flow of magnetic lines 
at the end of half a cycle and D at the end of three-quarters of a 
cycle. Arranging a table to show the magnetic condition of 
cores 2, 3, and 4 at the given instants, we get the following: 
Tablh II. 





Poles 1 


Instant-5 


. 


2 


3 


4 


5+ar-l- 





V 





- 


}i period 


- 





X 





a " 





- 





\ 


\ " 


+ 





- 





End cf period 





+ 





- 



Shunt el 



Fig. 165. 

An examination of Fig. 105 shows that, under the conditions 

assumed, the polarity shifts continuously from left to right. 

This, of course, is true of the other magnetic conditions. The 

shifting of the magnetic field induces 

currents in the disk, as already explained, 

and the reaction between these currents 

and magnetic field causes the disk to 

rotate. 

179. Practical Construction. — In Fig. 
p 166 is showii the essential parts of the 
magnetic circuit of the Weatinghouae 
single-phase induction meter. This 
shows that the construction differs very 
„ 1^ little from that of the General Electric 

meter. The principles of operation are 
exactly alike in the two instruments. The complete Westing- 
house type C meter with case removed is shown in Fig, 167. 
It is very evident that the meter is very compact and rugged. 
Type Ki induction meter of the Fort Wayne Electric Works 
applies the same principles in a somewhat modified manner. The 




WATT-HOUR METERS 



[ative position of the aeries and voltage coils ia shown in Fig, 
In actual construction, in the earlier iaatrumenta the coils 





To- Bearins 
Screw 


Registering '1 

"Mechanism i 




^S 


^^^H /Magnet 


AOXI&TMENT ^m 


^^ 


Bf WM "~n^OUNJ\Nd_ 

^H ■■ Frame 


m^^NT 1 


ICT 


H^ -^=^-MAGNEy 

W^ Clamping 
~ Screws A 


^H-. 




" Laminated 
Electro Magnet 




I had only air cores, but the coils of the later forms have laminated 
iron cores, just as the other makes. In place of a disk, the rotat- 
able element 13 an aluminum cylinder. The two figures, 169 and 



304 



ElECTRICAL METERS 



170, show clearly the actual construction of one form of 1 
instrument. Since the absorption of the Fort Wayne Electric 
Co. by the General Electric Co. type iC* haa been superseded 
by the type Ki meter which is exactly the same as the General 
Electric type 1-14 meters. 




FiQ. 170. 



Yet another way of securing a rotating or shifting magnetic 
field is shown in Fig. 171. The voltage element consists of a 
pair of fine wire coils. Each of these coils is wound on a lami- 
nated sheet-steel core of rectangular form as shown. The mag- 




netic circuit is very nearly all confined to the steel core, but at 
the bottom, near the disk, is a narrow slot where some leakage 
will naturally occur. This leakage flux must pass through the 
disk. In doing so it sets up the desired eddy currents. 



WATT-HOUR METERS 



205 



The series coils are mounted on short laminated cores which 
differ from the potential-circuit cores in not forming closed 
magnetic circuits, but instead present exposed ends to the 
aluminum disk. The series coila are placed below the disk but 
displaced with reference to the pressure-circuit windings. A 
complete view of the Columbia induction meter is shown in 
Fig. 172. 

180. Sangamo Inductioa Meter. — Since the expiration of the 
Tesla patents, more companies have taken up the manufacture 




of the induction-type watt-hour meters. The front of the San 
gamo single-phase meter with cover removed is shown in Fig. 
173, and the back of the meter is shown in Fig. 174. 

The operating principle is exactly the same as that already 
described, but there are some details of construction which 
distinguish it from (he meters of other companies. A front view 
of the polyphase meter is shown in Fig, 175. 

181. Balance of Elements. — An interesting feature of the 
Sangamo polyphase meter is the provision for equalizing the 
torque of the two elements. This equalizing device consists of 




206 



ELECTRICAL METEfiS 



a plate carrying the two series yokes and coils, arranged so t 
it may be clamped to the base of the meter by two screws. In 
the center of the plate is an eccentric stud or scxew aeceasible 
from the front. Rotation of this stud wO! cause the plate carry- 
ing the two yokes to move up or down through a short distance, 
thus changing the air gaps of the two series magnets until equality 
of torque between the two elements is obtained. 



Hant^ng Lug — 
ShunI Magnei— . 



^Saie 



iife 



Lighl Load 
-Cla.-np Screw 



Type and Numlwr Plait 



bne Wiie Bushing! 
FlO. 173. 



182. Duncan Induction Watt-hour Meter. — In so far as prin- 
ciples of operation are concerned, the Duncan meter in the same 
as those already described. A front \'iew of this meter with 
cover and dial removed is shown in Fig. 176, and the construction 
of the series and potential elements is shown in Fig, 177. 

There are some interesting construction features which dis- 
tinguish this meter from other makes. Thus only one retarding 
magnet is used, and it is mounted in such a manner that both 
poles are above the disk. Directly below the poles of the magnet 
and disk is placed a screw with a large flat head, Fig. 176. 



WATT-HOUR METERS 



207 



The head of the screw serves as a magnetic shunt. Some of the 
magnetic flux passes from one pole of the magnet through the 
disk to the head of the screw and then through the disk to the 
opposite pole. To make adjustment for full-load retarding 
torque, the screw is turned up or down. As it is brought closer 
to the poles of the permanent magnet, the reluctance of the 
3 is decreased and more f]ux passes through the disk, and 




the retarding torque is xionsequently increased. The opposite 
movement of the screw will result in a decreased retarding torque. 
The light-load compensating device is very similar to those 
already explained. 

The quarter-phasing or lagging device consists of a heavy 
one-piece die-made copper plate. By moving this up or down, 
as required, the proper adjustment is secured. 



208 



ELECTRICAL METERS 



183. Full-load Adjustment. — The fundamental principles of 
operation of these .various makes of induction meters are all the 
same. Similarly the full-load adjustment is performed by vaiy- 
ing the retarding effect of the permanent magnets. This, in 
general, is accomplished in two ways, either by changing the 
position of the magnets with reference to the shaft, or by shunting 
some of the magnetism. 

The full-load speed of the General Electric and Westinghouse 
meters is adjusted by moving the permanent magnets either 
away from, or nearer to, the shaft aa the case demands. 







Lowu- Shuu Magr 



FlO. 175. 

The retarding torque is proportional to the product of eddy 
currents and strength of magnetic field. The eddy currents are 
proportional to the magnetic field strength and speed of disk, 
hence the torque is proportional to the product of the square of 
the magnetic field and speed of disk. Mathematically this can 
be expressed by 7* = H'^w where ^ is the fiux, r is the mean 
radial distance from the shaft of the disk to the poles, « la the 
angular speed, and k a proportionality constant. 

If the magnet is moved outwardj the distance r is increased 
and, hence, the speed must decrease if the torque is to remain 



210 



ELECTRICAL METERS 



constant. If the speed does not decrease, the retarding torque 
increases in proportion to r. 

If the disk is replaced by a cylindrical cup, as in the older Fort 
Wayne meter, moving the magnets up or down does not change 
the radial distance. In this case a change in retarding torque is 
secured by changing the flux that passes through the aluminum 
cylinder. By moving the magnets down beyond a certain point, 
some of the magnetic lines pass below the edge of the cylinder 
and have no effect in inducing eddy currents. Under this 
condition, the retarding torque is less and the meter runs faster. 
Moving the magnets upward will obviously have the opposite 
effect. 

A change in torque may also be secured by providing for the 
magnetic lines a bypass or magnetic shunt, whose reluctance 
may be varied. This is the method used on the Sangamo meters 
and the Duncan induction-type meter. An adjustable armature 
bridges the gap between the poles of the magnets, and a change 
in the position of this armature with reference to the magnet poles 
diverts a greater or smaller part of the flux around the disk. 

184. Relation between Torque and Power. — According to the 
principles just explained, an expression may readily be derived 
for the driving torque. For, if we represent the mean of the 
eddy currents by 7, and the average flux by $, the driving force 
at a given position of retarding magnets is given by 

T = k^I. 

But the eddy currents are proportional to the product of flux 
and relative speed of magnetic field and disk. Since r is a con- 
stant quantity, the driving torque in general is then given by 



= fc"$^ajr where i 



. the relative speed. But in 



Chapter VI it was shown that 4> is the equivalent of two magnetic 
fields rotating in opposite directions at the same angular speed. 
If then in Fig. 46, OF, and OF represent *i and *!, the two 
opposite torques due to these rotating fields are 






i + ") 



and r, = fci*,« (ui - w). 

Where ui is the angular speed of rotating fluxes and is equal to 
2jr/, w is the angular speed of disk. 



WATT-HOUR METERS 211 

The retarding torque due to the permanent magnets when at 
a fixed distance from the shaft is likewise given by 

Tz = ^2^8*0) 

where i>8 represents the flux of the permanent magnets. 

The retarding torque, due to the permanent magnets, is in 
the same direction as Ti, hence Ti + Tz retard the disk, while 
T^ drives it. When constant speed has been reached, the 
algebraic sum of these torques must be zero, or 

^2=^1 + Tz, 

That is, ki^%\o)i - w) = ki^i^ (wi + «) + fcs^s^w. 

Reducing we get fci(f»2^ — ^i^) wi = fci (f»2^ + ^i^) w + kz^z^ca. 

But ^2^ = £r,2 + H2^ + 2H1H2 sin ^0 

and <E>i« = Hi^ + H^^ - 2H1H2 sin ^0 (see Art. 73). 

Hence ^2^ - ^i^ = 4ff 1^2 sin ^0 

and <E>22 + <E>i2 = 2(£ri2 + Hi"), 

Therefore, AkJIiH^i sin ^0 = 2ki (Hi^ + H^^) co + kz^z^ co. 
wi is equal to 27r/, and for any given frequency is constants Re- 
placing Sirfci by if 1, we get, 

KifHiHz sin ^0 = 2kMHi'+H2^)+ kz^z^o). 

The term KifHiH2 sin ^0 represents the driving torque, and the 
two right-hand members represent the retarding torque. The 
term 2fcico {Hi^ + H2^) represents the retarding effect of the 
rotating fields, and fca^a^o is the retarding effect of permanent 
magnets. When w is low, the effect of 2fci {Hi^ + H2^) « is 
negligible and the retarding effect is wholly due to Kz^z^oi, 
Under this condition the relation between driving and retarding 
torque is 

KifHiH2 sin ^0 = kz^z^o) 

Now Hi is proportional to the voltage, and H2 is proportional 
to the series current. We may then write 

Hi = k'E 
and H2 = k''I, which, substituted in the above equation, 

give Kik'k'JEI sin ^0 = fca^a^w 

or EI sin ^0 = Ko^z^o), 

where Ko = 



kz 



Kik'k'J 



212 



ELECTRICAL METERS 



That is, the product of current, pressure, and sine of phase dif- 
ference between the magnetic field due to series and voltage 
currents respectively is proportional to the speed of the disk. 
The actual power is, however, equal to EI cos 9, hence if the 
meter is to register accurately 

sin Co — cos fl 



For correct registration, it is thus imperative that the pbaee 
difference between the two magnetic fields be exactly one- 
quarter of a period when the power-factor of load is unity. 

If 2fci (Hi' + Hi')(ji is not neghgible in comparison with fc^s'u, 
the calibration curve of the meter will not be a straight line. 
If the meter is correct on light load, it will be alow on full or over- 
load, and vice versa. On any given voltage and frequency, Bi^ is 
constant; the inaccuracy in registration is then due to H-i^w, and 
in order that this may be negligible both Hi and o) must be small. 
This is taken care of in the design of the meter. 

186. Lagging Induction Watt^hour Meters.— As has just been 
demonstrated, for accurate registration on circuits of low power- 
factor, the flux due to the pressure coil must be one-quarter of a 
period out of phase with the flux due to the series current when 
operating on circuits whose power-factor is unity. Mainly on 
account of the resistance, eddy currents, and hysteresis of the 
voltage circuit, this phase difference is not obtained without 
additional adjustment. 

The methods of lagging used by the General Electric Co. and 
the Westinghouse Co. are identical in principle. The manner 
in which this is carried out in practice is shown in Figs. 157 and 
167. Cofl L, Fig. 157, is known as the lag coil, and consists of 
a few turns of a high-resistance wire wound around the end 
of the voltage-coil core. A similar coil is shown in Fig. 167 
where it is labelled "power-factor adjustment." The function 
and operation of the lag coil is explained in Article 116. As 
there pointed out, part of the flux due to the voltage coil, passes 
through the lag coil. The resistance of the lag coil is adjusted, 
until the phase displacement of the resultant flux is exactly 
90° in time phase from the flux due to the current coils. The 
greater part of the pressure-coil flux does not pass through the 
lag coil, but takes the shorter path as indicated in Fig. 161. 



WATT-HOUR METERS 213 

This fact is not shown clearly in Fig. 159, for in that case direct 
current was used for excitation and the inductance of lag coil 
had no effect. 

186. The Effect of ' Over and Underlagging. — The driving 
torque of an induction meter is given by 

T = Kkif^HiHi sin ^o where Hi and H2 are the maximum 

values of the voltage and current fields respectively, and ^0 is 
the time-phase difference between them. The power in the 
load circuit is, however, given by 

P = EI cos d. 

In order that the torque may be proportional to power, ^0 must 

TT 

be equal to « + ^» Iii case this relation does not exist, the 
torque will be either too large or too small and the registration 

TT 

will be in error. For instance, suppose ^0 = o + « ± ^, or that 

the meter is overlagged. Then sin ^o = sin ^ + (« ± ^) = cos 
(a ± 6) and the driving torque will be given hy T = K'EI cos 

(a ± e). 

When B is positive, or the current leads the pressure, cos (a + B) 
is less than cos B and the torque is too small. When ^ is an angle 
of lag, cos (a — B) is greater than cos By and the torque is too large. 
Thus, an overlagged meter will under register on leading current, 
and over register on lagging current. 

It can easily be shown that when the meter is underlagged or 

TT 

when ^0 = o — « ± ^> the meter will be slow on lagging and fast 

on leading current. The demonstration is left for the student. 

187. Light-load Compensation. — Exactly as in the electro- 
dynamometer type and other types of watt-hour meters, for 
accurate registration on light load, some means must be provided 
for overcoming the retarding torque due to friction. Owing to 
the absence of brushes, and to the fact that the movable elements 
of induction-type watt-hour meters are much lighter, and have 
a higher torque per unit weight than commutator meters, there 
is much less necessity for friction compensation. 

When compensating devices are used, they are operated by the 
voltage circuit as in other types of watt-hour meters. The 
compensation remains constant at all loads with a given adjust- 
ment; it may, however, change with the voltage or frequency. 



214 



ELECTRICAL METERS 



The general principles upon which the various compensating 

devices of different makers operate are fundamentally the same 
although the methods of applying these principles differ con- 
siderably. The fundamental principle consists in the production 
of an unbalanced or shifting magnetic field. The compensating 
device operates bo that at any instant the magnetic flux is not 
uniformly distributed over the pole face of the voltage-coil core. 
The variation in the distribution of the magnetic flux produces 
the same effect as a shifting field. 

This non-uniformity in flux distribution may be produced 
by interposing within the air gap a ehort-circuited conductor, 
or by modifying the voItagc-coil core in such a way that the flux 
density will vary in time from one side of the pole face to the 
other. 

The former method is made use of by the Westinghouse, Gen- 
eral Electric, Sangamo, and Duncan companies. Fig. 167 shows 
how this method is applied by the Westinghouse Co. 

As here shown, the light-load compensation is secured by means 
of two "light-load adjustment loops" which are in reality 
two copper punchings forming a closed electrical circuit. One 
side of each loop is in the air gap of the voltage-coil core, and the 
whole loop is mounted in such a way that it may be turned 
through a small angle, thus changing its position with reference 
to the magnet core. This adjustment is accomplished by means 
of two knurled nuts which are accessible from the front of the 
meter but not shown in the figure. 

It is clearly shown in Fig. 167 that turning either of these 
loops down or up permits more or less of the magnetic flux to pass 
through the loop. This flux as it passes through the loop induces 
a current therein, and the reaction of this current upon the flux 
retards its development when increasing, and vice versa. This 
retardation unbalances the main flux, and produces the same 
effect as a shifting field. The result is the development of a 
torque whose value is modified by any change in the position of 
the short-circuited loop. By carefully adjusting the position of 
these loops, a torque just sufficient to overcome the retarding 
torque of friction may be secured. 

A similar method is employed by the General Electric Co., 
as ia evident from Fig. 157. As shown, the light-load compensa- 
tor F consists of a rectangular copper punching, which is placed 
under the central prong of the voltage coil core. If this punching 



WATT-HOUR METERS 



ia not eymmetrically placed with reference to the core, the flux 
through the disk will vary in intensity from one side to the other. 




Pig. 178. 

This variation, or one may say shifting of flux, will produce 
enough torque to overcome that due to friction. 

Xight-load compensation of the Sangamo induction watt-hour 
meter is also secured by means of a copper punching within the 



21(t 



ELECTRICAL METERS 



field of the potential coil. This punching is mounted on a staff 
carried by a brass bracket which is fastened by screws to the 
back of the grid or frame. To the lower end of the staff is riveted 
a sector which meshes with a worm screw the head of which is 
accessible from the front. By turning the screw, the punching 
is caused to shift within the magnetic field. The amount of the 
shifting is indicated by a scale on the head oi the screw. Close 
compensation can thus be obtained. 

The second method of applying the general principle is exem- 
plified in the meter whose connections are shown in Fig. 178, and 
the induction meter of the Columbia Meter Co. 

In Fig. 178 is shown the auxiliary core (J)) which is pivoted in 
the middle. Loosening screw Si and tightening Sa moves the 
end that is near the cylinder from left to right. Such a change 
in the relative positions of the auxiliary and main cores causes a 
shifting of the magnetic flux. 
This shifting is similar to that 
produced by the other com- 
pensating methods. 

188. Flux -shunting Method. 
— In the older form of the 
Columbia induction meter the 
necessary unbalancing is ob- 
tained by means of a piece of 
soft iron adjustably bridging a 
part of the air gap in the 
vo!tage-coiI core. The bridg- 
ing piece of iron is held in 
place by two screws passing 
through a slot in the extension 
arm which carries it. By 

loosening these screws, the position of the bridging piece 
of iron can be varied. In the more recent designs the 
shunting of magnetic lines by means of a piece of iron 
across the air gap is no longer used. The method employed is 
shown in Fig. 179. As is evident from the figure, a specially 
designed piece is mounted in an adjustable manner on top of each 
voltage-coil core. The frame of the meter is made of non-magnetic 
material and, hence, any leakage flux will follow the path of least 
reluctance. The case of the meter is of magnetic material, and as 
it comes near the back of the voltage-coil cores some leakage flux 




WATT-HOUR METERS 217 

will pass through the case downward and enter the core again 
from the bottom through the armature disk. When the sliding 
pieces of iron are symmetrically placed with reference to the 
cores and case, the effect of the leakage flux from one core 
balances the effect of the leakage flux of the other core. When, 
however, the reluctance of the leakage-flux path is changed by 
moving one of the sliding pieces nearer to or farther away from 
the case, this balancing no longer exists, and the disk will be 
caused to rotate. If the right-hand piece is nearer the case, the 
disk rotates from left to right. If the other piece is near the 
case, the disk rotates from right to left when the voltage circuit 
alone is closed. Hence, by adjusting the positions of the two 
sliding pieces, any necessary degree of compensation can be 
produced. 
. ^^ 189. Influence of Frequency. — The current through the pres- 
sure coil of a watt-hour meter is given by 

^ (R^ + X^)^ 

where R is the resistance and X the inductive reactance of the 
coil. The resistance R changes only with the temperature, the 
effect of which will be discussed later; but X, which is equal to 
27r/L, varies with frequency. Hence, I will increase with decrease 
in frequency and decrease with increase of frequency. This 
increase or decrease will cause a corresponding increase in the 
voltage-coil flux, and as the torque is proportional to the product 
of the maximum value of the voltage-coil and current-coil flux, 
it will also vary. Again, the angle of lag of voltage-coil current 

X ^irfL 

may be obtained from the expression tan /3 = ~p = ~^b~' That 

is, the tangent of the angle of lag varies as the frequency. Since 
without great error, one may assume that the voltage-coil flux 
is in phase with the voltage-coil ciurent, it is evident that the 
angle ^o, in the expression for torque, viz., T = K0H1H2 sin ^0, 
depends upon the frequency. Any variation in frequency, thus, 
produces two effects: first, increases or decreases the voltage-coil 
flux; and, second, changes the phase relation of the two operat- 
ing fluxes. 

A decrease in the frequency increases the voltage-coif current, 
but a lowering of the frequency decreases the value of ^0, pro- 
ducing the same result as underlagging. It has been shown 
that an underlagged meter tends to run slow on lagging cur- 

22 



218 



ELECTRICAL METERS 



rent, hence the increase in torque, due to greater current, will 
tend to compensate for the phase-difference error. On leading 
current, however, the error will be increased. 

Similarly, when the frequency increases, the voltage-coil current 
increaaes, and the phase difference between the two operating 
fluxes increases. The effect of the difference in phase is the same 
as though the meter were overlagged. These two effects tend 
to neutralize each other on inductive load, but are cumulative 
when the load current leads the pressure. 

This double effect will be more readily understood from the 
vector diagram of Fig. 180. In this diagram OE represents 




both the magnitude and direction of the applied voltage and 

0*1 = voltage-coil flux at normal frequency, 

0*s = voltage-coil flux at a frequency below normal, 

04>s = voltage-coil flux at a frequency above normal. 

The corresponding lag-coil fluxes are given by 0*'i, O't'i, and 

0*'j. The meter is jiasumed to be properly lagged for normal 

frequency, i.e., By is 90°. At low frequency the resultant flux 

4'fl makes an angle 6% with the voltage and this angle differs from 

90° by the angle m. The phase relations are thus the same as 

though the meter were underlagged on normal frequency. 

The resultant flux 0^"a, when frequency is above normal, 
is out of phase by an angle 6^ = 90° -|- «:, and plainly the phase 
effect is the same as though the meter were overlagged on 
normal frequency. 



WATT-HOUR METERS 219 

The effect of variationa in frequency on the accuracy of the 
meter is shown in Fig. 181. 

The meter for which the curve is given was lagged for accurate 
registration on 60 cycles. It is seen that there is a falling off 
in accuracy both with increasing and decreasing frequency. 

190. Double Lagging. — The foregoing discussion shows that 
when meters are designed for two widely different frequencies, 
some provisions must be made for changing the effect of the lag 
coil. Such a device is called double lagging. A good example of 







It 


n. 


icy 


u... 


OOD 


... 


L« 


id. 


.^^.4 






f\ 














■~ 


— - 














y] 




















~ 


\ 








* L 






T 


'■ 






10 




1 







Fjo. 181. 



a double-lagged meter is the 60- or 133-cycle watt-hour meter of 
the Fort Wayne Electrical Works. The internal connections of 
this meter are shown in Fig. 178. 

As shown, the voltage-coil core consists of two parts, a and 
b; the main core (a) forms nearly a closed magnetic circuit, 
while & is a laminated piece of rectangular cross-section pivoted 
at P. This auxiliary core b is wound with an auxiliary coil, G, 
which is conected in series with a resistance, H, and shunted 
across a few turns of reactance coil, 7. 

The voltage coil consists of two parts : one D, which is wound 
around cores a and b, and / which has a separate iron core. 
The iron core of I forms a closed magnetic circuit and hence its 
inductance is much higher than the inductance of D whose core 
has an air gap. 

The lag of voltage current is due to the influence of both coils, 
but the magnetism developed by D alone is effective in causing 
rotation of armature, and it alone must be in exact quadrature 
with flux produced by coils C-C on the load of unity power-factor. 
To compensate for any discrepancy in the quarter-phase relation 
mentioned, there are provided two coils, E and G, On circuits of 
low frequencies, both coils are operative while on circuits of high 
frequency, coil E is opened and alone is effective. In general, 
a change in the frequency 'ffeot the speed of the 



220 ELECTRICAL METERS 

meter. This effect can be corrected by au adjustment of the 
position of the penniinent magnets when the meter is under 
test. 

191. Single-ptiase Watt-hour Meters on Polyphase Circuits. — 
It will be shown later that to measure power on polyphase cir- 
cuits, by means of single-phase instruments — with the exception 
of the two-phase system — there are needed as many meters as 
there are phases less one. That is, on a three-phase circuit two 
meters are sufficient, and by properly connecting single-phase 
meters to the polyphase circuits the energy will be equal to the 
algebraic sum of the meter readings, 

192. Three-wire Single-phase Induction Watt-hour Meters. — 
The three-wire system of distribution is much more economical 
than a two-wire system when any considerable amount of energy 
is to be transmitted. To measure the energy, either two single- 
phase two-wire meters or one three-wire meter may be used. 
When discussing three-wire meters of the electrodynamometer 
type, it was shown that the registration was correct only under 
certain conditions. Somewhat the same limitations apply to 
three-wire induction watt-hour meters, with the additional fact 
that these limitations are complicated by the characteristics of 
alternating currents. 

The alternating-current three-wire meter differs very little in 
construction from the two-wire instrument. Like the direct- 
current three-wire meter the instrument contains two series or 
current circuits and one voltage circuit. The series circuits are 
connected, one in each of the outside lines, and the voltage circuit 
may be connected either across the outside wires or between 
neutral and either outside wire. Which method of voltage-coil 
connection is used depends upon the design or make of instru- 
ment. The former method is perhaps the most common for 
reasons that will presently appear. 

Assuming the meter to be correctly adjusted, the accuracy of 
its registration will depend to a considerable extent upon the 
character of the load and connection of voltage coil. The influ- 
ence of these diilerent conditions upon the accuracy of the meter 
may then be considered under the following heads: 

I. Voltage coil connected across outside wires. 

1. Load balanced. 

2. Load unbalanced. 



WATT-HOUR METERS 221 

II. Voltage coil cotmected between neutral and one outside 
wire. 

1. Load balanced. 

2. Load unbalanced. 

193. Voltage Coil Connected Across Outside Wires.— Fig. 182 
is a diagram of an unbalanced single-phase three-wire system. 
Si and Si represent the series coils and V represents tlie voltage 




Pia. 182. 

coil of the watt-hour meter. The vector diagram of Fig. 183 
shows the phase relations of currents and voltages as produced by 
a most serious case of unbalancing. Very seldom would all the 
conditions there assumed be met at once. 




Pig. 183. 

If Elm and Ei„ represent the maximum pressures across loads 
Li and L2, then Em wilt be the maximum pressure between wires 
1 and 2. The current in load Li is assumed to lag 6 degrees 
behind Em, and ij>i degrees behind E„. If 7o represents the cur- 
rent in middle wire 0, then h will represent maximum current 
in load Lt. This current lags 8t degrees behind Et,,, and ^1 



222 ELECTRICAL METERS 

degrees behind Et„, According to the notation assumed, the 
instantaneous values of the electrical quantities involved are: 

e = i?m sin cot 

ei = Eun sin (o)t — ai) 

62 = E2m sin (cot + a2) 

U = Ii sin (o)t — <^i) 
H = 1 2 sin {cot — <t>2)» 

The instantaneous power being delivered to loads Li and Li is 

w = eiii + 621*2. 

Since the meter is direct-reading, the proportionality factor is 
taken care of by the calibration of the meter and is omitted. The 
instantaneous torque on the disk when the meter is properly 
adjusted is r = M^(*i + ^2) 

but e = 61 + 62. 

Hence, r = M(«i + ^2) (ii + ^2). 

If r is equal to w, the registration will be correct. When this 
is not the case, the error in registration will depend upon the dif- 
ference between w and r. 

Now w — T = eiii + 6212 — }4 (ei + 62) (ii + it) 

= K[(«i*i + ^2^2) - (61*2 + e2ii)]. 
But ei = Elm sin (cot — ai) 

and ii = 7i sin (cot — 0i). 

Then dii = ^im^i sin (co< — ai) sin (w^ — ^1) 

Expanding sin (cot — ai) and sin (co< — <^i) we get, 

eiii = Eimli[(sin cot cos ai — cos (at sin ai)(sin co< cos <^i — cos a)t 

sin <^i)] 
and the average of eiii equals the average of the right-hand mem- 
ber of the equation. 

Performing the multiplication indicated, and remembering 
that the average of sin^ cot and cos^ cot is 3^^, and the average of 
sin o)t cos cot is zero, the expression reduces to 

av. ei?i = }4EimIi cos (<t>i — ai). 
By a similar process of analysis the average of 

62^2 = E2ml2 cos (^2 + «2). 
The average of 

6211 = }4^2mll cos (</>i + at) 

and the average of 

eiit == H^imlt cos (4>t — ai). 



WATT-HOUR METERS 223 

Substituting these values, the expression for the difference be- 
tween power and torque becomes 

average of t(; — r = J4 [Eimli cos (<^i — ai) + E2ml2 cos (</>2 + «2)] 

- HlEjmliCos {4>2 - ai) + E^Ii cos {4>i + ai)]. 

The accuracy of the meter evidently depends upon the value of 
this expression. If the conditions are such that the expression 
reduces to zero, the registration is correct; if the expression is 
negative, the average torque is higher than the average load and 
the meter registration is too high, and when the expression is 
positive, the registration is too low. 

Conditions that are most likely to be met with in practice are 
I\ = 7i, El = Eif ai = a^ and <t>i = 4>2* When this is the case 
it is evident that the average of k; — r = and the meter 
registers correctly. 

194. Load Unbalanced. — When the load is unbalanced, in 
general the expression will not reduce to zero, even if the imbal- 
ancing is not sufficient to make Ei differ materially from E^- 

Let El = E2y oLi = «£ and 4>i = 02. Then 
ii?-r= Ji-Bim[/iCOs(0i-ai) - (7i- 72)cos(</>i+ai) -/2C0s(</>i-ai)] 
= M^im{(/i-/2)lcos(0i-ai)-cos(</>i+ai)]} 
= 3^J?i«(7i-72)sin0i sinai. 

So long as 7i is less than 7i and <t>i is less than ^ the meter will 

register too high. In practice ai will never be equal to 90°. 
If the power-factors of Li and L2 are each unity; then <t>i = 0, 
and the meter registers correctly. In general, the meter will 
register incorrectly on an unbalanced load when the voltage coil is 
connected across the outside wires. 

195. Voltage Coil Connected between One Outside Wire and 
Neutral. — Such a connection is indicated by the dotted line a6, 
Kg. 182. Using the same notation as in Article 193, the power 
is given by 

w = eiii + €212 
but torque r = eiii + €1X2 

and to — r = 6212 — • €it2. 

It has been shown that 

aV. 62*2 = }^E2nJ2 COS (^2 + "2) 

and av. eiu =}^EinJ2 cos (02 — ai) 

Hence average {w—t) = M-f 2[-B2mCOs(02 -f- a2) — -E?imC0s(</>2— ai)l. 



224 



ELECTRICAL METERS 



The meter will register accurately only when the average of 
(w-r) = 0. 

If the load ia balanced bo that E^m = Ei„, and aa = ai the average 
value of M> — T = — ]^Ei,^Ii 2 sin ij>i ain aa = — Ebnia sin^Ji sin a^. 

This expression is zero only when aj = 0, for only under such a 
condition will (j>3 be zero. 

It is perfectly clear, then, that a three-wire induction meter will 
not register correctly when the voltage coil ia connected between 
one outside wire and neutral even though the load on the three- 
wire system bo balanced. It will register correctly only when the 
load is balanced and the power factor is unity. When the voltage 



Source 



-111 — rt= 



Fin. 1S4. 

coil is connected between neutral and one outside main, the meter 
in general will be fast if the voltage impressed upon the voltage 
coil lags behind; and slow when the pressure-coil voltage leads the 
voltage between outside mains. This answers the question why 
it is preferable to connect the voltage coil between outside mains, 
a practice followed by most manufacturers. 

Upon three-wire circuits that are subject to unbalanced loads, 
two single-phase two-wire meters are preferable. Wten these 
are used they are connected as shown in Fig. 184, 

196. Polyphase Watt-hour Meters.- — In metering energy on 
pKily phase circuits, polyphase induction meters are usually 
employed, although the practice of some companies favors the 
use of two or of three single-phase meters, on the ground that 
when this is done the failure of one meter will not cause a com- 
plete loss of the record. The use of two single-phase meters 
has the advantage that from their registrations the average 
power-factor of the load can be computed. 

On the other hand, the use of more than one meter is subject to 
objection not only on account of the additional expense, but also 



WATT-HOUR METERS 



225 



on account of the difficulty of explaining to customers the 
characteristics of polyphase systems. 

197. Watt-hour Meters for Two-phase and Three-wire Three- 
phase Circuits.-^One make of polyphase watt-hour meter for 
a two-phase or a three-wire three-phase system is shown in Fig, 
185. The illustration shows clearly that the instrument is a 




Pig. 185. 

combination of two single-phase metering elements, the armature 
cylinders of which are mounted on the same shaft or spindle. 
Only one registering mechanism is thus necessary. The total 
driving torque is the sum of the torques exerted by the two 

I actuating elements, and the registration is proportional to the 
energy passing through both. 
It was pointed out that for correct registration on inductive 
load, the flux due to the load current must be in quadrature with 
the flux due to the voltage-coil current. Exactly the same con- 



ELECTIIICAL METEllS 



331 



t 



J^ Phase A 



O O / 00000 J fl^«c 

j-i kooo, 



s 



kiiflo/- 



1 I (|)(j) ~TjSiil^ 



4 



WATT-HOUR METERS 



227 



ditions must exist in each of the metering elements of polyphase 
meters. 

The manner in which two-phase and three-wire three-phase 
meters are connected to circuits is shown in Figs. 186, 187, 188, 
and 189. 

When used on four-wire two-phase circuits one operating ele- 
ment is connected in each phase exactly as though it were a 
single-phase meter and it is evident that under these conditions 
a meter theoretically correct will register accurately on balanced 
or unbalanced circuits. 

It is not so evident, however, that two single-phase meter 
elements combined into one instrmnent will register all of the 

-y— (5feh 



A^ 



T 



^ <?. /; 
&&' 



yijsm 







Fia. 190. 



energy supplied by a three-phase circuit. It is true, nevertheless, 
as can readily be shown. 

198. Relation of Power to Torque in a Y-connected System. — 
The two general methods of connecting three-phase receiving 
circuits are shown in Figs. 190 and 191. In the F-connected 
system if e©, Ci, 62 and to, Zi, and ^2 are the instantaneous voltages 
and currents applied to loads Lo, Li, and L2, the instantaneous 
power is 

w = Coio + eiii -f- ^2^2 

but the torque exerted by the two meter elements is 

r = e\ii + e\i% when the meter is properly adjusted. 

The difference between w and r is 

i« — r = {eoio + e\i\ + 62^*2) — (e'lti + e\i%) 
but e'l = 60 + 61 

and e'2 = €0 + 62 

therefore, 

w — T = ieoio + eiii + 62^2) — [i\{eo + ei) + t2 {eo + et)] 

= {coio + eiti + e%i^ — {fioii + Ciii + eoi% + e^it) 

= eo{io — ti — ii). 



228 



ELECTRICAL METERS 



Since the middle wire at each instant may be considered as the 
return for wires 1 and 2, then to — ii — ta = under all conditions. 
Hence 

w — T ^ eo{io — i\ — is) = 

and the watt-hour meter registers correctly the total energy in 
a F-connected system no matter whether the load be balanced 
or unbalanced. 

%OQbO/ 




'f * I • 

^ I — l\ "T lo 

.... 

% % = %2 — lo 



Fig. 191. 

199. Relation between Power and Torque in a A (delta) -con- 
nected System. — Using the same notation in Fig. 191 as in Fig. 
190 the instantaneous power supplied to loads Lo, Li, L2, is 

w = Colo + C\ii + 62^2, and the torque r = eii\ + e^i' 
but 
and 
hence 

w — r = Colo + eiii + 62^2 — (^i^i + ^\io + ^2^2 — ^iio) 

— Coifo '~~ ^1^0 "T" ^2^0 

= ioico — ei + 62) 
but 60 — 61 + 62 = 

therefore, ly — r = 0. 

Again the torque at each instant is just equal to the power, and 
hence, the average torque must be equal to the average power 
and the meter registers correctly on both balanced and unbalanced 
loads. 

It should be noted that no conditions have been imposed upon 
the character of the electromotive forces or curi*ents and, there- 
fore, the demonstrations are true no matter what the form of 
voltage or current wave or what the power-factor may be. 
When the meter is theoretically correct and properly connected 



WATT-HOUR METERS 



229 



to the circuit it will register correctly under all conditions of 
load. That is, any inaccuracy will not be due to the method of 
use, but will be due to faulty characteristics of the meter. 

Furthermore, it must be perfectly clear that two separate single- 
phase meters may be used in place of the polyphase meter and 
that the sum of their registration will give the true energy. One 
single-phase meter alone will not register the correct energy 
unless the separate phases are accurately balanced. As this is 
seldom the case it is best to use either two single-phase or one 
polyphase meter. 

200. Polyphase Meters for Four-wire Three-phase Systems. 
— In Fig. 192 is shown a y-connected four-wire three-phase 



f 



' 3 



L 



A/ 




Fig. 192. 

receiving system. In Article 198 it was shown that a three-wire 
polyphase meter registered correctly when e<,(io — i\ — ii) = 
and that under the conditions there assumed to — ii — 12 always is 
zero. When, however, another wire is added, as shown in Fig. 
192, to may no longer be equal to Zi + 12. When io ^ ii + 12, w is 
no longer equal to r and the meter registration is in error. Thus 
it is seen that a three-wire polyphase watt-hour meter cannot be 
used on four-wire circuits. 

A combined Y and A four-wire receiving system is shown in 
Fig. 193. Representing the instantaneous currents and pressures 
by i and e with proper subscripts and primes, the instantaneous 
value of power consumed in the system is 



but 



w = eiii + 62X2 + Cziz + e\i\ + e'ii't + e'zi\ 
e\ = ei — ez] e\ = ez — €2; e\ = 62 — 61 



Substituting these values of e'l, e'l, and e'» we get 
V) = eiii + 6212 + eziz + i\ (^i — < * * '- ^' 



+ i'% ie% - ei) 



230 ELECTRICAL METERS 

or tt = ei (ti + i'l - i'j) + c, {(J + I'j ~ ij) + ci (i, + i'l - tT 
but 

t'l + i'l — I'l = i"i; Is + i't — i'\ = t"»; ti + t'l — I'l = i"j 
hence, to = eii"i + eii"i + fit"*. 

ei, ei, and Cg are the voltages between neutral N and mains 
1, 2, and 3 respectively; and i"i, j"j, and i") are the currents in 




the corrDBponding mains. To measure the energy, either three 
single-phase watt-hour meters or a specially designed polyphase 
meter is necessary, 

A four-wire three-phase meter differs from a three-wire meter 
mainly in the winding of the current coils. The four-wire meter 




PiQ. 19-1. 

contains four series coils, two of which, one on each element, are 
connected in series and carry the current in one line wire. The 
other two scries coils, one on each element, are separate, and each 
carries the current in one of the other line wires. A < 
of such a coonection is shown in Fig. 194. 



WATT-HOUR METERS 231 

Representing the voltages between mains 1, 2, 3, and neutral 
by Ely Ei, and E3 respectively, then according to Article 200 the 
total power at any instant is equal to 

w = eiii + 62^2 + ^zU- 

The methods of connections employed show that the driving 
torque in terms of electrical quantities must be 

r = eiii + eiZ2 + ^3^2 + ^3*8« 

Hence, to — r = eiii + 6212 + Wz — ^i^i — ^1^2 — e^it — ^sis 

= 62^2 "" 61*2 "~ ^3^2. 
W — T = {2 (^2 — Ci — 63) 

but 62 — ei — ez = 

hence, the total energy will be registered by a four-wire meter 
when connected as shown in Fig. 194, however unbalanced the 
circuits may be. 

201. Balance of Metering Elements. — In order that the poly- 
phase meters may register correctly when the circuits are im- 
equally loaded, they must be adjusted so that the driving torques 
of the actuating elements are equal when the same amount of 
power is passed through each. If these two torques are not equal, 
the meter wiU run too fast when one side is carrying most of the 
load and too slow when the other side is loaded more heavily. 

Since the driving torque is proportional to the product of the 
maximum values of current and voltage-coil fluxes, it is evident 
that changing the number of turns on the voltage coil will change 
the torque. This is the method of balancing used by some 
makers. Another method based on the same fundamental 
principle consists in changing the reluctance of the path of the 
voltage flux. This is accomplished by the use of a short-cir- 
cuited turn, called "balancing loop," upon the voltage-coil core. 
Changing the position of this loop changes the reluctance of 
that part of the magnetic circuit, and causes more or less of the 
flux to pass through the disk and interact with the flux of the 
current coils. This again increases or decreases the torque of 
that element. The method employed in the Sangamo meter is 
explained in Art. 181. 

202. Interference of Elements. — One source of error to which 
polyphase meters are liable is due to the electromagnetic inter- 



232 



ELECTRICAL METERS 



action between the elements. This source of error was invM 
gated by the Electrical Testing Laboratories and it was found 
that different makes differed considerably in this respect. In 
Bome makes the effect of interference of the elements was so 
small that careful tests failed to detect any error due to this 
cause. In other makes, tlie interference was such that relatively 
serious errors might under certain conditions be produced. 
These facts were brought to the attention of the manufacturers 
whose meters were defective in this respect, with the result that 
these defects have been remedied, and polyphase meters now on 
the market are practically free from errors due to this cause. 

SiD3. Effect of Power-factor on Operation. — In Articles 198 
and 199 it was shown that a polyphase meter connected as 
shown in Figs. 190 and 191 will correctly register the total 
energy transmitted no matter whether the load be balanced or 
unbalanced. 

The instantaneous torque on each element is 

Ti = fill, 

and T» = eii'a, where ej, a, ii, and ii are the instan- 

taneous line voltages and currents, respectively. In a A-eon- 
nected system Ci and ei are the instantaneous voltages at load 
terminals, and ii and ij are the differences between currents in 
mains 1 and and mains 2 and 0, Fig. 191. Thus, in Fig. 195, 
tin, lin, and /o„ are maximum values of currents in branches 
AO, BO, and AB of Fig, 191. /i„ is shown as lagging 9 degrees 
behind Ei™. The vector difference between /i« and 1^ is /« 
which evidently lags 30° behind /i„ and {8 + 30) degrees behind 
Ein- The average torque on one element is then T\ = EI 
cos (0 ■+■ 30) degrees, and by a similar process of reasoning it 
can be shown that the average torque on the other element is 

T, = EI COS (e - 30) degrees, 

where E is the effective pressure between mains and / is the 

effective value of current in mains. 

When 5 = 0, Ti = Tt = EI cos 30°, 

When = 30°, Ti = EI cos G0°, 

and Ti = EI or Tj is twice 7",, 

when e = 60°, T, = EI cos 90° = 0, 

and Tt = EI cos 30° = HVsEI. 

That is, the total driving torque is exerted on one element only. 



WATT-HOUR METERS 

When e = 90°, Ti = EI cos 120° = - ^> 

£7 



233 



and 



Ti = £7 cos 60° = + 



In this case the two torques are equal and opposite. When is 
> 60° and < 90°, Ti is negative while T^ is positive. The 
effect of Ti is thus to drive the meter in a direction opposite to 
that of Ti. 

This clearly shows the importance of properly connecting a 
polyphase meter to a circuit. 




Zj 'Z-X 



//j> 0/9 



■^s 



<w 



FiQ. 195. 



204. Effect of Improper Connections. — ^A three-wire three 
phase meter will in general have six free terminals; four for the 
series coils and one each for the two voltage coils. From Figs. 
190 and 191 it is evident that the series coils may be connected 
in any two of the line wires, but that when so connected the 
free ends of the voltage coils must be connected to the third wire, 
preferably to the same point. It has already been pointed out 
that when properly connected, the torque on the two elements 

23 



234 ELECTRICAL METERS 

is in opposite directions on loads whose power-factor is less than 
0.5. It is thus erroneous to assume that the meter will register 
correctly if the meter disk rotates in the proper direction when 
either voltage coil is disconnected. Hence, disconnecting the 
voltage coils in succession and noting the direction of rotation 
cannot be used as a check upon the correctness of the connections 
unless the power-factor is known. 

One wrong connection for a three-phase three-wire meter is 
shown in Fig. 196. The series coils Si and S2 are properly con- 



6ener€rtot 






.^ 






LJ LbteL--i 



IbLoacf 



4. 

Fig. 196. 



nectbd but the voltage coil of Y\ is connected to main 2 instead 
of main as it should be. When so connected, the instantaneous 
torques on the two elements are 



Ti = Col'l 



and Tj = €2^'* 

The average torques on balanced circuits will be 

T\ = average eoi'i 
and T^ = average e^i'^ 

Now Eom is (150 + ^) degrees out of phase with /« as shown in 
Fig. 175. Hence 

Tx = EI\ cos (150 + 6) degrees 

= EI cos (150 + S) degrees where E 
and / are effective voltage and current respectively. It has been 
shown, Article 203, that 

^2 = EI cos (30 - S) degrees 

When ^ = 0, Ti = - >^ ^EI, and 5^2 = ^ Vsi?/. 

The two torques are thus equal but in opposite directions. 
Reversing the connection of the pressure coil of Fi, its torque is 
reversed and the total driving torque is 



WATT-HOUR METERS 235 

and the meter registers correctly. When 6 = 30°, Ti = EI 

and Ti = EI and T = 2EL The load, however, is VsEJ cos 
30° = l.5EIy and the meter registers 333^^ per cent too high. 
This shows that although the meter registers correctly on load 
of unity power-factor, it will not register correctly on loads whose 
power-factor is less than unity. The registration will also be 
incorrect when the three-phase system is unbalanced. For cor- 
rect registration, the four-wire three-phase meter may be con- 
nected to the circuit in practically one way only. This is due to 
the fact that there is only one neutral wire, and the voltage coils 
must both be connected to this neutral conductor. It is very 
necessary then to know the exact order in which the mains are 
to be connected, and which is the neutral conductor. Since the 
voltage between the neutral and any line wire is less than between 
any two mains, which of the four wires is the neutral conductor 
can easily be determined by means of a voltmeter. When this 
is determined, the diagram of connections furnished by the maker 
must be carefully followed. 

206. Prepayment Watt-hour Meters. — In many instances it is 
advisable to collect pay for energy in advance of its use. For 
instance, the use of prepayment watt-hour meters simpUfies the 
station bookkeeping, and relieves the proprietor of all responsi- 
bility as regards electrical bills when meters are installed in apart- 
ment buildings whose tenants frequently change. For such and 
other service of like nature, prepayment meters have been 
developed. 

The principles of operation of the meter proper are the same 
as those already discussed. That is, on the electrical side the 
instrument is either a direct- or alternating-current watt-hour 
meter to which has been added a device which by the insertion 
of a coin and the turning of a knob automatically closes a switch 
and keeps the circuit closed until the energy paid for has been 
used, when the circuit is automatically opened. The external 
appearance of a General Electric prepayment meter is shown in 
Fig. 197. 

206. Prepayment Device. — One form of prepayment device is 
shown in Fig. 198. This consists of a drum the front of which 
is formed by the crediting dial and the back by the double gear 
wheel B. The wheel B contains both spur and annular gears, the 
second are not shown as they are within the drum. Within the 
drum is also an actuating spiral spring C, and two gear wheels. 



ELECTRICAL METERS 





WATT-HOUR METERS 



237 



One of the gear wheels is mounted on the knob stem to which it 
is locked by the coin. The other intermediate gear plainly 
shown, is mounted on a stud which is fastened to the front dial 
plate. This intermediate gear meshes with the pinion on the 
knob stem and the annular gear of wheel B. The spur gear of 
the wheel B meshes with a pinion of the escapement mechanism 
D. This mechanism is released by the operation of the registering 
mechanism of the meter proper, one gear of which meshes with 
pinion E. 

207. Operation. — The prepayment mechanism is operated as 
follows: The coin that is inserted in the slot in the crediting knob 
Btem acts as a key and locks the stem of the knob to the pinion 
on its end. On turning the knob one-half turn to the right, the 
pinion is carried with it, causing the intermediate gear to roll 
round on the annular gear of the wheel B and to carry with it 
the crediting dial. This action winds up the springs and at the 
same time, by the action of a cam, the switch lever F is moved 
upward, closing the circuit through the meter. This operation 
of crediting may be repeated until the coin register at the bottom 
of the meter shows that the full number of coins for which the 
meter is designed has been inserted. When current is taken 
the intermediate gear and dial are driven by the main spring in 
the opposite direction. The pinion E, which is driven by a gear 
of the meter registering train, carries a cam G. This cam as it 
revolves osciUates the bell-crank H, which in turn moves a finger 
backward and forward across the rim of the release gear I in 
mesh with the damper fan. 

Pinion E makes one complete rotation during one oscillation 
of the finger; during the first half of the rotation, the finger dis- 
places a catch from a pin set in the rim of the gear I, and during 
the second hah of the rotation it is withdrawn from the pin. 
When the finger K has returned to its outer position, the gears 
of the escapement mechanism are free to rotate under the action 
of disk B, which is driven by the main spring. The gear D makes 
one rotation every time the catch is released. A pin on this gear 
pushes the catch back into the path of the stop-pin on gear I 
and so arrests its motion after it has made the requisite number 
of rotations to permit the turning back of the crediting dial one 
place. At every rotation of pinion E this operation is repeated 
until the purchased energy has been used, when a cam on the 
dial plate automatically opens the meter circuit. 



338 ELECTRICAL METERS 

It is very evident that since the prepayment device is control 
by the registering mechanism of the watt-hour meter, it can be 
used on watt-hour meters of any type. In fact, a sUght modifi- 
cation of the device and the meter with which it is to be used, 
permits the installation of the prepayment mechanism at points 
distant from the meter. When the device is to be installed 
separately, the escapement mechanism is controlled by an electro- 
magnet connected directly into the line. The excitation of the 
electromagnet is governed by 
suitable gears and the com- 
mutating device in the regis- 
tering mechanism of the watt- 
hour meter. 

There are several other de- 
signs of prepayment meters 
manufactured, especially in 
England. In this country 
the use of the prepayment 
meter is quite limited, con- 
sequently no other forma will 
be explained. The general 
appearance of the Westing- 
house prepayment meter 
with cover removed is shown 
in Fig. 199. 

208. Bases of Energy 
Rates. — The coat of supply- 
ing electrical energy depends 
not alone upon the amount supplied but also upon the time 
and rate of supplying the same. Any equitable method of 
charging should take these things into consideration. The com- 
mon method of charging, which allows discounts in proportion 
to the quantity of energy used, is just in some respects, but it 
does not take into consideration the time and rate of supply 
elements as mentioned above. 

In order to take into consideration these two elements, two 
types of instruments have been devised. One type, known as the 
two-rate meter, permits the collection of two different rates; a 
relatively high rate for energy used during the peak of the load, 
and a relatively low rate during the rest of the day. This method 
of charging tends to discourage the extravagant use of electrical 




WATT 'HOUR METERS 239 

energy during heavy load, and increase its use during periods of 
light loads, thus increasing the load factor. The second type of 
instrument is described in Chapter XV. 

209. Two-rate Meters. — The essential difference between a 
two-rate or double-tariff meter and a regular watt-hour meter is 
the addition of an extra registering train 'and clock. The clock 
controls a suitable switching-over clutch mechanism for throwing 
on or off the separate registering mechanisms. One registering 
mechanism indicates the energy consumed during the time of 
peak load, and the other during the other hours of the day. The 
clock automatically, and at the proper time, connects either the 
high- or low-rate train; a high rate being charged for energy con- 
sumed during the hours of the peak load. The use of a two-rate 
meter has not met with great favor in this country. From a 
mechanical standpoint the two-rate meter is practical and has 
been successfully carried out in practice. 



CHAPTER XIV 
INTEGRATING METERS, AMPERE-HOUR METERS 

210. Introduction. — In many industries using electric current, 
it is advisable and often necessary to know the quantity of 
electricity that has been used within a given time. This is 
especially true in industries whose operation depends upon 
electrolytic processes, and in charging storage batteries. 

The unit of quantity of electricity is the coulomb, and a cou- 
lomb has been defined as the quantity of electricity given by 
1 amp. in 1 sec. In 1 hr. a constant current of 1 amp. will give 
3,600 coulombs. For practical purposes, the coulomb is too 
small a unit, and hence 3,600 coulombs, called the ampere-hour, 
are used as the unit. Commercial instruments whose registra- 
tions are proportional to the quantity of electricity passing are 
called ampere-hour meters, and are of two types: electromagnetic 
and electrolytic. 

211. Electromagnetic-t3rpe Ampere-hour Meter. — In the dis- 
cussion on watt-hour meters it was shown that the registration is 
proportional to EIL Hence, it is evident that if E remain con- 
stant the registration will be proportional to It. If t is in hours 
the scale may be graduated in ampere-hours. Thus, a watt-hour 
meter with constant voltage-coil excitation may be made to 
register in ampere hours. 

Since alternating currents cannot be used for electrolytic 
processes, an alternating-current ampere-hour meter would be of 
little practical use. For direct currents the constant field excita- 
tion is best obtained by the use of permanent magnets. 

The essential features of the Sangamo ampere-hour meter are 
shown in Fig. 200. The similarity between the ampere-hour 
meter and the mercury watt-hour meter is plainly evident. In 
place of the electromagnet of the voltage field the ampere-hour 
meter is provided with a permanent magnet. The operation 
of the ampere-hour meter is in every respect exactly like that of 
the watt-hour meter. The current flowing from one terminal 
through the disk to the other terminal reacts with the permanent- 
magnet field. This reaction produces a torque upon the disk, 
24 241 



242 



ELECTRICAL METERS 



causing it to rotate. Since the field is constant, the torque, 
and hence speed, is directly proportional to current strength. 
The counter-torque is obtained by rotating an aluminum disk, 
which 13 mounted on the shaft between the poles of permanent 
magnets exactly as on watt-hour meters. The dial ia graduated 
in ampere-hours instead of watt-hours. 

It is well known that the efficiency of a storage battery varies 
with the rate of charge and discharge, and that the number of 




ampere-hours required to charge the battery is greater than is 
given out on discharge. In order that an ampere-hour meter 
may indicate the condition of the battery with a reasonable 
degree of accuracy some provision must be made whereby this 
difference in ampere-hours is automatically corrected. In the 
Sangamo meter this ia accomplished by shunting the movable 
element by a variable resistance. This variable resistance con- 
sists of a small copper bar pivoted at the center and immersed in 
mercury, as shown in Fig. 200. This bar is free to rotate 
through a small angle from a position directly in line with the 



two contact poii 
ber. The move 
which ia adjusta 

The resistor 
chamber of the 
from the poles o 
chamber bo that 
have the same 


AMPERE-HOVR METERS 

ts at the opposite sides of the mercury 
ment of the bar is limited by two stops, 
3le. 

element is clamped below the main m 
meter and there ia sufficient magnetic le 
f the permanent magnet through this m 
any current flowing through the copper b 
effect as the current through the meter 

ITppar Scle - PBiomOiie of luil It 
Locsr Sols- AmDen Lool 
100 MO 2M SM 300 


243 

cham- 
ane of 

rcury 
akage 
jcury 
r will 
disk. 














































































































- 
















































































































































































^102 






































































































>.- 




-- 


- 




















































































































































When the meter 

position indicate 

the resistance of 

will register a q 

charge the batte 

^K battery ia discha 

^H chamber is rever 

^P increasing the p 

the resistance of 

current through 

movable element 

^B sequent increase 

^M fltop-pina may be 


FiQ. 201. 

IS recording the charge, the copper bar ia 
i in Fig. 200, that is, it is in such a poaitio 
the resistor is a minimum, and thus the 
uantity somewhat less than that requir 
ry. The meter is slow on charge. Whe 
rging, the current through the resistor me 
ed; the copper bar is deflected through an 
ath of the current through the mercury 
mercury is about 60 times that of coppe 
the resistor is decreased and that throug 

of the meter is relatively increased with 
in the speed of the meter. The postion 

adjusted so that the meter will operate a 


in the 
itbat 
meter 
ed to 
n the 
rcury 
angle 
As 
r, the 
h the 
icon-. 
)f the . 
t any 



344 



ELECTRICAL METERS 



percentage of battery overcharge desired between the limits of 
and 25 per cent. 

212. Accuracy Characteristics. — Two curves showing the per- 
centage of accuracy of a 10-amp. meter with and without shunt 
are shown in Fig. 201. It will be observed that on currents below 
5 and above 15 amp, the accuracy falls off quite rapidly. This 
falUng off is much more rapid at low values of current than at 
the higher values. The cause of the deviation of the percentage 
of accuracy curve from a straight line at low values of current is 
undoubtedly due to the effect of friction, as no compensating 




device is used. The deviation at the higher values is due pri- 
marily to fluid friction. An external view of a Sangamo am- 
pere-hour meter is shown in Fig. 202. 

213. Electrolytic Ampere-hour Meters. — The principles ac- 
cording to which electrolytic or ampere-hour meters operate were 
discovered by Faraday, and are, therefore, known as Faraday's 
laws. These were discussed in Article 17. The passage of 
electricity through an electrolyte decomposes the chemical com- 
pound, and the mass of the metal deposited is a measure of the 
ampere-hours. As long as the voltage remains constant, the 
energy transmitted is proportional to the ampere-hours; hence, on 
qonstant-voltage circuits such instruments will indicate a quan- 
tity proportional to ampere-hours. The name wattmeter com- 
monly applied to these instruments is plainly a misnomer. 



AMPERE-HOUR METERS 



245 



214. Edison Electrolytic Ampeie-houi Meter. — The Edison 
electrolytic or chemical meter employed two zinc plates in a solu- 
tion of zinc sulphate, the bottle containing the plates being placed 
in the meter at the beginning of the month and replaced by a simi- 
lar bottle at the beginningof everymonth. Oneof the zinc platea 
(the anode) was carefully weighed before and after this term of 
service, and from the loss, the current, and hence the monthly 
bill, wag calculated. To pass the whole current through the 
bottle was impracticable, on account of the large size of platea 
that would be needed; the bottle was, therefore, put in a shunt 
circuit, and only about 1/1,000 part of the main current passed 
through it. This shunting caused a large part of the theoretical 
accuracy and reliability of the electrolytic meter to disappear; 
the voltage causing electrolysis being very low at light load, any 
polarization in the cell, or abnormal resistance due to oxidation 
of the plates, would make the meter indications too low. 

This meter was used to a considerable extent, and may, perhaps, 
still be found in some installations. 

215. The Bastian Ampere-hour Meter. — An electrolytic meter 
that is still on the market, and perhaps the simplest in construc- 
tion, operates by decomposing water. The whole current passes 
through acidulated water, decomposing it into its constituent 
gases which are allowed to escape. The drop in the elevation 
of the liquid is a measure of the ampere-hours supplied to the 
consumer. 

In the older type, two platinum electrodes are suspended in the 
liquid at the bottom of a long glass tube open at the top. The 
bore of the tube is as uniform as possible throughout its length. 
The suspending leads are enclosed in two vulcanite tubes screwed 
into a vulcanite frame which forms a protection for the platinum 
electrodes enclosed by it. A scale graduated in watt-hours or 
kilowatt-hours at a definite voltage is fixed in front of the tube 
in such a manner that the level of the electrolyte can be readily 
read. The glass vessel is enclosed in a cast-iron or sheet-iron 
case in front of which is a long window. The electrolyte is a 
dilute solution of sulphuric acid and water. Since only the water 
is decomposed, it is necessary to refill the tube with water alone. 
To prevent evaporation, paraffin oil is poured on top. There are 
several objections to this meter. Among the most important are 
the following: 



146 ELECTRICAL METERS 

1. Large and variable pressure drop. 

2. Necessity for refilling with water. 

3. If left too long in circuit, all record is lost. 



The pressure drop across the elec- 
trolyte is never less than 1.5 volts, 
and in a 5-anip. meter, under full 
load, may be 3 volts. This drop is 
variable, depending to some extent 
upon the height of the column of the 
quid in the tube. 

Since different consumers use dif- 
ferent quantities of energy, the re- 
filling of the meters becomes quite 
complicated. If left too long all 
record is lost, and disputes are liable 
to arise between the consumers and 
the supply company. 

The advantages claimed for this 
meter are : 

1. Extreme simplicity. 

2. Small chance of getting out of 
order, when properly cared for. 

3. Low first cost. 

In a later form of meter the 
platinum electrodes have been re- 
placed by nickel, and the electrolyte 
Fig. 20a. '9 an alkaline solution which has no 

action upon the electrodes. The 
substitution of nickel for platinum permits the use of larger 
electrodes at a reasonable cost, and the resulting pressure drop 
is less. Fig. 203 shows the complete instrument. 




CHAPTER XV 
DEMAND INDICATORS 

216. Introduction. — In Article 208 it was mentioned that two 
types of instruments have been devised for the purpose of making 
energy rates more" equitable. The two-rate meter has been 
briefly mentioned. With the other type of instnunent, known 
as the maximum demand indicator, the charge is at a rate depend- 
ing upon the ratio of consumption to the maximum demand. 
These instruments may be classed under three heads: thermal, 
induction, and mechanical. 

217. Thermal Type. — The main features of the Wright maxi- 
mum ampere demand indicator whose operation depends upon 
the heating effect of the electrical current are shown in Fig. 204. 
The principle of operation is that of the recording thermometer. 
That is, the meter does not directly indicate the maximiun ampere 
consumption, but indirectly by heating a column of air whose 
expansion is proportional to the square of the current passing. 
As shown in Fig. 204, the instnunent consists of a U-shaped 
tube with a bulb at each end partly filled with sulphuric 
acid and hermetically sealed. A resistance of platinoid is 
wound around bulb A and connected in series with the cur- 
rent or a shunted part of the current. The heat generated by 
the current flowing through the resistance expands the air in the 
left bulb, and this expansion forces the Uquid into the right hand 
part of the V. As the liquid rises above a certain height, it flows 
over into the index tube. The amount of liquid flowing over into 
this tube is proportional to the expansion of the air in bulb A 
above that in bulb B. The expansion of the air is proportional 
to the square of the current flowing through the resistance coil. 
If the tube has a uniform bore, the height of the liquid in the indi- 
cator tube will be a measure of the square of the maximiun cur- 
rent. The head generated by a current in a resistance is equal to 

where / Is current, R resistance, and i is the time. It will thus 
require some time for the air in tube A to reach a maximum 

247 



248 



ELECTRICAL METERS 



tiimpemturc, or ii temperature aufficieiitly high to indicate 
iiiaxiinuni current. The manufacturers state that if the load 
continuca for about 40 miu. the full 100 per cent, is indicated. 
Momentary overloads are not recorded. An overload continuing 
for some time will, however, fill the index tube and make an 
accurate record impossible. 

Since the indication is proportional to the square of the current, 

the scale cannot l>e uniform if the bore of the indicator tube 

18 uniform. An examination of the 

scale will show that the divisions 

increase from the bottom up. 

After a reading is taken, the 
instrument is reset by tilting and 
allowing the liquid to flow back 
into tube B. To prevent the pas- 
sage of air from one side of the U 
to the other, small inverted glass 
funnels called "traps" are rigidly 
fastened to the bottom of the U. 
When the indicator is being reset, 
-Capiikny ^iig traps remain covered by the 
liquid, preventing the passage of 
air into the wrong aide of the tube. 
Indicators whose maximum 
capacity is 25 amp. may be used 
interchangeably on direct- or al- 
ternating-current circuits without 
shunts. Indicators of larger than 
25 amp. and less than 200 amp. 
are provided with shunts and may 
be used on either direct or al- 
ternating currents. Current transformers must be used in all 
cases on alternating-current circuits where the voltage exceeds 
1,150 volts, and also where the current capacity is over 200 amp. 
The fact that the indications of the thermal type of indicator 
depend upon the square of current only, makes it evident that it 
will not give correct indications of maximum power on circuits 
whose power-factor is other than unity, or on circuits of variable 
voltage. 

218. Inductioo Type. — The registration of the induction-type 
maximum-demand indicator is determined by the maximum 



Capillary 







Pin. 204. 



DEMAND INDICATORS 



249 



power consumed for a definite time and not upon the maximum 
current, as in the case of the thermal type. Since the deflection 
of a wattmeter is determined by the power, it is evident that an 
ordinary wattmeter could theoretically be used to indicate the 
maximum watt demand if the meter were provided with another 
pointer which would remain at the point of maximum deflection. 
Since it is not desirable to keep records of momentary fluctua- 
tions, such a scheme is not used. The recording wattmeter 
records not only the maximum and minimum demand but also 
the duration of such a demand. 

Since the torque on the movable element of the watt-hour 
meter varies with the load it too may, with some modifications, 
be used to indicate the maximum watt 
demand. The polyphase maximum 
watt demand indicator of the General 
Electric Co., shown in Fig, 205, is es- 
sentially a polyphase induction watt- 
hour meter with both actuating ele- 
ments acting upon the top disk. 

To secure the proper time lag, the 
retarding system consists of several 
powerful permanent magnets arrange tl 
around the periphery of the lower disk. 
In addition to the retarding effect of tht* 
permanent magnets, the motion of the 
movable element is opposed by three Fio. 205. 

spiral springs connected in series. 

There are enough convolutions In these springs to permit the disks 
to make three complete rotations. The regular registering mech- 
anism is replaced by a circular dial with a scale over which move 
two pointers. One of these pointers is driven by the movable 
element of the instrument by means of a reducing gear so that 
it makes only one complete revolution while the movable ele- 
ment makes three. The second pointer is moved by the first 
in a forward direction only, and is left at the extreme position 
reached by it, being held in place by a ratchet. The second 
pointer indicates, therefore, the maximum energy that has passed 
through the indicator since it was last set. The second pointer 
is reset by a thumb nut. Since the driving torque of an induc- 
tion watt-meter is proportional to the power, and the reaction 
of the spiral spiing is equal to the torque, it follows that the 
scale of such an indicator is uniform. 





250 



ELECTRICAL METERS 



219. Time Lag. — As already mentioned, momentary fiuctua- 
tions of load would not be a juet basis for rate-making, as they 
might not indicate a legitimate demand. Hence, some time 
should elapse before the indicator pointer reaches its extreme 
position. This time interval ia controlled by the amount of 
magnetic damping of the disk and counter-torque of spiral 
spring. The following demonstration, which may be omitted 
by students unacquainted with the calculus, shows this: 

Assuming the change in the load to be instantaneous, the driv- 
ing torque is proportional to the change in load, and is constant 
so long as the load is constant. The counter-torque is due to the 
damping magnets and to the reaction of the spiral controlling 
spring. The torque due to damping magnets is proportional to 
the speed of the disk, and the torque due to spring ia directly 
proportional to the deflection. This may be expressed by 

Torque = Koi^ + KiS 

where u is the angular speed, and 6 is the deflection. 

But " ~ di "^ '"^'^ ^* which deflection is changing. 

Then Torque = T = K„-,- + A',fl 



and 

whence 



Tdt = Ktd9 + K,edt 



Integrating between t = 0, and t = ii, which limits for time 
correspond to 9 = 0, and fl = ffi we get 



, - K f"— *?— 



'I<^- 



This shows that /i ia a logarithmic function of 9. 
Solving the above for KiOi, we get 



Xifli = r 1 -eK- 



The time lag ia defined as the interval of time taken to record 
90 per cent of any change in load, which amounts to the same 
thing as to aay that it is the interval of time required for the 



DEMAND INDICATORS 261 

pointer to deflect 90 per cent, of the maximum deflection due to 
a given change in load. According to the equation for Kidi, 

when the pointer has deflected -th of the maximum deflection 

Ki-ei = -T. 
n n 

■ 

Then 

where U is the time required for a deflection of - d\ 






and e*» = 



n- 1 



and -f^ h log e = log 



Xo ^ ^n- 1 

1 ^ 
and gg ^^n~l 

^' ■" Ki log e 
If the deflection is to be 90 per cent of the maximum deflection 

- = 0.9 

n 

and n = -q- 

Then ,, = fl2ii0.2.3f'- 

Ai log 6 A.1 

This shows that the time lag h depends mainly upon the ratio 
of Ko to Ki. Now Ko is determined by the strength of the field 
of the permanent magnets and their distance from the shaft. 
Ki is determined by the physical properties of the controlling 
spring. Ko is large when the permanent-magnet field is strong, 
and Ki is small when a spring of many convolutions is used. 
t2 then is large when many permanent magnets and weak con- 
trol springs are used. It is also clear that changing either one 
of these factors will change the time lag. Curve of Fig. 206 
shows the relation between the per cent of deflection and time. 



H^ 253 ELECTRICAL METERS V 

^H If Ko and Ki were known, this curve could be plotted from V 
^^M the equation H 

^H H 

^m A',e, = ^(l - e~A-. d)- ■ 

^H This iustnunent has the advantage that the maximum demand H 
^H can be read at once from the dial, and that it is easy to maintain. H 
^^M The disadvantage is that no record of demand is obtained other H 
^H than that taken down by the meter reader, and that the time H 
^^^^^^ at which the maximum demand occurred is not indicated. fl 


























































































^^1 ;^^M.v^ 
^V Pi(i. 20G. 

^^1 The polyphase watt-demand indicator may be used on single- 
^H phase as well as polyphase circuits. When it is to be used on 
^^M single-phase circuits, the current coils are connected in series 
^H and the voltage coils in parallel. 

^H 220. Westinghouse Demand Indicator. — Instead of employing 
^H a separate instrument f<jr indicating the maximum demand, the 
^^^ Westinghouse indicator is a combination of a watt-hour meter 
^H and a demand indicator. The meter is essentially a watt-hour 
^H meter which has been modified by the addition of another disk 
^H which is driven by the shifting magnetic field in exactly the same 
^H manner as the watt-hour meter disk. The tendency of the 
^H auxiliary disk to rotate, however, is counteracted by a spiral 
^r spring. The construction and operation will be readily 
understood from Figs. 207 and 208. The auxihary disk 2 has 
its motion counteracted by the coiled or spiral spring 4 at the 



DEMAND INDICATORS 





254 



ELECTRICAL METERS 



upper end of the shaft. Upon the shaft is mounted a gear < 
which meshea with gear 10 on the counter which transmits the 
motion of the auxiliary disk tlirough a dog drive to the pointer. 
The pointer is held in its position of raaximura deflection by a 
fine-toothed rachct and pawl. In this respect the demand mech- 
anism does not differ materially from that of a wattmeter. 
In order that the pointer be not deflected instantly, further modi- 
fications are necsssary. The mechanism by which this is accom- 
plished consists of an escapement wheel 8 which engages with 
an escapement 13. The other end of the escapement lever is 
forked, and within this fork rotates an eccentric. This eccentric 
is rotated by the main disk through gears 11, 12 and 15. The 
schematic diagram of Fig. 207 shows the connections more 
clearly. The movement of the pointer is thus controlled by the 
motions both of the auxiliary and of the main disks. The motion 
of the auxiliary disk causes the pointer to deflect, and the speed 
or rate of deflection is governed by the main disk. As soon 
as energy flows through the meter, the auxiliary disk tends to 
deflect instantly to indicate the load just as the disk of the in- 
duction wattmeter, but it cannot do so on account of the action 
of the escapement. The main disk through the gears and eccen- 
tric already mentioned oscillates the escapement and thus per- 
mits the rotation of the escapement wheel one tooth at a time, 
just as in a clock, until the counter-torque of the control spring 
just balances the torque developed in the disk. The time lag 
is thus fixed and depends upon the gear ratio of the gears be- 
tween the shaft of the main disk and escapement, and the number 
of teeth on the escapement wheel. It is likewise constant, since 
the deflection of the pointer and the rate of deflection bear a con- 
stant relation to each other. 

221. Mechanical Type.^For the want of a better term, we 
shall call the third form of demand meter the mechanical type, 
since it is merely an automatic printing attachment to a watt-hour 
meter. The attachment is operated by clockwork in connection 
with the registering mechanism of the meter, while the printing 
device leaves a record of the rate of the use of energy on a moving 
tape. 

222. Operation. — The mechanical features of one make of the 
" Printometer, " as this typo of demand register is called, is shown 
in Fig. 209. 

The printometer can be attached to any type of watt-hour 



DEMAND INDICATORS 



253 



meter, and when so connected the type or recording wheels of the 
instrument are electrically interlocked with the registering 
mechanism of the meter. The movement of the recording mech- 
anism of the printomoter is thus in synchroniem with the move- 
ment of the meter register, and hence the record is an indication 
of the rate at which energy is being used. The printometer 
record is made on a paper tape by means of a copying ribbon 
which, at regular intervals, is pressed against the type wheels by 




a rubber platen. The rubber platen is actuated by a solenoid 
whose circuit is closed at regular intervals by a contact-making 
clock. 

In addition to the energy-recording mechanism, the instru- 
ment contains an hour wheel containing numbers from 1 to 24. 
This hour wheel is also automatically advanced so that by every 
imprint of the energy there js left a record of the time. This 
hour wheel is connected to the printing platen through a star 
wheel and pins, which are plainly shown in Fig. 209. By chang- 
ing the position of the pins, the wheel can be advanced in such a 
way aa to give readings every hour, half hour, 20, 16, 10, or 5 
nun. Fig. 210 shows a record of hourly readings. 

The circuit of the solenoid that advances the type wheels is 



256 



KhKCTRTCAL METERS 



closed through a (ionmiutator, which is mounted on one of the 
spindles of the meter register. Thia is shown in Fig. 211 and 
212. On the end of this commutator is a slip ring which is 
connected to a number of bars across the face. The number of 
bars depends upon the constant to be used with the 
attachment. There are three contact brushes, one 
bearing upon the slip ring, and the other two at op- 
posite points on the commutator in such relative posi- 
tions that they alternately close the circuit of the 
type-wheel actuating solenoid. To prevent the de- 
struction of the commutator by sparking, the circuit 
is broken by the forward movement of the plunger 
of the solenoid. As this moves forward it turns a 
contact wheel which is made of alternating segments 
of conducting and non-conducting material joined by 
a metal slip ring. Three brushes make contact with 
this wheel; one with the slip ring, and the other two 
with the segments. The distance between the two 
brushes is such that when one rests on a conducting 
segment the other rests on a non-conducting segment. 
The operation of the commutator and contact wheel 
in closing and breaking the circuit is much the same 
as that of two three-way switches. The closing of 
the circuit by the commutator on the registering 
mechanism of the meter excites the solenoid and 
drives the plunger forward. The turning of the contact 
wheel by the forward movement of the plunger changes the 
position of the brush on the conducting segment to a non-conduct- 
ing segment, thus breaking the circuit 
which again will be closed after the 
commutator on the meter register has 
rotated the proper distance. The 
solenoid circuit is thus closed by the 
slow-moving commutator and opened 
by the quickly moving contact wheel. 
Another form of maximum demand 
indicator is shown in Fig. 213. This is a device whichin conjunc- 
tion with a watt-hour meter indicates the maximum demand. It 
consists essentially ofa demand-registering and timing mechanism 
mechanicallyconnectedandmountedwithiu the same case. The 
demand-registering element is driven electrically from the roister 



■ffl 5 9 


.M 6S 


■■1 48 


IS 1 7 J 


M 1 7 B 


1 1 8 4 


■ IS! 


J 1 53 


4 1 9 J 


.19' 


,!02 


,207 
• 2 10 



Fig. 210. 




Fk;. 211. 



DEMAND INDICATORS 257 





258 



ELECTRICAL METERS 



of the watt-hour meter, wliile the tuning mechanism is driven by the 
action of a shifting magnetic field on a separate disk in the alter- 
nating-current indicator, or a clock in the direct-current indicator. 
The actual operation will be readily understood from a considera- 
tion of Fig. 214 which shows diagrammatically the essential 
parts of the alternating-current indicator. The contact on the 



Operetirtf Coil 




watt-hour meter opens and closes the electromagnet circuit t^ter 
a definite number of rotations of the watt-hour meter disk, that is, 
after the passage of a definite number of watt-hours. Every 
time the electromagnet circuit is closed the armature lever is 
moved forward and by means of the pawl or dog, ratchet wheel, 
and train of gears the friction pointer is moved along the dial. 
The interval of time during which the pointer is moved forward 
is determined by the timing mechanism. This consists of a disk 
and an actuating mechanism similar to an induction watt-hour 
meter. The disk is driven at a constant speed, and through a 
suitable train of gears it operates a trip lever by means of which, 



DEMAND INDICATORS 



259 



^ter a definite number of revolutions of the disk, the gear on the 
ratchet wheel arbor is disconnected from the train permitting the 
spring on the pointer staff to return the pointer actuating gears 
to zero. The pointer is held in its extreme position by friction, 
and hence will not advance unless the energy consumption during 
some succeeding interval of time exceeds that of the first. The 
position of the pointer thus indicates the maximum demand. 

223. Graphic Demand Meter, Type G. — -Type G demand 
meter of the General Electrical Co, does not merely indicate the 
maximum demand during a definite time interval, but it also 




^IG. 215. 

shows the time and duration of the demand. The external ap- 
pearance of a portable indicator is shown in Fig. 215. Its 
operating mechanism consists essentially of two parts, a register- 
ing element and a timing element. In addition to the device 
proper, the register of the watt-hour meterj with which it is to be 
used, is equipped with a cam and contact bri^hes for opening and 
closing the electromagnet circuit of the demand meter. 

The operation of this demand meter is well exemplified by the 
diagram, Fig. 216, The recording element consists of the stylus, 
electromagnet, ratchet and pawl mechanism, and gearing to trans- 
mit motion from the armature of the electromagnet to the stylus. 
The timing element is driven by an 8-day clock. 



360 ELECTRICAL METERS 

In service, the demaml meter is electrically connected to tne 
watt-hour meter with which it operates, and the contact device 
placed on the watt-hour meter register alternately makes and 
breaks the electromagnet circuit of the demand meter. 

When the contact device in the watt-hour meter closes the cir- 
cuit through the operating coil of the electromagnet of the de- 
mand meter the armature of the electromagnet is attracted, the 
armature lever is moved forward, and the pawl at the end of the 




Fig. 21G. 



armature lever turns the ratchet wheel, which through a system of 
gears moves the stylus upward over the chart. When the con- 
tact device opens the circuit through the operating coil of the de- 
mand meter, a spring returns the armature lever and pawl to their 
original positions. 

The stylus continues to move upward over the chart as the cir- 
cuit through the operating coil of the demand meter is alternately 
closed and opened by the contact device until the end of a time 
interval ia reached. At the end of each time interval, a cam, which 
is driven by the clock mechanism, has rotated to such a position 
that the first of two trip levers falls, thus disengaging a sliding 
pinion from the gear with which it meshes. This opening of the 



DEMAND INDICATORS 261 

gear train allows a spring to return the stylus mechanism to the 
zero position. Further rotation of the cam then allows the sec- 
ond trip lever to operate, thus returning the sliding pinion to its 
former position, and reestablishing the gear train between the 
armature and the stylus. 

The mechanism is now in position to again drive the stylus up- 
ward over the chart as the watt-hour meter registers the energy 
consumption during the next time interval. Since the clock 
mechanism rotates the chart continuously, each succeeding 
curve drawn by the stylus falls in a more advanced position on the 
chart. 

224. General. — Several other forms of demand indicators are 
now on the market. The maximum-demand instrument is used 
chiefly in connection with the sale of energy in large quantities, 
especially when this energy is supplied by polyphase systems at 
high voltage. The use of the maximum-demand meter is made 
necessary by the attempt to base the rates for electrical energy 
upon the cost to each customer. One of the elements of the cost 
of service is the current or power capacity of the generating equip- 
ment and of the distribution system. This capacity is, however, 
a function of the time and amount of the maximum demand of 
the customer, hence the use of demand indicators is at present 
slightly on the increase, especially among the public utilities 
that are subject to public regulation. 

With the exception of the thermal types the indications of de- 
mand indicators are proportional to watts or kilowatts. As the 
capacity of generating equipment is limited primarily by current 
rather than by power on a constant-potential system, it would 
seem more logical to measure maximum demand in amperes or 
kilovolt-amperes rather than in kilowatts. 



26 



CHAPTER XVI 

INSTRUMENT TESTING 

226. Introduction. — Every person who has the care and use of 
electrical instruments of any kind should observe certain pre- 
cautions in handling them. This is especially true with reference 
to portable instruments which are easily damaged by careless or 
ignorant use. 

226. General Precautions. — Too much care cannot be exercised 
in connecting apparatus for experimental or test purposes. The 
student should in every case do his thinking in advance and not 
depend upon correcting mistakes after some trouble has devel- 
oped. Avoid trouble by arranging everything properly before 
beginning the test. The supply mains should always be con- 
nected through a double pole in a two-wire system or a three-pole 
switch and each circuit should be protected by fuses. The main 
switch should be left open until all other connections have been 
made. When everything is properly arranged, a diagram should 
be made of the connections and examined in order to be sure that 
they are not endangered by overloads or short-circuits. When 
everything has been examined, the main switch may be quickly 
closed and opened to see if there is any indication of short-cir- 
cuits; if everything is in correct working order the main switch 
may be closed, and the work proceed; a sharp lookout for trouble 
during the early stages of the work must, however, be main- 
tained. The best general direction to a student is — do not 
guess — be sure you are right and then go ahead. While making 
adjustments, gently tap the dials of all indicating instruments so 
as to free them from frictional errors. 

227. Kinds of Tests. — The kind of test to be used in any case 
depends upon the degree of accuracy desired and facilities for 
conducting the test. In practice, there are two kinds of tests; 
these may be called standardization and checking tests. The 
standardization test consists in comparing the readings of the 
instrument tested with the fundamental units; the checking or 
comparison test consists in comparing the readings of the tested 
instrument with the readings of a similar instrument that has 
been previously standardized. The second test is the one usually 
used in central stations, especially the smaller ones. 

27 263 



264 



ELECTRICAL METERS 



9 ff 



228. Apparatus for Instrument Testing.— 'Primary standi 

instruments, that is, instruments for comparing meters with 
fundamental units, are not suitable for general use, but should 
be maintained in a few well-equipped laboratories. Large 
central stations may also be justified in keeping an equipment of 
these instruments. The instruments used to check working 
instruments may properly be called secondary standards. From 
time to time the secondary standards should be checked by some 
reliable standardizing laboratory, the Bureau of Standards at 
Washington, D. C, being one of the best. The number and 
kind of secondary standards to be provided will depend consider- 
ably upon the number and kind 
of working instruments. The 
most essential secondary in- 
struments are portable indicating 
ammeters, electrodynamometers, 
voltmeters, wattmeters, variable 
resistances or rheostats, and one 
or more of the portable stand- 
ard integrating watt-hour meters. 
If some of the simpler stand- 
ardizing tests are to be made, 
it will be well to include 
standard cells, galvanometer, 
potentiometer, and standard 
shunt resistances. 

229. The Standard CeU.— 
The International Electrical 
Congress of 1908 officially adopted the Weston cell as the standard 
of electromotive force. This cell is constructed of mercury sur- 
rounded by mercurous and cadmium sulphate paste for the posi- 
tive pole; cadmium amalgam for the negative pole; and a solu- 
tion of cadmium sulphate for the electrolyte. The cells must be 
built up according to definite specifications, and when so con- 
structed pressures of different cells agree to a few thousandths of 1 
per cent, when tested under like conditions. A cross-section of 
a saturated cell is shown in Fig. 217. The unsaturated cell is 
preferable for use with the potentiometer. 

On Jan. 1, 1911, the Bureau of Standards adopted a new value 
for the electromotive force of the Weston normal cell, namely: 
E = 1.01830 international volts at 20''C. 




Ca amalgam 



i - ^CdSQ. 



\^t^t^S 



■/^.iT/ec/roe*e 



Fig. 217. 



INSTRUMENT TESTING 



265 



The effect of temperature on the Weston cell is slight, so that for 
commercial measurements no corrections need be made. For 
more accurate measurements the electromotive force may be 
calculated from the following formula: 
E, = 1.01830 - O.OOOOlOeCf" - 20°) - O.OOOOOOSSCC* - 20'')» 
where the temperature f is in Centigrade degrees. This new 
unit of electromotive force is larger than the old, the change being 
equal to about 0.08 of 1 per cent, in the value of the international 
volt. Thia change affects to a slight extent all measurements of 
the electric current, electromotive force and power, and in some 
cases necessitates slight changes in measuring instruments. 




Fio. 318. 
230. Galvanometer. — It is beyond the scope of this text to 
give an extended discussion of all of the characteristics of a 
galvanometer, since it is usually classed as a laboratory instru- 
ment. The principle of operation of the galvanometer is the 
same as that of the permanent magnet, movable-coil ammeter. 
In fact, the ammeter was developed from the galvanometer. 
The movable coil of the galvanometer contains many turns and 
is suspended between the poles of a strong permanent magnet. 
The controlling force is due to the twisting of the suspension 
fiber, and the deflection is read by means of a telescope and scale. 
One malie of galvanometer suitable for use with a potentiometer 
is shown in Fig. 218. The essential difference between a galvan- 



266 ELECTRICAL METERS 

ometer and a milliammeter is the high sensibility of the former. 
This higher sensibility permits measurements of a much higher 
degree of accuracy. 

231. Potentiometers. — The potentiometer is a combination of 
accurately adjusted resistances used for the comparison of un- 
known electromotive forces with the electromotive force of a 
standard cell. For simplicity potentiometers may be considered 
under two heads; namely, the slide-wire type and deflection type. 

232. Slide-wire Type. — The fundamental principle upon which 
the operation of either form is based is Ohm's law, or in other 
words, the fact that the voltage drop along a conductor is directly 
proportional to the resistance so long as the current remain a 



/I P^AAAAAAAAAAAAAAAAA^ 



H^i|# 



storage Botferif 

Pig. 219. 

constant. The application of this principle to the comparison or 
measurement of electromotive forces wilt be best understood by 
reference to Fig. 219. This figure shows a storage battery con- 
nected in series with a high resistance AB. A part of this resist- 
ance is shunted by a circuit CD, the contact D being movable. 
In the shunt circuit is connected a sensitive galvanometer G and 
the unknown source of electromotive force E. The connections 
of E are reversed with reference to those of the storage battery. 

233. Operation.- — When a measurement is to be made, the con- 
tact, D, is moved either to the right or left, as the case demands, 
until the galvanometer shows no deflection. When this condi- 
tion is reached there is no current flowing through the shunt 
circuit, and if / is the current in the battery circuit, whose resist- 
ance from C to i) is iJ, the voltage drop between CD equals /fl. 
Since no current flows through the shunt circuit, this voltage 
must equal the unknown voltage E, or 
E = IR. 



INSTRUMENT TESTING 267 

If now E be replaced by a standard cell and the position of D 
be again adjusted until the galvanometer shows no deflection, the 
voltage drop is equal to the electromotive force of the standard 
cell. Let this new resistance between C and D be Ri, 
then 

E. = IRi 
E IR R 

^^^ EriRT K 

Thus, if the instrument is adjusted so that R and Ri can be read 
oflf from a dial, E can be calculated, for 

E = Ea p~* 

234. Leeds and Northrup Potentiometer. — One make of the 
slide-wire type of potentiometer is shown in Fig. 220. A diagram 
of the internal connections of this instrument is shown in Fig. 221. 
The similarity between this and the diagram of Fig. 219 is plainly 
evident. As shown in the diagram, the essential part consists of 
three resistances, D to A, A to C, and C to B, connected in 
series. The contact points of resistance, D to A, are marked to 
correspond to the electromotive force of the standard cell when 
corrected for temperature according to formula of Article 229. 

The resistance, A to C, consists of fifteen 5-ohm coils adjusted 
to a high degree of accuracy. CB is a 5.5-ohm slide-wire wound 
around a marble cylinder. 

236, Operation. — When an unknown electromotive force is to 
be measured, the connections are made as indicated in the dia- 
gram. Fig. 221. The contact T is set at a point corresponding to 
the electromotive force of the standard cell when corrected for 
temperature; the switches U and V are moved to the left, and key 
V is closed. If the galvanometer shows a deflection, rheostat R is 
adjusted until the galvanometer shows no deflection when V is 
moved to the right and closed, and balance is again obtained by 
adjusting R, When this adjustment has been made, the current 
through AC is exactly 0.02 amp. The voltage drop across any 
one of the 5-ohm coils is consequently 0.1 volt, and that across CB 
is 0.11 volt. It will be observed that the unknown electromotive 
force is connected between M and Af ' in series with the galvan- 
ometer. Since both M and Af ' are movable, the maximum voltage 
drop from A to B is 1.61 volts. To measure the unknown elec- 
tromotive force M' is placed at zero, U is moved to the right and 



ELECTRICAL MICTERR 





INSTRUMENT TESTING 



269 



M is moved from lower to higher values until a change of one 
contact reverses the direction of the deflection of the galvan- 
ometer. M is then moved back one point so the deflection is in 
the same direction as before, and Jlf ' is adjusted until the galvan- 
ometer shows that no current is flowing when V is on Ro. The 
value of the unknown electromotive force may then be read 



/" 

^ 



o^'^S 



•/OOC ohms- 



^ 6^AAAAAAAAAAAAW\/§^^ 

^90 




Fig. 222. 

from the positions of M and Af '. The value of the electromotive 
force is marked on the dial in place of the resistance. 

To measure pressures higher than 1.5 volts the unknown pres- 
sure must be connected across a high resistance commonly called 
a volt box, while the potentiometer terminals are shunted across 
a definite fraction of the high resistance. This method of connec- 
tion is shown in Fig. 222. The potentiometer is connected to 



o 



6 



JS 



Fia. 223. 

a and 6, and by moving switch M the potentiometer reading may 
be 0.1, 0.01, or 0.001 of the unknown electromotive force. Cur- 
rent measurements can also be made on the potentiometer by 
measuring the drop in volts across a standard shunt. The cur- 
rent is calculated by Ohm's law. The connections for current 
measurements are shown in Kg. 223, in which S represents the 
standard shunt whose resistance is known. The potentiometer 



270 



ELECTRICAL METERS 



terminals are represented by a and b. For precision measure- 
ments of direct current and electromotive force, the potenti- 
ometer method is far superior to any other, and is today the stand- 
ard method for such measuronicnts. For conmiercial work, 
however, which does not require such a high degree of accuracy 
the method possesses several disadvantages. The two chief 
disadvantages are the time required to make the measurements, 
and the cost of the apparatus. 

236. Deflection-type Potentiometer. — For checking portable 
instruments Mr. H. B. Brooks of the Btireau of Standards has 
designed a potentiometer which combines to some extent the 




accuracy of the alide-wire potentiometer and the speed of opera- 
tion of deflection instruments. 

It was pointed out that the final adjustments of the Leeds and 
Northrup potentiometer are made by moving contact M'. This 
adjustment is time-consuming and for most commercial measure- 
ments unnecessary, were it possible to read or estimate the un- 
balanced electromotive force. Brooks' deflection potentiometer 
differs from the slide-wire form mainly in that it permits the 
reading of the unbalanced electromotive force and the modifica- 
tions necessary to bring this about. 

Fig. 224 shows the complete deflection-type potentiometer as 
designed by Mr, Brooks and built by Leeds and Northrup Co. It 
is seen that the galvanometer is built into the apparatus, so that 
the instrument is self-contained with the exception of the stand- 
ard cell and auxiliary storage cell. If the instrument is to be 
portable, the storage cell could be replaced by two dry cells, 



INSTRUMENT TESTING 



271 



which, with the standard cell, could be enclosed in the case, 
making the entire apparatus self-contained. 

237. Theory and Operation. — The essential principles of the 
instrument will be understood from Fig. 225, which is a diagram 
of the connections of a simple potentiometer for measurements 
of voltage and current. 

When voltages higher than the voltage of the standard cell are 
to be measured, it is necessary to use a volt box or some high 
resistance as already pointed out. Such a connection is shown at 







\AAAAA/^ 






.j-X^^^J^ 



\AAAAAAA 



-7 i * 



^^? 




/& 



's 



Kaaaaaaa 



fa) 



y^T 



rj>) 



I'iG. 225. 



(a), Fig. 225. R is such a resistance. A suitable fraction of 
this resistance J?/p is connected to the circuit rir2. When r\ has 
been adjusted so that the galvanometer shows no deflection, 
we have: 

V ri+r2 

or 

where p is the ratio of the whole resistance R to the portion -K/p; 
or p is the multiplying factor of the volt box. The current 
through the galvanometer is then 

E 



ei 



h = - 



ri+r2 p 
rir2 



'•+f;+;,+«'i'r 



272 



ELECTRICAL METERS 



The first term in the numerator of this expression is the voltage 
drop in the portion ri of the potentiometer wire when the galvan- 
ometer circuit is open; it is therefore numerically equal to the 
setting of the potentiometer. The second term in the numerator 
is the voltage drop which would exist around the portion R/p 
if the galvanometer circuit were open. The denominator is the 
total resistance in the galvanometer circuit. The expression 
shows that the current through the galvanometer is equal to the 
unbalanced portion of the electromotive force divided by the 
total resistance of the galvanometer circuit. 

Similarly, by the aid of (b) , Fig. 225, it can be shown that when 
the potentiometer is used for current measurements the cur- 
rent through the galvanometer is given by 



-E 



, r,r_i 



This and the preceding expression show the possibility of reading 
any desired part of the pressure on a properly calibrated galvan- 
ometer scale provided the total resistance of the galvanometer 
circuit is kept constant. 

When used for current measurements, the current through R 
is in general not equal to the line current whose value is desired, 
being greater or less than the line current by the amount of the 
galvanometer current. It has been found that a simple expedient 
will correct for this difference and make the reading of the poten- 
tiometer (when divided by R) give accurately the value of the 
line current. 

The manner in which these principles are worked out in detail 
is shown in Fig. 226. Anyone wishing a more complete explana- 
tion of the principles of the deflection potentiometer is referred 
to Bulletin of The Bureau of Standards, vol. 8, No. 2, from which 
the foregoing explanation is abstracted. A view of the potenti- 
ometer with its accessories is shown in Fig. 227, which also shows 
a wattmeter connected for test. The voltage supply line is at 
the left, a slide resistance being used to set at the desired value. 
The current is supplied by a storage battery, not shown in the 
figure. The current is controlled by the carbon rheostat at the 
right. The volt box, auxiliary storage cell, and standard cell 
are back of the potentiometer. 



274 



ELECTRICAL METERS 



238. Standard Resistances or Shunts. — For accurate measure- 
ment of current a set of manganin standard resistances is re- 
quired. These are usually made for oil immersion and give from 
0.01 to 1.5 volts drop at maximum current, those intended for 
high currents giving the lower full-load drop. To keep down the 



HUr^ 




size of the shunt, the accuracy for very heavy currents is usually 
less than for more moderate ones. The resistances are made 
accurate to a small fraction of 1 per cent, so the results obtained 
by their use leave little to be desired for commercial piu^wses. 
The usual values of these shunts are 1.000, 0.1, 0.01, 0.001, and 
0.0001 ohm. 

The resistances are made in two forms. Fig. 228 shows a 1- 
ohm standard of the Reichsanstalt form. Fig. 229 is a 0.00002- 
ohm shunt of different form. 



INSTRUMENT TESTING 



275 



With the slide-wire form of poteatioraeter it has been common 
practice to use current shunts whose values are decimal multiplea 
or submultiples of an ohm. These, however, are not the most 
convenient for al! cases, as sometimes calculations will have to 
be made during the test to determine the setting of the potenti- 
ometer to correspond to the ammeter reading in order to expedite 
the work. To facilitate and expedite the readings when a de- 
flection potentiometer is used, it is necessary to choose shunts 
whose value will not make these calculations necessary. 

Assuming that the fundamental range of the potentiometer ia, 
say, 150 "dial units," for rapid and convenient work, one scale 
division on an instrument under test should correspond to one 
dial unit. Under such conditions the resistance of shunt R is 
given by 

_ e. m.f. corresponding to one dial unit 
amperes per division of ammeter 

If one dial unit equals 0.01 volt, current shunts required for 
ammeters of 1, 2, 5, 10, and 20 amp. per scale are 0.01, 0.005, 
0.002, 0.001, and 0.0005 ohm, respectively. A single shunt will 




Fu;. 230. * 

usually do for several ranges; thus the 0.01-ohm shunt is suit- 
able for 100-amp. 100-division, 120 amp. 120-division, and 150- 
amp. 150-division instruments. The same shunts are equally 
convenient in testing wattmeters of corresponding current range. 
239. Variable -resistance Rheostat. — In many tests it is neces- 
sary to connect to the circuit a resistance which can be varied 
gradually so as to maintain the current constant. One of the 
most convenient forms of rheostat is shown in Fig. 230. The con- 
struction and operation of the rheostat is easily understood from 
the figure. The resistance consists of many carbon plates rest- 
ing on slides made of insulating material. The resistance ia 



276 



ELECTRICAL METERS 



varied by corapreaaing, by means of a hand screw, the plates 
more or less firmly. 

The chief advantages of such a rheostat are the nicety with 
which the current can be controlled, the large current-carrying 
capacity and non-inductive property. This last property makes 
it suitable for alternating as well as direct currents. 

240, Lamp Bank. — A convenient resistance for many tests 
can be made from carbon filament incandescent lamps. A 
suggestive diagram of a lamp bank is shown in Fig. 231. The 
resistance of the lamp bank can be varied through wide limits by 
closing different switches. For instance, if switches a and b 




alone arp closed, the lamps in circuit 1 will be lighted; by closing 
a, b, and c, circuits 1 and 2 will be in parallel, etc. 

Connecting circuits in parallel, decreases the resistance and 
increases the current. To increase the resistance, either unscrew 
enough lamps in one circuit until the current is the required value, 
or close switches a and d, or a and /, which will connect the cir- 
cuits 1, 2, and 3, or 1, 2, 3, 4, and 5 in series. The maximum 
resistance that can be obtained by the device shown is the resist- 
ance of five lamps in series; the smallest resistance is the resist- 
ance of all lamps in parallel. An ingenious student can readily 
modify the arrangement suggested to meet his particular needs. 
Such a lamp bank can be used for many purposes in a central 
station. 



INSTRUMENT TESTING 277 

241. Water Rheostat. — In case of an emergency or when very- 
heavy currents are to be measured, the water rheostat is about 
the only controlling device that can be used. The water rheostat 
consists of two or more metal plates, usually iron, in a vessel of 
salt water. The vessel, is usually a wooden water-tight box or 
barrel. The resistance of such a rheostat is varied by immersing 
more or less of the iron plates, by moving them nearer together 
or farther apart, or by changing the amount of salt in the solution. 

Other forms of apparatus will be discussed in connection with 
the tests where used. 



CHAPTER XVII 

TESTING AMMETERS 

242. Introduction. — As pointed out in the previous disouasion, 
all ammeters have a very low resistance and are to be connected 
in series with the circuit in which the current is to be measured. 
On account of the extremely low resistance great care must be 
exercised in connecting them to be sure that excessive current 
will not flow through the instrument when the circuit is closed. 
In no case should an ammeter be connected to a circuit without 
a resistance or rheostat in series with it — the resistance being 
sufficiently large to reduce the current to a proper value. If the 
conditions do not enable the student to know beforehand the 
approximate value of the current, the resistance may be cau- 
tiously cut out after final connections have been made. 




^ 



^ 



I ^AAAAAAAA 




Fi«. 232. 

243. Comparison of Ammeters. — The readings of two or more 
ammeters may be compared by connecting them in series to a 
suitable source of electromotive force. In series with the 
ammeters should be connected the lamp bank or other suitable 
resistance. The resistance is varied stepwise beginning with a 
small current, and both instruments should be read at the same 
time. If one of the ammeters has previously boen standardized, 
a comparison of its corrected readings with the readings of the 
other ammeter will enable the student to determine the correction 
for the second ammeter. The connections for this test are shown 
in Fig. 232. In this figure, D is the source of electromotive force 
which is preferably a storage battery; A i and ilj arc the ammeters 

278 



TESTING AMMETERS 



279 



to be compared, and R the variable resistance. The lamp bank 
will serve very nicely for this purpose, although the carbon 
rheostat is preferable when a low-voltage storage battery is avail- 
able. S' is a double-pole switch which should be left open until 
all other connections have been made, and S" is a short-circuiting 
switch for the ammeters. This switch should be kept closed 
except when the readings are being taken. When direct-current 
ammeters are compared or tested, care must be taken to see that 
they are connected so as to deflect in the proper direction. 

244. Calibratloii Curve. — A curve showing the relation be- 
tween the correct values of the quantity measured and the indica- 



















/ 




















/ 








5, 












A 










1 










/ 












1 








/ 


/ 


















/ 














fi 






/ 




















/ 




















/ 




l-Vto- 


W/V 


y/9/^ 


DC 


Am. 


fxfi: 






/ 






/I 


■n/ne 


ler f 


'eaa, 


TgS 









Fio. 233. 

tions of the instrument should be drawn irom the data obtained 
when an instrument is tested. Thus in the case just considered 
if the readings of one ammeter are known to be correct, these 
values may be plotted vertically or as ordinates, while the read- 
ings of the inaccurate ammeter may be plotted horizontally or as 
abscissas. A curve or line drawn through the points thus deter- 
mined will show at a glance the variations in the readings; or if 
a reading on the inaccurate ammeter is known, the correct value 
of the current can be at once found from the curve. This is 
brought out more clearly in Fig. 233, which is drawn from data 
obtained by comparing a Weston direct-current milliammeter 
with a Kelvin balance. The data are as follows: 



ELECTRICAL METERS 



EXAMPLE 



Test Ho. 1.— Compari 

Apparatus. — Weaton milliummeter.' 

Kelvin centiamppre balance. 

Rheostat. 
Temperature 22''C. 

Table III 



llimnuieter witli Kelvin balance. 



Ammoter readiDBS 


B>l>nc« riBdiDes 


C..r«tba 


110 


122.48 


+12-48 


202 


222.25 


+20.25 


230 


250.00 


+20.00 


330 


362 80 


+32.80 


365 


402 00 


+37.00 


425 


463.90 


+38,90 


fl68 


722.20 


+54.20 


752 


821.80 


+69.80 


800 


870.00 


+70,00 


900 


983.00 


+83.00 



In Fig, 233, the ammeter readings have been plotted horizon- 
tally and the correct, or balance readings, vertically. Through 























y 




1 60 
















y 


y 


















^ 










I 






^ 


■B^ 


















' 


^ 




An 


meft 


r P, 


adir. 


IS 









loo eoo <ieo ^£io soo eco wo eoo aoo 

Fio. 234. 

the points thus determined the straight line has been drawn. 
This curve shows that the per cent error of the ammeter is practi- 
cally constant. Furthermore, if the milUammeter has been used 
in practice and a reading of 600 milliamp, obtained, it is easy 
to determine the correct value of the current from the curve. 
Thus, the ammeter reading of 600 corresponds to the vertical 
' This milliameter had previously received very severe use. 



TESTING AMMETERS 



281 



line marked 60 at the bottom; rimning vertically on this lino 
we find it intRrsecta the curve at the point A which corresponds 
to 650 on the vertical scale; hence, the correct reading is 650 
milliamp. Any other reading can be interpreted in the same way. 
It is often just aa advantageous to draw a curve showing the 
relation between the correction to be applied and reading. Such 



tr.c 


1 — 


i-± 


rn 












1 — 1 




p—i 






~i 




rj 


»=| 


i— 1 


p=| 


a 


n 






= 


=d 


— 








- 


- 


- 


- 


- 


- 


- 


- 


r 










- 




a 
















































fee 










■ 




























- 


■£ 




, 




- 


—4 


_ 








_ 


_ 


_ 














^ 










- 




















' 


~ 




"■ 


















-% ' 


^ 


=3 


= 






^ 


_ 


M 


_ 


^ 


P_ 


_ 


_ 


_ 


J 








_ 


- 




» 


;r 


" 


- 










- 


- 


-^ 


- 


- 


- 


- 


- 


- 








- 


- 


















































^ 


1? " 






' 






































■<> 




























































































5 ' 
















































^ 


== 


^_ 






























































"^ 


~ 








^ 




















































"<i ^ 
















































































































- 






























































— 


-H 






*^ 














— 


-■ 


-■ 


-- 
























-Zi 




























































































■ 




















_^ 


_ 




_ 


_H 


,— 








— 


-■ 






~L 












— ' 


" 

























































































































MO /eo leo 



rve is shown in Fig. 234, which is also drawn from the data of 

Table III. The irregularities of curve, Fig. 234, are perhaps in 
this case due to friction and lack of sensibility as the milliammeter 
tested had received some rough usage. 

In Fig, 235 are shown the correction curves of eight American- 



282 ELECTRICAL METERS 

make switchboard ammeters whose movements are shown in 
Fig. 26. Since all of these instruments were new when tested, 
the irregularities seem to indicate that the scales do not fit, and 
also that the sensibilities were not closely adjusted. Where the 
deviation is pronounced, the discrepancy may be due to non- 
uniformity of the magnetic field. A straight-line caUbration 
curve which shows a constant percentage error is due to a change 
in the strength of the controlling spring or in the strength of 
the magnetic field. 

245, Calibration of Direct-cunent Ammeters by Means of 
Standard Resistance and Voltraeter.^Since currents can be 
accurately determined by mensuring the voltage drop across a 
standard rraistance, the same principle can be used for calibrating 




ammeters. The only apparatus necessary is a standardized milh- 
voltmeter and shunt and rheostat or other adjustable receiving 
circuit. A good instrument for this purpose is shown in Fig. 236. 
This is a voltmeter with three ranges, 0-1.5, 0-3, and 0-150 
volts. The lower range is the most convenient for current 
measurements. The scale is divided in such a way that it can be 
read accurately to 0.2 of a scale division, and the accuracy of the 
instrument is such that measurements of potential may be made 
within 0.1 of 1 per cent. When direct-current ammeters are to be 
calibrated they are connected in scries with a source of potential, 
the resistance R, and shunt as shown in Fig, 237. The voltmeter 
;cted across the terminals of the shunt as shown. The 
3 of the ammeters and voltmeter are taken simultaneously, 
the current is changed and new readings taken, etc. By such 



TESTING AMMETERS 



283 



a stepwise process the ammeters can be calibrated over the whole 
scale. The correct values of current are calculated in accordance 
with Ohm's law. K fi, is the resistance of the shunt and E is 
the millivoltmeter reading, the current for any one reading is 

E 



I = 



R. 



When the current is changed E will change, but in each case the 
current is obtained in the same way. Thus, if the millivoltmeter 
reading is 0.456 volts and the shunt resistance is 0.01 ohm the 
current is 

Ammef^rs fo^ caiibrated \ \ 

r^m^^ lOOOO 




Shunt 



oaaAaa/ LMJmLj-I 




Fig. 237. 

1 = TwyT = 45.6 amp. 

The calculated values should be plotted vertically and the am- 
meter readings horizontally, as shown in Fig. 233. 

When many ammeters of different ranges are to be calibrated, 
more than one standard shunt will be necessary. Suppose that a 
full-scale deflection of the millivoltmeter is obtained with a cur- 
rent of 500 amp. ; with 50 amp. the deflection will be only 10 per 
cent of the full scale; below this, the percentage error of the 
readings will impair the result. Thus, if ammeters below 50 
amp. are to be calibrated, another shunt of ten times the former 
resistance should be used; it will give a full-scale deflection for 
50 amp. and may be used down to 5 amp. For smaller currents 
still other shunts should be used. 

Millivoltmeters are made for any range from 15 millivolts to 
1,500 millivolts for full-scale deflection, and, therefore, it is 
necessary to know the relative values of the shunt and millivolt- 
meter resistances if appreciable errors are to be avoided. For 
instance, if the resistance of the millivoltmeter is Rv and of the 
shunt Rt, the current through the instrument is 

^' R. + Ri 



284 



ELECTRICAL METERS 



where I is the current through the ammeter. The per cent error 
in the cahbration will then be 

JOOKj_ 

B. -i- R,' 
When R, = k^Ri the error is 1 per cent. If appreciable errors 



246. Deflection Potentiometer Method.— When the deflection 

potentiometer is used, it replaces the milhvoltineter, and if the 
proper shunts are available the t«st can be performed without any 
calculations. The observer at the ammeter seta successively 

on 10, 20, 30, etc divisions of the scale, and the observer 

at the potentiometer sets the main dial to the same numbers, and 
depresses the key. The small deflection of the galvanometer 
gives the correction to he appHod to tho rf ading of the instrument 



I 




under test, one division of the galvanometer corresponding to 
0.1 division of the ammeter. The correction curve can be plotted 
at the time the readings are being taken by putting the pencil on 
the proper vertical line, Fig. 238. If the galvanometer reads two 
divisions to the right, the ammeter is in error by 0.2 amp., and the 
pencil mark is made two divisions below the zero line on the chart; 
if the galvanometer reading is one division to the left, the mark b 
made one division above the zero line of the chart. The scale 
points may be checked several times if desired, and a smooth 
curve drawn through the pencil marks. Thus a correction curve 
may be quickly drawn without recording a single figure, and with- 
out any computation. 

For rapid work, where ammeters of different ranges are to be 
tested the shunts may be arranged as shown in Fig. 239. This 
method may be used with a millivoltmeter as well as potentiome- 
ter. As indicated in the figure the shunts are soldered together, 



TESTING AMMETERS 



285 



and their free ends are connected to a millivoltmeter. The line 
current enters at A, and may leave at B, C, or D. The section 
AB is of low resistance and large current-carrying capacity; BC 
is of lower current capacity and higher resistance, etc. 

It will be evident that the method outlined above may be used 
for calibrating not only ammeters, but shunts and millivoltme- 
ters as well. Thus, if the ammeter and millivoltmeter have been 

standardized, the value of the resistance of the shunt can readily 

E 
be obtained. According to Ohm's law R = y, and, when 

E and / are known, R can be determined. Similarly E = fi/, 
and a standardized ammeter and shimt may be used for calibrat- 
ing the millivoltmeter. In case the ammeter cannot be depended 
upon, an ammeter shunt can be calibrated by connecting it in 



A 



A^^^^^^^^^^-^^/S^^^^f^-ymmw^mMt^ 




/^fmti 



Pig. 239. 



series with a standard shimt, and connecting the millivoltmeter 
first across the standard shunt, and then across the shunt to be 
calibrated. The ratio of the millivoltmeter readings is the ratio 
of the resistance of standard to the resistance of shimt being cali- 
brated. This can be shown as follows: 
The current through both resistances is the same and equal to /. 

Let R = resistance of standard, 
and R' = resistance of shunt being checked. 
Then E = IR 
and jE?' = 1R\ 

R 
" R' 



Whence ■^, = j^, 



and R' = 



E'R 
E 



where E is the millivoltmeter reading across the standard and E' 
the reading across the shunt. 



286 ELECTRICAL METERS 

247. Difference between Direct-current and Alternating- 
current Ammeters and Voltmeters. — The essential differences 
between direct-current and alternating- current instruments have 
been pointed out in detail. A brief summary of the main points, 
with reference to calibration, is necessary. In direct-current 
ammeters and voltmeters, the force actuating the pointer may be 
any function of the current, although in most cases it is propor- 
tional to the first or second power of the current; the straight-line 
relation being the most convenient on account of the consequent 
uniformity of scale. 

In alternating-current ammeters and voltmeters the instan- 
taneous value of the actuating force is proportional to the square 
of the current or electromotive force at that instant. The aver- 
age force upon which the steady deflection depends is propor- 
tional to the average square of the current or electromotive 
force. The indications of alternating-current ammeters and 
voltmeters are really a measure of the average value of the 
square of the alternating quantity. 

Alternating-current indicating instruments, whose indications 
are independent of frequency and wave form, when calibrated 
by using direct current, indicate correctly effective values when 
used in measuring alternating current or electromotive force. 
This relation may be shown as follows: 

Let / = direct current causing a given deflection 
and let Ia = alternating current causing the same deflection. 
Then the deflection with direct current is equal to KP, and with 
alternating current it must be K times the average of x'. 



whence 
and 



KP = K average i* 
P = average i^ 
I = V average i'' = I^- 



Si nce the inst rument scale is graduated in values of I, it indicates 
V average i', or effective values when used on alternating-current 
circuits. Thus, alternating-current ammeters whose indications 
are independent of wave form and frequency when calibrated on 
direct current, indicate correct effective values of alternating 
current. The instruments which may be calibrated on direct 
current are the hot-wire, electrodynamometer, and electrostatic 
types. 

It is evident from previous discussion of the hot-wire indicating 



TESTING AMMETERS 287 

instruments that the indications are proportional to P when di- 
rect current is flowing, and to the average value of i^ when alter- 
nating current is being measured. The indications of the 
instrument are correct effective values when the instrument is 
used on alternating-current circuits. 

The electrodynamometer when standardized on direct current, 
indicates effective values when used for measuring alternating 
currents. When the two coils are connected in series, the torque 
exerted upon the moving system, for a given relative position of 
the coils, is proportional to the square of the current as already 
pointed out, and the torque is independent of the direction of 
the current. Most makes of this type of instrument give read- 
ings of equal accuracy on either direct or alternating currents of 
ordinary commercial frequencies and wave form. Owing to eddy 
currents in surrounding metal, and non-uniformity of current 
distribution in conductors, some makes are subject to slight errors 
on even commercial frequencies, and on circuits of high frequen- 
cies the same causes will produce errors in the readings of all 
electrodynamometer type instruments. 

in addition to the foregoing, the electrodynamometer ammeter 
has certain limitations. If the current is carried into and out of 
the moving coil by the usual spiral springs only small currents 
may be used without injury to the springs. In one of the earliest 
forms the current is taken into and out of the moving coil by 
mercury cups; in the Kelvin balance the axis about which the 
moving system turns is horizontal, and ligaments of fine wire are 
used as supports and conductors. Both of these instruments are 
slow and inconvenient to use and require that the current to be 
measured be quite steady. The readings of the Kelvin balance 
change appreciably with heating, when kept in circuit for any 
length of time. The balances also have frequency errors which 
increase with the ampere capacity of the balance. Several 
European makers arrange the fixed and movable coils in parallel 
so that the latter carry only a small part of the current to be 
measured. In order to avoid errors in the division of the current, 
due to inductance, the ratios of the inductance to the resistance of 
each coil are made small and as nearly equal as possible by adding 
non-inductive resistances to each coil. These instruments are 
suitable for checking alternating-current ammeters which cannot 
be accurately calibrated with direct current. 

Both the fixed and movable coils of the electrodynamometer 



ELECTRICAL METERS 



voltmeter are made of fine wire and connected in serieB with a 
uon-inductive high resistance. The high-resistance multiplier 
reduces to a low value the time constant (ratio of inductance to 
resistance) of the electrodynamometer coils, and, hence, well- 
made voltmeters of this type, calibrated on direct current, show 
practically negligible errors on commercial alternating-current 
circuits. These instruments, if properly made, are suitable for 
checking other working instruments. 

Since alternating-current voltmeters require considerably 
larger currents than the moving-coil direct-current types, some 
provision should be made for ventilation. Unless this provision 
is made, the relatively large current develops considerable heat, 
which accumulates, raising the temperature of the springs and 
other parts of the instruments and affecting the readings. For 
very accurate work the aeries resistance should be mounted sepa- 
rately from the instrument and ventilated. 

248. Calibration of Altemating-ciirrent Ammeters. — From the 
foregoing discussion, it is evident that some types of alternating- 
current ammeters can be calibrated in exactly the same manner as 
direct-current ammeters. The soft-iron and induction-type 
ammeters should, however, be calibrated on alternating current 
of the same frequency as that on which they are to be used. The 
most satisfactory method of calibrating these instruments is by 
the use of an intermediate direct-current alternating-current 
standard, such as a hot-wire ammeter or an electrodynamometer. 
A convenient method of connections for such tests is shown in Fig. 
240. The diagram shows a standard direct-current ammeter 
connected to a source of direct-current electromotive force. By 
means of a double-throw switch the instrument C, which may be 
an electrodynamometer or hot-wire ammeter, can be connected 
in series first with the direct- current ammeter, and then with the 
alternating-current ammeter to be calibrated. The instrument 
C thus acts as an intermediate standard, and if it is a hot-wire 
ammeter, its zero reading should be maintained. If the pointer 
does not return to zero, it may be set to zero by means of the ad- 
justing screw. 

For measuring high-frequency alternating currents of low value, 
the DuddeU thermo-ammeter described in a previous chapter 
is very convenient. Its chief advantage Ues in the fact that it 
can be calibrated on direct current and when so calibrated will 
indicate correct effective values of alternating current of any 



TESTING AMMETERS 



289 



frequency or wave form. Furthermore, it has very little self- 
induction or capacity and may be used as an ammeter or volt- 



OC Supply 




ACAmmekr fip§ 



ACSuppfy 
o 



A.C 'D.CAmnjefer 



Pig. 240. 

meter, according to whether it is constructed with a high- or 
low-resistance heater. 



CHAPTER XVIII 

TESTING VOLTMETERS, WATTMETERS, POWER- 
FACTOR, AND FREQUENCY METERS 

249. Introduction. — Some of the most common and convenient 
methods of checking ammeters are, with slight modifications, 
applicable to voltmeter calibration as well, the main dijBference 
being in the manner of connecting the instrument to circuit, and 
the necessity of some means of adjusting the pressure instead of 
current. 

250. Comparison of Direct-current Voltmeters. — Fig. 241 shows 
the connections for comparing a voltmeter Vi with the standard 
voltmeter V2- The standard voltmeter discussed in Article 246 





AAAAAAAA 



J 




Fig. 241. 



is well suited for direct-current low-range voltmeter tests. As 
is clear from the diagram, the two instruments a^e connected 
in parallel with each other, and in series with a high resistance. 
Different readings are obtained by varying the series resistance. 
As pointed out in the discussion on indicating voltmeters, the 
deflection or indication of the voltmeter is proportional to the 
current through the instrument. This current, under constant 
pressure, is determined by the resistance in the circuit. If Rv is 
the resistance of voltmeter, R the series resistance, and E the 
electromotive force, the deflection may be expressed by 



d = K 



E 



R + R, 



From this it is evident that the deflection will depend upon R, 

290 



TESTING METERS 



291 



and that increasing R decreases the indication of the instrument. 
The value of R must be high in order to get a low reading if E 
is large. Thus, to reduce the reading one-half, the value of R 
must be equal to Rv. 

If it is not convenient to provide a large enough series resistance 
for a suflBicient number of readings, the connections may be modi- 
fied as shown in Fig. 242. To get the maximum desired deflection 
the two voltmeters are connected across a suflSicient number of 
lamps in series. For lower readings, the voltmeter connections 
are changed so as to include one lamp less. The deflection in 
each case will be determined by the voltage drop across the num- 
ber of lamps included between the voltmeter terminals, so long as 
the current through the lamps remains constant. Thus, if r is the 
resistance of one lamp, I the current, the voltage drop across one 
lamp is /r, across two lamps 2/r, etc. 

/ & ^ 4- s e 

oooooo 



Mams 




^\ 



Fig. 242. 

Where it is possible to vary the electromotive force of the 
source, the voltmeters may be connected as shown in Fig. 241, 
with R omitted. Different readings are then obtained by chang- 
ing the excitation of the generator, if that is used, or by changing 
the number of cells in series, if a storage battery is used. 

Both instruments must be left in the circuit when readings are 
taken if the connections of Fig. 241 are used. Both instruments 
should also be read at the same time. When multipliers and 
leads are used, they should be checked with the instrument for 
which they are intended. 

251. Potentiometer Method. — The most accurate method of 
checking voltmeters is by means of the potentiometer. The de- 
flection potentiometer is especially well adapted to this class of 
work. If the procedure outlined in Article 246 is followed, the 
checking may be done accurately and rapidly. The correction 
curve. Fig. 238, may be plotted as the work of checking pny** 



292 ELECTRICAL METERS 

The connections for such a test are the same as shown for the 
voltage coil of wattmeter, Fig. 227, the current line being dis- 
connected. 

262. Testing Altematiug-curreiit Voltmeters. — Alternating- 
current voltmeters, whose indications are not aflFected by fre- 
quency and wave form, may be compared in the manner just 
explained. For calibrating induction voltmeters, an intermediate 
standard ia most convenient. 

The connections for an intermediate standard are shown in 
Fig. 243, where V is either a hot-wire voltmeter or some other 
instrument unaffected by frequency and wave form ; Fi is a direct- 
current standard and Vs the alternating-current voltmeter to be 
tested. The connection.s of the diagram are practically the same 




FiQ. 243. 



as those of Fig. 241. That ia, the voltmeters are connected in 
series with a high resistance R, and the source of electromotive 
force. Different readings are obtained by changing R. The dia- 
gram of Fig. 244 shows a system of connections similar to those 
of Fig. 242, In addition to the two-pole double-throw switch, a 
single-pole double-throw switch is most convenient to use. In 
place of this, however, two single-pole single-throw switches will 
answer. In case this system of connections is used, R may be 
most conveniently made up of lamps in series, and different read- 
ings obtained by changing the connection a. 

When the double-pole switch S is closed to the right, the inter- 
mediate standard and direct-current voltmeter are connected in 
parallel to the direct-current circuit; and when the switch is closed 



TESTING METERS 



293 



to the left, the intermediate standard and alternating-current 
voltmeter are connected in parallel to the alternating-current 
circuit. The single-pole switch must be changed every time the 
main switch S is changed. 

253. Calibration Curves. — Calibration curves should be drawn 
for voltmeters in the same way as for ammeters. The following 
table will show how to arrange the data obtained from a volt- 
meter test. 




nc Mcffps 



FiQ. 244. 



EXAMPLE 

Test No. 2. — Test of voltmeter. 

Apparatus. — Weston direct-current voltmeter No. 19,229.^ 

Weston laboratory standard voltmeter No. 316. 

Lamp bank. 
Temperature 22°C. 

Table IV 



Standard 


Instrument tested 


Correction 


Remarks 


75 


80.0 

83.0 

88.0 

97.0 

111.0 

116.5 

132.0 

138.5 

147.0 


-5.0 
-2.0 
0.0 
+1.0 
+1.0 
+1.5 
+2.0 
+2.5 
+3.0 


See curve, Fig. 245 


81 




88 




98 




112 




118 
134 


• ••••«••• 


141 




150 









Calibration curves for eight switchboard, moving-coil perma- 
nent-magnet type of voltmeters are given in Fig. 246. Curve A 
shows that the controlling spring was too strong, or else the 

^ Students had used this voltmeter very carelessly. 



ELECTRICAL METERS 



magnetic field too weak for the scale used. The errors as a 
whole are small. 































































^ 


— 


U 




5 








^ 










•" 
























? 




/ 






























« 




/ 












































_ 


_ 


_ 


_ 


_ 


_ 







































*e 
















































































































































tBi 


- 


^ 


=■ 


























































'I 










































































































I- 












































































































































i:. 
































•^ 










































































































>■■ ' 




































.^ 










































































































" 


































' 




















































^ 


- 




















-ec 






























*e 






































































H 




































' 





































Fig. 246. 

2M. Test of Electrodynamometer-type Wattmeter. — The 
indications of wattmeters are proportional to the product of 
amperes and volts supplied. On direct currents, the product of 



TESTING METERS 



295 



amperes and volts gives the correct power, but od alternating 
currents this product must be multiphed by the power-factor of 
the circuit. This, however, is not a aerioua objection, for when a 
wattmeter is caUbrated with direct current it indicates correct 
power when used with alternating current, provided the induct- 
ance of the pressure coil is negligible. This fact was demonstrated 
in Chapter X. 

A wattmeter should indicate correct power supplied to a circuit 
when either the current, or pressure, or both, vary in value within 
their respective limits Btated on the instrument. In connecting a 
wattmeter to the testing circuit, provision must be made for 
varying both the current and electromotive force, and for measur- 
ing these accurately. This is best 
done by connecting the instruments 
as indicated in Fig. 247. In this 
diagram, B represents a storage 
battery or other source of electromo- 
tive force; the battery is shunted by 
a high resistance, R, to one terminal 
of which is connected one terminal 
of the potential coil of the wattmeter 
Wm, while the other terminal of the 
wattmeter is connected to a movable 
contact K, The current coil of the 
wattmeter is connected in series with 
the load L and ammeter Am. L may 
be the adjustable lamp bank already 
described. A standardized voltmeter 
Vm is connected in parallel with the 
potential coil of the wattmeter. When compensated wattmeters 
are tested, the independent connection is used for potential con- 
nection; this cuts out the compensating coil as is evident from 
Fig. 82. When the connections are made as shown, three 
separate tests can be made as follows: 

1. With constant voltage and variable current. 

2. With variable voltage and constant current. 

3. With variable voltage and variable current. 

To make the test with constant voltage, carefully read the 
instruments, all circuits being opened. Insert the smallest load 
desired and close the switch jS. By inserting a smaller or greater 
number of lamps, the desired value of current can be obtained. 




Fia. 247. 



296 



ELECTRICAL METERS 



Close K and move it along until the voltmeter indicates the 
proper voltage. 

To obtain reading for different currents, vary the number of 
lamps. For variable-voltage test, adjust the current through 
the ammeter for the maximum desired value. Move iC so as to 
get the lowest voltage desired. For other readings move K 
until a sufficient number up to maximum is obtained, the cur- 
rent in the meantime is kept constant. For variable current 
and voltage, adjust the number of lamps and move K until 
suitable readings on the voltmeter and ammeter are obtained. 
For different readings change these adjustments. In each case, 
the three instruments should be read simultaneously. The re- 
sults may be tabulated as follows: 



EXAMPLE 

Test 3. — Calibration of wattmeter. 
Apparatus, — Weston wattmeter No. 4,263.* 

Standard voltmeter No. 316. 

Standardized ammeter No. 21,131. 

Lamp bank and rheostat. 
Temperature 22.5°C. 

Table V 



Voltmeter 
reading 



110 

no 
no 
no 
no 
no 
no 
no 



Cor- 

reoted 

volts 



Ammeter 
reading 



Cor- 
rected 
amperes 



True 
watts 



Watt- 
meter 
reading 



Correc- 
tion 



111.5 


2.50 


2.75 


306.62 


283.90 


+22.7 


111.5 


4.50 


4.95 


551.92 


511.00 


40.9 


111.5 


6.50 


7.20 


802.80 


747.00 


65.8 


111.5 


8.70 


9.57 


1,067.50 


1,000.00 


67.5 


111.5 


13.00 


14.35 


1,600.00 


1,500.00 


100.0 


111.5 


17.50 


19.25 


2,137.00 


2,000.00 


137.0 


111.5 


22,00 


24.00 


2,675.00 


2,500.00 


175.0 


111.5 


27.00 


29.70 


3,212.50 


3,000.00 


212.5 



Remarks 



Curve, Fig. 248 



Fig. 248 shows the correction to be applied at any wattmeter 
reading with constant voltage and changing current. Similar 
curves may be plotted for the other two cases, viz., when current 
is kept constant and voltage is changed, and when both current 
and voltage are varied. 

The foregoing method of calibration applies only to watt- 
meters whose indications are independent of frequency and wave 

* This wattmeter had received rough and severe use by students* 



TESTING METERS 297 

form. Induction wattmeters cannot be calibrated on direct 
current. Wattmeters of this type are most conveniently cali- 







































































- 






^ 
























^ 


■' 










1 
















^ 


'' 
























^ 


- 


-^ 


























^ 








» 


,/« 


r/ff^ 


»«»^ 


. 













brated by placing them in circuit with an electrodynamometer 
wattmeter which hafl previously been standardized. A good 




instrument for this purpose is the Watt dynamometer shown 
in Fig. 249. Each phase of a polyphase wattmeter must be 
calibrated separately. A diagram of connections for testing 



298 



ELECTRICAL METERS 



induction wattmeters is shown in Fig. 250, where W> represents 
the standardized wattmeter and Wi the induction instrument to 
be tested. The current through the potential coil is partly 
determined by the frequency of the alternating current under 
constant voltage, and hence the frequency at which the instru- 
ment was calibrated should alwaj'S be recorded. 




Fig. 250. 



255. Testing Single-phase Power-factor Meters. — ^The power- 
factor of a circuit has been defined as the ratio of the true power 
to the apparent power being delivered by an alternating current. 







Fig. 251. 



If / and E are the effective values of current and pressure re- 
spectively, the power is given by the expression TF = KIE = IE 

cos ^, where X, or cos Q is called the power-factor. Thus K = 

W 
T yy fj ' ^ can be measured by means of a standard wattmeter 



TESTING METERS 299 

and / and E by means of a suitable ammeter and voltmeter. The 
correct power-factor can thus be calculated from the readings 
of three standardized instruments, wattmeter, ammeter, and 
voltmeter, connected as in the diagram of Fig. 251. The cor- 
rection to be applied is then obtained by subtracting the indicated 
power-factor from the calculated power-factor. In order to 
use this method for calibrating a single-phase power-factor meter, 
the load L must be inductive and variable. The methods of ob- 
taining loads of variable power-factor are described in Chapter 
XX. At this point it may be noted that a small induction or 
synchronous motor can be used for the inductive load. The 
power-factor of the induction motor may be varied by loading 
it more or less, and the power-factor of the synchronous motor 
may be varied by varying its field excitation. This is hot the 
most satisfactory method, as the range through which power- 
factor can be varied is limited. 

266. Testing Polyphase Power-factor Meters. — When the 
separate circuits of a polyphase system have the same power- 
factor, the power-factor of the whole system is equal to the power- 
factor of one of the phases. When the load is unbalanced so that 
the separate phases have different power-factors, there is no 
one power-factor that has a definite value or physical significance. 
The power-factors of the separate phases of a three-phase system 
are cos ^i, cos 62, and cos Oz, while by definition the power-factor 
of the system is 

Power-factor = „ y \ ^ j — x yp r - The polyphase meter, 

however, gives the mean of cos ^1 + cos 62 + cos ^3. The power- 
factor as given by definition is evidently not the same as that 
indicated by meter. When the load is balanced, the power- 
factor is 

Power-factor = — 



^ZEJi VSEI 

where W represents the power expended in balanced load, E 
the voltage between mains, and / the current in one main. To 
test such an instrument on balanced load, it is sufficient to deter- 
mine the power-factor of one phase and compare that with the 
instrument indication. For tests of polyphase power-factor 
meters, the testing apparatus necessary are a standardized am- 
meter, voltmeter, and wattmeter. These must be connected to 



300 



ELECTRICAL METERS 



each phase successively in the manner shown in Fig. 251. Pro- 
visions bIiouIJ be made for transferring the instrument connec- 
tions from one phase to another without disturbing the flow of 
energy. This is readily accomplished by the aid of a polyphase 
tneterboard shown in Fig. 252. While the test is under way, some 
characteristics of the meter may also be observed. Disconnect 
the potential circuit, and observe the rotation of the vane under 
the influence of the revolving field produced by the series windings 
alone. Reverse two of the series connections and observe the 
effect. The revolving field of an induction motor will behave in a 
similar manner. Reverse the potential connections and observe 
the effect. Can you explain this? 

Polyphase power-factor indicators will give correct indications 
only on balanced circuits, although slight unbalancing will not 
greatly affect the reading. Determine what effect an unbalanced 
load has on the indication. The Westinghouse Klectric and Manu- 
facturing Co. suggests the following 
method for checking their instru- 
ments: The moving parts should be 
perfectly balanced; that is, when 
no current is passing through the 
coils, the pointer should remain in 
any position in which it is placed. 
The instrument should now be cor- '"*' ^''^' 

rectly connected to the circuit in the usual manner with the 
exception that the wire to the lower left-hand binding post 
should remain disconnected. If the meter is correct in calibra- 
tion, the pointer, with full-load current on the meter, will come 
to rest at a position coinciding with a rod line in the upper left- 
hand part of the scale. Should the pointer not come to rest at 
this point, it should be shifted on the shaft until it rests on the 
red line. Care should be taken not to disturb the balance by 
moving the pointer. This procedure simply insures the main- 
tenance of the original calibration. 

267. Testing Frequency Meters. — The frequency of an alter- 
nating current depends upon the speed and number of poles of 
the generator. Thus, if the generator has p field poles and makes 
n revolutions per minute the frequency is 




-,x, 



, cycles per second. 



TESTING METERS 301 

To test the accuracy of a frequency meter it is only necessary to 
measure the speed of the generator, count the field poles and 
calculate the correct frequency by the above formula. The speed 
can easily be determined by means of an accurate tachometer 
or speed counter. 

Any inaccuracy in the resonance type of frequency meter can 
be corrected by filing ofif, or adding to the solder weight at the 
top of the reed. It is not advisable for an inexperienced person 
to attempt this. 

In place of a calibration curve it is preferable to arrange a 
table showing the instrument indication and correct frequency. 
The induction type of frequency meter may be calibrated in 
exactly the same way, but adjustment is made by varying the 
series resistance until the instrument reads correctly. 

268. Testing Recording Meters. — Since recording instruments 
are mainly modified forms of indicating meters, they may be 
tested in exactly the same way as indicating meters of the same 
type. 



CHAPTER XIX 

TESTING WATT-HOUR METERS 

259. Introduction. — In order that higher efficiency in the 
operation of watt-hour meters may be maintained, not only the 
most reliable meters must be used, but constant vigilance is neces- 
sary in keeping these meters accurate. For this purpose, the 
meter departments of some companies are equipped with the 
highest grade of primary standards and all necessary appliances 
for checking the accuracy of the secondary standards which are 
employed in meter testing. To the secondary standards already 
mentioned should be added the rotating standard watt-hour 
meter. 

260. Rotating Standard Watt-hour Meter. — The instrument 
to which has been given the name ''rotating standard" is at best 
only a secondary standard. The principles of operation of the 
rotating standard meter are the same as those of the service 
watt-hour meters, the construction, however, is modified to meet 
certain conditions. The conditions that necessitated changes in 
construction are portability, wide range of current capacity, and 
ease of determining the number of revolutions. The first con- 
dition is fulfilled by omitting the iron case and enclosing the 
operating parts of the meter in a carrying case as shown in 
Fig. 253. 

While it is not difficult to make the series winding so that 
different loads might be safely carried, for accuracy and rapidity 
of testing, it is necessary to construct the series coils in such a 
manner that the torque will be the same at different loads. 
This is accomplished by making the current coils in sections, and 
mounting the sections so that they can be connected in series or 
parallel. The number of ampere-turns of the series coils are made 
equal at different full-loads by either a sliding contact, or by 
changing the external connections. The field windings are 
usually for full-loads of 1, 5, 10, 20, and 40 amp., or for 1, 5, 
10, 50, and 100 amp. 

The last condition is fulfilled by affixing a pointer to the end 
30 303 



304 ELECTRICAL METERS 

of the ehaft. This pointer moves over a dial graduated into 1 

parts making it possible to read to j-ioo of a revolution, and 
even closer. The whob number of rcvolutionB is indicated by 




Pig. 253. 

two smaller pointers, plainly shown in Fig, 253. Fig. 254 shows a 
aide view of the Duncan rotating standard watt-hour meter with 
case removed. In Fig. 255 is shown a General Electric induction 
teat meter. The figures plainly show the similarity between the 



TESTING WATT-HOUR METERS 



305 



regular service meter and tbe teat meter as the rotating standard 
should be called. The use of the portable standard watt-hour 
meter has several advantages, among which may be mentioned: 

1. The use of only one instrument greatly facilitates the 
testing of meters in service. 

2. Both test and tested meters are subjected to the same 
conditions; and hence, any variation in load during the teat is 
automatically corrected by the test meter. 

3. Only one man is necessary for testing, as the time of starting 
and stopping the test meter may be controlled by a push button. 



E 


1 " 0^'^' 1 


! 


p 




1 


|[ 




1 



4, The portable test watt-hour meters are more rugged than 
indicating instruments, and consequently, they will stand harder 



Against these advantages must be placed the fact that the 
results obtained are liable to be less accurate than those obtained 
by the use of well-calibrated indicating instruments. 

261. Meter Timing Device.— A very ingenious method of 
determining the correct interval of time that energy is flowing 
through a meter under test has been devised by Mr. F. A. Kartak, 
Director of the Standards Laboratory, University of Wisconain, 



306 ELECTRICAL METERS 

A aimpU£ed diagram of the easeutial features of the device are I 
shown in Fig. 256. 

The apparatus automatically closes and opens the voltage 
circuit of the meter under test. The controlling element is a 
standard seconds-beating clock whose pendulum P operates a 
three-point magnetic switch. This switch consists of two per- 
manent magnets, M and M', one of which is mounted at the 
lower end of the pendulum and swings with the pendulum above 
the other magnet M' which is pivoted so that as the pendulum 




Piu. 255. 

swings the lower magnet makes contact first with point C and 
then with point C in each of which positions it remains until 
it is moved on the return swing of the pendulum. When the 
pendulum swings to the right, the circuit of battery B is closed 
at C and relay R is magnetized and its contacts are closed 
against the action of the spring S. When this secondary cir- 
cuit is closed, the electromagnet M, is energized with a conse- 
quent forward movement of its armature. This movement 
of the armature rotates the ratchet wheel Ra one step. 



TESTING WATT-HOUR METERS 



307 



Upon the shaft of the ratchet wheel is mounted an insulated 
selective switch. This switch consists of a circular disk of 
insulating material carrying on its edge two contact points Ki 
and K2. These contact points are connected to two slip rings 
and then to the circuit by means of brushes. The rotation of 
the ratchet wheel thus moves forward the contact points on the 
insulating disk. 

When Ki comes into contact with brush fi, and the magnetic 
switch M' closes the circuit at C, leg Li of the differential relay 
DR is energized, attracting the armature A, depressing the 




Fia. 256. 



needle N into the mercury cup Hg, and closing the voltage circuit 
of the watt-hour meter. This voltage circuit remams closed 
until contact Ki is moved forward and closes the circuit with 
brush fi, and M' again comes into contact with C, when the leg 
Lt of the differential relay is energized with a consequent openii^ 
of the voltage circuit of the watt-hour meter. The duration of 
the energy flow through the meter is thus determined by the in- 
terval of time between the closing of the circuits by Ki and K^ 
at /i and /j respectively. This interval of time can be varied by 
changing the space between Ki and Jf », The use of the stop 



308 ELECTRICAL METERS 

watch with the accompanying inaccuracies is thus eliminated and 
a much more accurate measurement can be made, 

262. Kinds of Tests. — Tlie meter committee of the National 
Electric Light Association recommends that in view of the diver- 
sity of conditions, and the lack of recognized standard testing 
methods, meter tests be classified as follows: 



1. Shop tests. 

2. Installation tests. 

3. Periodic tests. 

4. Complaint tests. 



5. Inquiry tests. 

6. Retests. 

7. Repair tests. 

8. Special tests. 



263. Shop Tests. — Upon the receipt of the meters from manu- 
facturers, also when removed from service and before being 
placed in the stock room, all meters should be carefully examined 
and tested. Any defects that may be discovered should be cor- 
rected at that time. These tests, preliminary to installation or 
storing, are called shop tests, 

264. Installation Tests, — Even if a meter is found to be correct 
in the shop, it is not safe to assume that it will be correct after 
being placed in service, and therefore, a test after installation is 
necessary. In the case of commutator meters, a test is impera- 
tive. One good plan is to inspect the meter immediately after 
being connected to service, and then after about 4 weeks test 
the meter to determine its ptTcentage of accuracy. 

The commutator of a new meter is not ahvaj-s in good working 
condition when installed and it is advisable to place the meter in 
service for a time before making a final test. Then again, acci- 
dents affecting the accuracy of the meter are liable to occur 
during the installation of the meter and it is necessary to deter- 
mine whether the accuracy of the meter has been affected. 
Induction meters should be tested as soon after their installation 



The best method of making installation tests is by means of a 
standardized portable watt-hour meter. 

265. Periodic Tests. — No matter how good the construction 
of a meter, nor how accurate its registration, its accuracy will 
diminish with time. Tests at regular intervals are, therefore, 
necessary to determine whether the permissible error is not 
exceeded. 

Those periodic tests should be made at intervals to suit the 
circumstances. Commutator meters, being more liable to be- 



TESTING WATT-HOUR METERS 309 

come inaccurate, should be tested more frequently than induction 
meters whose rugged construction and absence of commutator 
makes them immune to certain troubles. No definite rule can be 
formulated for determining the interval of time between periodic 
tests of different capacities of meters and for different classes of 
business, yet every company should appreciate the necessity for 
testing every class of meters before its maximum error exceeds 
the permissible limits. The interval between tests must be deter- 
mined by experience, cost of metering, amount of bill, etc. 

266. Complaint Tests. — When a consumer complains of his bill, 
it is frequently customary to test the meter unless a test has 
been made very recently. Complaint tests are conducted in the 
usual manner, except that it is customary to test the meter, 
not merely on light and full loads, but also on the other loads, 
especially on the normal load or load most generally used. 

267. Inquiry Tests. — Inquiry tests are tests ordered by the 
company itself before the bill is rendered, to determine whether 
or not the meter has been operating properly. 

268. Retests. — Retests are tests made before current is 
reintroduced to meter which has been out of service for a long 
time; or if the meter has been opened by any one not authorized; 
or if the meter has been moved or reconnected. 

269. Repair Tests. — Meters that have been repaired in service 
should be tested immediately after the completion of the repairs. 
Such tests are properly termed repair tests. 

270. Special Tests. — ^Any tests not properly coming under any 
of the foregoing headings may be classed as special tests. 

271. Meter Constants. — Since the number of revolutions of the 
meter disk is merely proportional to the energy that has passed, 
some constant must be used to convert the number of revolutions 
into watt-hours or kilowatt-hours. Two kinds of constants are 
used in practice, namely — dial constant, and test constant. 

272. Dial Constant. — On large-capacity meters the difference 
between any two readings seldom gives the watt-hours directly. 
To get the energy that has been registered, the difference between 
the dial statements must be multiplied by a constant which is 
usually marked on the dial. This is known as the dial constant. 
It has different values for meters of different capacities. 

273. Test Constant. — Manufacturers of meters usually stamp 
or print upon some part of the meter a constant which is used in 



310 ELECTRICAL METERS 

testing, but as there is no uniformity in the meaning of this 
constant, its significance must be explained. 

274. Watt-hour Constant.— Since the meter registers in watt- 
hours, for every revolution of the disk, a definite quantity of 
energy must have been delivered to the load circuit. This 
energy, in watt-hours corresponding to one revolution of the 
disk, is called the watt-hour constant. 

276. Watt-minute or Watt-second Constant. — A watt-hour b 
the energy delivered by 1 watt in 1 hr. ; similarly, a watt-minute, 
or watt-second, is the energy or work done by 1 watt in 1 min. or 
1 sec, respectively. A watt-minute is thus equal to J^o watt- 
hr., and a watt-second equal to 3-^.600 watt-hr., and hence, 
the watt-minute constant is equal to 60 X watt-hour constant, 
and a watt-second constant is equal to 3,600 X watt-hour constant. 
Let JC* = watt-hour constant, 

K„ = watt-minute constant, 
and K, = watt-second constant, 
then K. = 3,600K^ = 60 K„. 
The test constant as used by manufacturers is either one of these 
or a multiple of one of these constants. 

276. Use of Constant in Testing. — The accuracy of a meter is 
expressed by the ratio of its indication to the actual watt-hours 
in per cent. In algebraic symbols this may be expressed by 
irui ^, meter watt-hours 
^^ ^ actual watt-hours = Percentage of accuracy. 

The numerator is, of course, the indication of the watt-hour 
meter during a given time, while the denominator is the actual 
number of watt-hours, as measured by standard instruments. 
If the actual watt-hours are determined by means of an indicating 
wattmeter, the indication will have to be multiplied by the time 
during which the observations were made. Thus, the actual 
watts as given by the indicating instruments multiplied by 
r/3,600, will give the actual watt-hours. T is the duration of 
test in seconds, and 3,600 is the number of seconds in 1 hr. 

It is usually impossible to determine accurately the meter 
watt-hours for a short time from the dial indications of the meter, 
and, hence, in practice the number of revolutions of the disk 
during a definite time is determined by means of a stop watch or 
other timing device. The meter watt-hours are then computed 
as above. 



TESTING WATT-HOUR METERS 311 

Since the watt-hour constant has been defined as the number 
of watt-hours, corresponding to one revolution of the disk, the 
total number of watt-hours will be equal to the watt-hoiu* con- 
stant times the number of revolutions, or 

watt-hours = Kh X R 

where R is the number of revolutions counted in time T. We 

can, therefore, write 

T 
Meter watts X qqqq = Kh X R 

_ . ^ ^^ KhXR X 3,600 
or Meter watts = jp 

This is the standard formula as used, in one form or another, 
by all meter manufactiu'ers. If all meter manufacturers used 
this formula the watt-hour constant would be the test constant, 
but as different manufacturers use dififerent modifications, this 
simple relation does not hold in every case. The constants as 
used by the various companies are: 

General Electric Co. : 

Test constant = watt-hour constant 

or Kh = Kg. 

Duncan Electric Manufacturing Co. : 

Test constant = watt-minute constant 

Westinghouse Electric and Manufacturing Co. : 
Test constant = watt-second constant 

• ^^^*^3^^''' 
Fort Wayne Electric Works : 

Test constant = 36 times the watt-hour constant 

rr Kf 

Where Kh represents the watt-hour constant and Kg, Kd, Ku,^ 
Kf, represent the test constants of the General Electric, Duncan, 
Westinghouse, and Fort Wayne companies, respectively. 



V 



ut.-. ^ 



312 



KLKCTIifCAL METERS 



100 - 



= percentage of accuracy. 



If a rotating stiiinliird wuU-liour mctt-r has been used for 
detormiriing tlio actual cni-'rgy piiHiu^d through the meter under 
teat, the percentage of accuracy is givan by 
RXK (of m e ter under lest) 
R'XK' (of Btandard) 
R and K are the number of revoUitions and constant of the meter 
under teat, while R' and A*' arc the corresiMnding quantities of 
the rotating standard. It is thus evident that l)L'forc the above 
formula can be used, K and K' will have to he reduced to the 
same basis. That is, a Westinghouse rotating standard cannot 
be used to teat a Fort Wayne meter until the constants have been 
reduced either to watt-hnnra or watt-secunda (see Table VI). 

277. Methods of Loading. — In practice there are several differ- 
ent methriils of loading meters under test. The most common 
methods are: 

1. The consumer's load. 

2. Portable lamp bank. 

3. A specially designed and con- 
structed load box. 

4 Portable storago batteries. 

5. Step-down transformers. 

278. The Consumer's Load. — While 

this method is convenient, in that little 

accessory apparatus is necessary, the 

annoyance to the consumer and the liability to misundcratand- 

ing make it advisable to avoid this method as much as possible. 

279. Portable Lamp-bank Method. — One form of lamp bank 
which may be used for thia purpose has been suggested. These 
lamps are operated at the lamp voltage and the load is changed 
by changing the number of hitnps in the circuit. 

280. Special Load-box Method, — I^ond boxes may bo merely 
self-con tallied non-inductive retiistftncoB to which may be attached 
indicating instruments. Ono form of such a load box is shown 
in Fig. 257 which ia known as the Knopp load box. This ia a 
variable resistance box upon which is mounted an indicating 
ammeter. The resistance box has several coils which may bo 
connected in different ways for different loads. The exact [wwer 
consumption under a given voltage may bo predetermined and 
marked on the box. In aeries with the loading resistance ia 
connected a second resiataneo whoso value may be varied by 
eliding oontaots. By the use of this second resistanoo the voltage 




t'lu. 257, 



TESTING WATT-HOUR METERS 



313 



drop across the load coils may be made equal to the voltage at 
which the power consumption of the coils was determined. The 
pressure coil of the watt-hour meter is connected so that the 
voltage impressed upon the meter is the same as that impressed 
upon the load coils. Tho reading of the ammeter is thus suffi- 
cient for determining the load. Fig. 258 shows the internal 
connections of the Knopp load box. When the box is to be used 
on 110-volt circuits, the plugs 0, a, b, and c, are used. On 220- 
volt circuits additional resistance is connected in scries by using 
plugs 0', a', b', and c'. The Knopp load box may be used on 
either direct-current or alternating-current circuits. 




ffififiSffiBh 



Fig. 258, 



Pig. 259. 



281, Portable Storage -battery Method. — For testing direct- 
current meters on the consumer's premises the portable storage 
battery has many advantages. The load current is supplied at a 
low voltage and hence the energy required for making the test is 
much less than when the load current is taken from the line. Any 
desired current can be obtained in a simple manner, and when once 
the adjustments are made, the current will remain practically 
constant. For ease of manipulation and rapidity of operation, 
some regulating device must be used with the battery. One 




314 ELECTRICAL METERS 

good arrangement of resistances is shown in diagram,. Kg. . 
Other devices can easily be designed. 




282. Low-voltage Transformer Method. — There are on the 
market several different makes of low-voltage transformers com- 
bined with resistances for alternating-current meter testing. 




Fio. 261. 

The general principles of all are the same, hence only one will be 
described. The appearance of the Rollinson load box is shown 
in Fig. 260, the internal connections of which are shown in Fig. 
261. The diagram clearly shows that the load box is primarily 



TESTING WATT'HOUR METERS 



315 



a step-down auto-transformer, the secondary of which supplies 
current to the series coils of the tested and testing meters. The 
resistances for controlling the voltage impressed on the primary- 
are Bi, R2, and the circular-dial rheostat. The load current is 
thus varied by connecting these resistances in series or parallel 
by adjusting the rheostat, and by connecting in the load a greater 
or smaller number of secondary turns. 

The manner of connecting the tested and testing meters to the 
load box is shown in Fig. 262. 




fhfBrtriet 



OfandiBtx/ M€tier 



Fig. 262. 



Where step-down transformers are used, it is advisable first 
to make a thorough test of the influence of the transformer upon 
the power-factor. The power-factor of the testing circuit will in 
most cases be less than unity and under extreme conditions 
unduly low power-factors may be obtained. It is thus necessary 
to test all such load boxes for power-factor under working 
conditions. 

283. Determination of Watt-hour Constant, Experimentally. — 
To determine Kh^ for a direct-current watt-hour meter experi- 
mentally, connect the instruments as shown in Fig. 263, where 



316 



ELECTRICAL METERS 



M represents a direct-current integrating meter, VM a voltmeter, 
and MVM a standard niillivoltracter with its shunt S. The 
source of power is preferablya storage battery. Both the pressure 
and current are kept constant and the exact time of a definite 
number of revolutions is determined by means of the stop watch. 
The current is obtained from the milhvoltmctcr indications, 
divided by the resistance of the shunt. K is then calculated 
from 

_ watts X T 




ztms: 



k 



284. Method of Procedure. — Before taking any readings, 
enough time must clapae for the pressure coil to reach normal 
temperature. This is true of both direc^currcot and alternating- 
current meters. This time can be shortened considerably if 
some provision is made for subjecting the pressure coil to double 
voltage for a short period. This can easily be done on three- 
wire circuits, where pressure coils are connected between neutral 
and one main. Before taking any readings, make a white mark 
on the disk, adjust the voltage to the proper value, and insert all 
of the load resistance where a variable reistance is used. If the 
lamp bank is used, Jiiaert three or four lamps in series, and gradu- 
ally increase the current until the armature commences to rotate. 
Repeat this three or four times and take the average of the 
currents. All values of the current below this value are not 
recorded by the meter, since they do not cause rotation of the 
armature at the normal voltage. 

Adjust the resistance of lamps so that the full-load current 
passes through the meter, count the revolutions in 1 min. or 
some other suitable interval of time. 



TESTING WATT-HOUR METERS 



317 



Repeat the test with decreasing values of load current. Care 
must be taken that the speed is not affected by external causes, 
such as air draughts, touching with the hand, etc. If the test 
constant, as given by the manufacturers, is not given in watt- 
hours, it can readily be obtained by means of relations already 
given. 

This constant should be ^ 
determined at different loads 
and different temperatures. 
When this is done, it will be 
observed that the value of the ^ 
constant depends to some ex- /© 
tent upon the temperature 
and load. A diagram show- ov 
ing this relation for a com- 
mutator-type watt-hour a^ a4 as aa w 
meter is shown in Fig. 264. 
It will be observed that the 
constant at any given temperature first decreases to a minimum 
and then increases with increase in load. This increase is even 
more prominent at overloads. A change in temperature has a 
similar effect, namely, as the temperature increases the constant, 
K, decreases. 




LOAD 

Pig. 264. 




Fig. 265. 

In Fig. 263 a storage battery is represented as the source of 
current for the series coils. For testing the commutator type, or 
direct-current watt-hour meters, it is a good plan to provide a 
few cells of a storage battery, preferably of the portable form, 
for supplying the load current, and many small cells for the 
excitation of the voltage circuit. When two sources of pressure 



318 



ELECTRICAL METERS 



Table VI. — Table Testing Constants op Standard Types op Watt- 
hour Meters 



Capacity of 
meters in 
amperes 



Sangamo types "F" and "D" 



Testing constant 



100-125 volts 



Watt- 
liouis 



Watt- 
secouds 



200-250 volts 



Watt- 
hours 



Watt- 
seconds 



G. E. types "CO." "J2," and "D2" 



Testing constant 



100-120 volts 



Watt- 
hours 



Watt- 
seconds 



200-220 volts 



Watt- 
hours 



Watt- 
seconds 



2H 

3 

6 

5 

10 

15 

20 

25 

30 

40 

50 

60 

75 

80 

100 

150 

200 

300 



H 
H 

H 

• ■ 

IH 

• • 

2 
2H 



5H 
6?^ 
10 

13H 
20 



1.800 "F" 
2.400 "D" 
2,400 



4,800 

7.200 
0.600 

14.400 

19,200 
24,000 
36,000 
48.000 
72,000 



1 

IH 

IH 

• • ■ • 

2H 

• • • • 

4 
5H 

• • • • 

8 

• • • • 

10?i 

13H 
20 

26H 
40 



3,600 '*F*' 
4.800 "D" 
4.800 

• ••••• 

9.600 



14.400 
10.200 

28.800 

38,400 
48,000 
72.000 
96,000 
144,000 



H 
H 
H 



450 



2 

• • 

3 

• • 

4 

6 

mi 



720 
1.440 
2.160 

3.600 



7.200 

10.800 

14.400 
21.600 

45.iD00 



I • • • 

H 



000 



6 

• • • • 

7H 
12>i 

• • • • 

25 



1.440 
2.700 
4.500 

7,200 



14,400 

21.600 

27.000 
45.000 

90.000 



Table VI — Continued 





a. E. types "J." "JI." "JN." •'FN," 
••DN."and*'Dr' 


G. E. type "I" 


Capacity of 
meters in 
amperes 


Testing constant 


Testing constant 


100-101 volts 


200-220 volts 


100-130 volts 


200-260 volts 




Watt- 
hours 


Watt- 
seconds 


Watt, 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 

• 


2H 

3 

5 

6 

10 

15 

20 

25 

30 

40 

50 

60 

75 

80 

100 

150 

200 

300 


• • 

H 

• • 

M 

1 

• • 

1 

2 


720 
1.800 

1.800 
3.C00 

3,600 
7.200 


• • • • 

H 

1 

• • • ■ 

1 

2 

• • • • 

2 

4 


1.440 
3.600 

3,600 
7,200 

7,200 
14.400 


• • 
H 

Mo 

• • 

H 

1 

• • 

IH 

• • 

• • 

3 

• • 

5 

• • 

6 
10 

12M 
20 


720 
1.080 

2.160 
3,600 

5,400 

10.800 

18.000 

21,600 
36,000 
45.000 
72,000 


• • • • 

H 
H 

• • • • 

2 

• • • • 

3 

• • • • 

• • • • 

6 

• • • • 

10 

• • • • 

12H 
20 
25 
40 


1.440 
2.160 

4.500 
7,200 

10.800 

21.600 

36.000 

45.000 

72.000 

90.000 

144,000 



TESTING WATT-HOUR METERS 



319 



Table VI — Continued 





Westinghouse types "B" and "C" 


Fort Wayne type "K" (345,000 
and above) 


Capacity of 


Testing constant 


Testing constant 


meters in 
amperes 


• 

100-110 volts 


200-220 volts 


110 volts-2w 


220 volts-2w 




Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


2H 

3 

5 

5 

10 

15 

20 

25 

30 

40 

50 

60 

75 

80 

100 

150 

200 

300 


• • • • 

• • • • 

H 

• • • • 

H 

• • ■ • 

• • • • 

• • • • 

2H 

• • • • 

• • • • 

• ■ • • 

2H 

• • ■ ■ 

• • • • 

• • • • 

• • • • 


1,200 
2.400 
4.800 

9,600 
9,600 


• • • • 

• • • • 

H 

• • • • 

IH 

• • • • 

2H. 

• • • • 

• • • • 

• • • • 

• • • • 

• • • • 

• • • • 

■ • • ■ 

• • • • 

• • • • 


2.400 
4.800 
9.600 

19,200 
19,200 


• • • • 

• • ■ • 

yi 

• • • • 

H 
1 

• • • • 

2 

• • • • 

2H 

• • • • 

5 

7H 
10 

• • • • 


900 

1,800 
2,700 
3.600 
4.500 

7.200 

9,000 
13,500 

18.000 
27.000 
36.000 


• • • • 

• • • • 

• • • • 

1 

IH 

2 

2H 

• • • • 

4 

• • • • 

5 

7H 

• • • • 

10 
15 
15H 

• • • • 


1,800 

3.600 
5,400 
7.200 
9,000 

14,400 

18,000 
27,000 

36.000 
54,000 
57.000 



Table VI — Continued 





Fort Wayne type "K" (344,999 
and less) 


Gutmann meters 


Capacity of 


Testing constant 


Testing constant 


meters in 
amperes 


110 volts-2w 


220 volts-2w 


50 volts 


100 volts 




Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


2H 


• • • • 

H 
H 

1 
1 
1 

2 
2 
2 
3 
3 

• • • • 

4 
6 
8 


900 

900 

1.800 

3.600 

3.600 

3.600 

7.200 

7,200 

7,200 

10,800 

10,800 

14,400 
21,600 
28,800 


• • • • 

H 
1 

IH 

2 
2 

2H 

3 

4 

5 

6 

• • • • 

8 
12 
16 


1,800 

1,800 

3.600 

5.400 

7.200 

7.200 

9.000 

10,800 

14,400 

18,000 

21,600 

28.800 
43,200 
57,600 


• • • • 

• • • ■ 

• • • • 

H 
H 

• • ■ • 

• • • • 

« • • • 

1 

• • • • 

2 

• • • • 

2 
3 
6 








3 
5 
10 
15 
20 
25 
30 


1,200 
1,200 

1,800 


"ii 

H 
H 

1 


900 
1,200 
1,200 

3,600 


40 








50 
60 


3,600 


2 


7,200 


75 
80 


7,200 


2 


7,200 


100 
150 
200 


7,200 
10,800 
21,600 


3 
6 


10,800 
21.600 



31 



320 



ELECTRICAL METERS 



Table VI — Continued 





Duncan meters 


Columbia meters 


Capacity of 


Testing constant 


Testing constant 


meters in 
amperes 


100-125 volts 


200-250 volts 


110* volts 


220 volts 




Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


Watt- 
hours 


Watt- 
seconds 


2H 

3 

5 

10 

15 

20 

25 

30 

40 

50 

60 

75 

80 
100 
150 
200 
300 


ii 

1 

• • • • 

1 

• • • • 

• • • • 

2 

• • • • 

3 

• • • • 

4 
6 
8 

• • • • 


450 

900 
1.800 
3.600 

3,600 

7,200 

10.800 

14.400 
21.600 
28.800 


• • • • 

H 

1 

2 

• • • • 

2 

• • • • 

• • • • 

4 

• • • • 
6 

• • • • 

8 
12 
16 

• • • • 


1,800 

1.800 
3.600 
7,200 

7,200 

14,400 

21,600 

28,800 
43,200 
57,600 


• • • • 

M« 
H 
H 

• • • m 

VAs 

• • • • 

• • • • 

2^ 

• • • • 

4H 

• • • • 

SH 
11 H 
16K 


500 

1,000 
2,000 
3,000 

5.000 

10,000 

15,000 

20.000 
30,000 
40.000 
60,000 


Ms 

• • • • 

H 
IH 
IH 

• • • • 
27yi 

• • • • 

• • • • 

6M» 

• • • • 

SH 

• • • • 

im 

16 H 
22 ?i 

33H 


1,000 

2,000 
4,000 
6,000 

10,000 

20,000 

30,000 

40.000 

60.000 

80,000 

120,000 



are used, the connections of the voltmeter and voltage circuit 
of watt-hour meter are to be made according to Fig. 265. 

In making the foregoing test, it is best to take at least three 
readings at each load, and to vary the load so that the constant 
may be determined at 10, 25, 50, 100, and 125 per cent, of the load. 

From data obtained, a curve similar to that shown in Fig. 
264 should be drawn. If any reading is wrong, it will easily 
be detected by the corresponding point not coming on the curve. 

286. Test for Percentage of Accuracy. — In commercial practice, 
it is not often necessary to determine Kh or the watt-hour 
constant, as the test constant is given by the maker, ^^ well as 
the formula by which the number of revolutions are to be 
translated into watt-hours. The quantity that is of most interest 
commercially is the percentage of accuracy which is defined as 
the ratio of the registered watt-hours, expressed as a percentage, 
in a given time to the true watt-hours, or kilowatt-hours. That 
is, the important question is how much too fast or too slow is 
the meter, rather than the characteristics of the meter. 



TESTING WATT-HOUR METERS 



321 



When an ammeter and voltmeter are to be used in testing a 

direct-current watt-hour meter, the connections shown in Figs. 

263 and 265 may be used. The watts registered are calculated 

from the constant of the meter, number of revolutions of disk, 

and duration of test, thus: 

- - , ,, KkXBX 3,600 
Meter watts = — — — ™ 

The true watts are obtained from the readings of the indicating 
instruments and are equal tol X E. The percentage of accuracy 
is then equal to 

„ , , IOOKk XBX 3,600 
Percentage of accuracy = — — TXiXE 

It must be remembered that Kh is the watt-hour constant, and 
as some manufacturers of meters use other constants, the value 



-1 

5 .^ 

IT^_ 



Pig. : 



of the manufacturer's constant in terms of Kt. will first have to 
be determined before substituting in the above formula. The 
percentage of accuracy should be determined for 10, 25, 50, 100, 
and 125 per cent of load, and a curve plotted for the load and 
percentage of accuracy. The form of such a curve is shown in 
Fig. 266. 

EXAMPLE 
Test Ho. 4.— 
Test ot Scheefer direct-current watt-hour meter. 
Capacity 30 ajnp. 
ApporatuB. — 

Portable wattmeter, Weston. 
Stop watch. 
Lamp bank. 



ELECTRICAL METERS 
Table Vll 





Ko. ravc- 


Timo. 


Molcc 


Corrwt 












WBlU 


watu 




Romiir I 


10 


10 


IS5.3 


259.0 


300 


82.5 




25 


10 


68.8 


67 5 


750 


90 2 


Poorly com- 


50 


20 


67.3 


1,426.0 


1,500 


95.1 


pensated 


100 


30 


60.0 


2,880. C 


3,000 


96.0 


for friction. 


125 


40 


53.6 


3,581,0 3,750 


95.5 


Curve, Fig. 2G6 



L 



It is evident from the form of the curve that the friction of the 
bearings and commutator is not properly compensated at light 
loads. The speed of the rotat- 
ing element in a well-designed 
meter should be proportional 
to the load. Whether this 
relation is fulfilled is well sbown 
by the curve of Fig. 267, where 
the load current is plotted hori- 
zontally and speed vertically. 
286. TestofaDirect-current 
Three-wire Meter. — The three- 
wire-direct current meter dif- 
fers from the two-wire meter 
in having its aeries or current 
coil divided into two coils that 
are, or should be, exactly alike. 
These two coils are connected, 
one in each outside wire of a 
three-wire circuit, while the common voltage coil may be con- 
nected between the neutral and an outside wire, or across the 
outside wires, according to the design of the meter. The limita- 
tions of the different connections have already been discussed. 
The second method of connection is shown in Fig. 268 in which 
CC are the current coils and S the shunt or pressure coil. 

The connections for testing such a meter are shown in Fig. 269, 
The current coils are connected in series and also in series with 
one wire of a two-wire circuit. If potential cells are available, 
the best plan is to connect the voltage coil to a separate source 
of electromotive force, as shown, otherwise it may be connected 
in parallel with the current ooib. The operation of the test is 



















/ 








/ 








4 


% 








/' 
































Current C Mtryni 

ifui. 267. 



TESTING WATT-HOUR METERS 



323 



the same as other tests that have been described in which a 
millivoltmeter is used to measure the current and a standard 
voltmeter to measure the voltage. A wattmeter may be used 
in place of voltmeter and millivoltmeter. 



OOmMOOOiTOOOOOOOO^ 




Fia. 268. 

287. Test for Balance. — In addition to the foregoing test for 
balanced load, it is also necessary to determine the effect of each 
current coil in causing rotation. In a well-designed meter, the 
coils should supply equal torques. To determine whether the 
torques are equal, two simple tests may be' made. The simplest 
method consists in connecting the two-current coils in series, but 




Fia. 269. 



in such a way that the resulting torques are in opposition. If 
the two coils exert equal torques, no motion will result. When 
this is not the case, the armature will rotate either forward or 
backward, depending upon which coil exerts the greater torque. 
The resulting speed will undoubtedly be very slow, and for that 
reason it will be advisable to overload the coils for a short time. 

32 



324 ELECTRICAL METERS 

The second method consists in connecting to the circuit only 
one of the series coils at a time. If the two coils are exactly 
balanced, the resulting speeds should be exactly equal, so long as 
voltage and current remain unchanged. The speed with only 
one current coil should also be equal to one-half the speed when 
both coils are operating, current and voltage remaining constant. 

288. Test of Ampere-hour Meters. — The simplest and most 
convenient method of testing an ampere-hour meter is by means 
of a standardized ammeter of proper range and a stop watch. 
The ammeter is connected in series with the ampere-hour meter 
through a rheostat or lamp bank. The current is adjusted to the 
value desired and maintained constant throughout the test. 
The ammeter reading multiplied by the duration of test in hours 
gives the actual ampere-hours passed through the meter. The 
calculated ampere-hours compared with the registration of the 
meter will indicate the error. The number of ampere-hours 
registered by the ampere-hour meter may be calculated from 
the number of rotations of the disk and ampere-hour constant. 
The chemical ampere-hour meters that are graduated in watt- 
hours can be tested either with a wattmeter or standard test 
watt-hour meter in the same way as watt-hour meters. 



CHAPTER XX 

METHODS OF OBTAINING DIFFERENT POWER- 
FACTORS 

289. Introduction. — Since alternating-current meters must be 
tested on loads of different power-factors, it will be advisable 
first to discuss some methods of obtaining these. Several 
methods may be used for this purpose; the particular one to be 
used in any case will depend upon conditions present and appara- 
tus available. 

290. Reactance-coil Method. — As has already been pointed 
out, the current flowing through an inductive circuit is expressed 

by 

E 



I = 



{R^ + LW) ^ 



and the difiference in phase between the pressure E and current 
I is obtained from tan ^ = "n * Evidently, if Lw is varied, tan B, 




ADJUSTING 
RCS I STANCE 



lU 



I 

o 

^ u. 



I 



Fig. 270. 

and hence 6, can also be varied. This relation will perhaps be 
better understood by referring to Fig. 270. An alternating 
current of frequency/, supplies current to a resistance and induct- 
ance coil. If / is the current flowing through the inductance 
coil R2L2 and E the electromotive force between its terminals, 
the relation between these quantities is then shown by the vector 
diagram. The voltage drop due to the resistance of the inductance 
coil is R2I, while that due to self-inductance is ^kJLJL. BJL is 
33 325 



326 



ELECTRICAL METERS 



in phase with the current, and 2j/Li7 is at right angles or { 
ahead of 7. Drawing OC = R^I, and CA = 2TrJLJ, we get the 
right-angled triangle OCA, of which OA, the vector sum of OC 
and CA, is the electromotive force E. The value of $ thus 
depends upon OC and CA and can be changed by changing either. 
In practice, the change in power-factor is commonly obtained by 
changing the inductance. This is accomplished by providing 
a movable iron core for the inductance coil as shown in Fig. 
271. By introducing or withdrawing the laminated iron core, 
different values of power-factor can readily be obtained. The 
exact value of the power-factor ia calculated from the readings 
of the wattmeter, voltmeter, and ammeter. It has already 




V\a. 271. 



been pointed out that at low power-factors corrections must 
be made to the wattmeter readings. 

291. Two -transformer Method. — Another method of securing 
an inductive load for single-phase watt-hour meters is by means 
of two transformers connected one to each phase of a two-phase 
circuit. The secondaries of the transformers are provided with 
several taps and are connected in series. The manner of con- 
necting transformers and instruments to the circuits are shown 
in Fig. 272. As is evident from the diagram, the current coil 
of the meter to be tested is connected to one phase of the two- 
phase circuit, while the pressure coil is connected in series with 
the secondaries of the transformers. The ammeter, wattmeter, 
and voltmeter are connected aa usual. The value and position 



OBTAINING DIFFERENT POWER-FACTORS 327 

of the pressure applied to the meter will evidently be equal to the 
vector sum of the secondary voltages of the transformers. By 
varying the relative values of these, different values of power-fac- 




PiG. 272. 

tor can be obtained. The vector diagram of Fig. 273 shows how 
this is accomplished. Let OA = Ei represent the secondary 
voltage of transformer Ti. This voltage will be in phase with 
I, the current through the meter. 

If the secondary voltages of the trans- 
formers are equal in magnitude, OB will 
represent the secondary pressure of the 
transformer Tt. The resultant voltage, 
or that impressed upon the pressure coil 
of the meter, is then equal to DC, which £^ ' 
leads the current by the angle $. By 
changing the relative values of the sec- o~ 
ondary voltages, the value of $ can be 
changed from to 90°. The vector 
diagram shows the relative values of these pressures for a phase 
difference $'. It is clear that not only the power-factor, but theim- 
pressed pressure may be varied between wide limits by changing 
connections A and A' in Fig. 272. If two transformers are ape- 




328 ELECTRICAL METERS 

cially constructed for this tost, the connection of Si and S3 may 
be made to a circular switch. The power-factor and voltage for a 
given position of the switch may be calculated once for all and 
marked on the switch. If that is done, the position of the switch 
will indicate the voltage and power-factor, and the voltmeter and 
ammeter may be omitted, unless needed for other measurements. 




292. Two-resistance Method. — ^Perhaps a simpler method con- 
sists in replacing the two transformers by two slide contact re- 
sistances as shown in Fig. 274. A vector diagram similar to that 
in Fig. 273 will show the relation of the quantities involved. The 
value and position of £ is determined 
by the position of the sliding contacts 
fit and Ri. That is, E is the vector 
sum of e and e', Fig. 275, which rep- 
resent the potentials between the 
sliding contacts and middle wire. 
The resistances Ri and R2 must be 
non-inductive and capable of with- 
^'"^' ■^'■*' standing the line voltage, and have 

a current capacity of 1 to 2 amp. A non-inductive load is con- 
nected to the meter as in the transformer method. 

By adjusting Ri and Ri, any desired value and phase position 
of E may be obtained. In most cases it may be possible to use 
lamps in place of resistances. The adjustment, however, will be 
much more troublesome. The power-factors may be calculated 
for certain positions of the contacts and the points so determined 





OBTAINING DIFFERENT POWER-FACTORS 329 

may be marked with the corresponding power-factor. When this 
is done, the ammeter and voltmeter may be omitted and the re- 
quired power-factor reproduced by simply setting the contacts at 
the same points. 

293. Two-generator Method. — A very convenient, and at the 
same time accurate, method of varying the power-factor for test- 
ing purposes may be obtained by providing a special motor- 
generator set consisting of one driving motor and two similar 
alternating-current generators, all connected to the same shaft. 
The alternators need not be alike in every respect, but should 
have the same frequency. One generator may preferably be 
of low voltage and comparatively large current output for supply- 



Loaet or 
fru*f9lmt/f9g 





Fig. 276. 

ing current to meters under test. The other generator may be 
of low current capacity but relatively high voltage to serve as 
a source of pressure. Fig. 276 shows the connections for such 
a system. If the generators are low-voltage, the current and 
potential transformers may be omitted. 

One of the generators must be connected to the shaft in such a 
way that the position of its armature may be shifted with reference 
to the other. The frequencies of the two generators will always 
be the same on account of the rigid connection, and by shifting 
the armature of one with reference to the other, any power-factor 
can be obtained. Furthermore, the power-factor can be calcu- 
lated from the relative position of the armatures if the position of 



ELECTRICAL METERS 



zero, or unity power-factor is accurately knowD. Thus, if eacii 
generator has four poles for every revolution of the armature, the 
current or voltage will pass through two cycles. That is, for 
every 360° of armature motion, the electromotive force passes 
through 720 electrical degrees, or 1 angular degree equals 2 elec- 
trical degrees. If then the armatures are in a position of unity 
power-factor, and one is rotated 5" on the shaft, there will re- 
sult a displacement of 10° between the electromotive forces. Tbe 
power-factor has then been changed from cos 0° to cos 10". In 
general, then, if ^ is the angle through which the armature of one 
machine has been shifted with reference to the other, p is the num- 
ber of poles on each generator, and cos 9 is the power-factor, we 
can express cos b in terms of and p thus, 

cos 8 = cos ^y. <t>. 

Measuring 4>, the power-factor can be calculated. Any error in 

^ is, however, multiplied ^ times, and, hence, for very accurate 

work 4> should be determined by the aid of a vernier. In some 
cases it may be more convenient to have the machines constructed 
in such a way that the armatures remain rigidly connected to the 
shaft, while the field of one is movable. Of course, the same 
effect is obtained as in the previous case. 

294. Phase-shifting Transformer. — The troubles accompany- 
ing the use of inductance coils for varying the power-factor for 
testing meters are readily obviated by the use of a so-called " phase- 
shifting transformer." The construction of such a transformer 
is very similar to that of an induction motor. The stator is 
wound with two sets of coils at right angles to each other as indi- 
cated in Fig. 44, when the supply is two-phase or single-phase, 
or with three sets of coils spaced 120° apart when the trans- 
former is to be used on three-phase circuits. The secondary is 
wound on a cylindrical iron core and consists of a single diametral 
coil. 

The relative position of the stator and rotor windings for a 
two-phase shifting-transformer is shown in Fig. 277, where 
AA' and BB' are the primary coils and MN is the secondary coil. 
The connections of such a transformer to a power circuit and to 
meters are shown in Fig. 278. 

The principles of operation will readily be understood from a 



OBTAINING DIFFERENT POWER-FACTORS 331 

consideration of the interactions of the primary and secondary 
coils when the secondary is turned on its axis. If the plane of 
the secondary coil is parallel to that of the primary coil AA', it 
will have induced in it an electromotive force in phase with the 




pressure applied to AA'. Strictly speaking, the induced voltage 
will be nearly 180° out of phase with the primary voltage applied 
to AA'. 




iwj-{wj-iTJwrj- 



Fia. 278. 

When coil MN is in this position, the Sux due to current in 
coil BB' will have no efifect upon MN. When MN is turned 
through 90°, the electromotive force induced will be in phase 
with the pressure applied to BB', hence, it will have been shifted 



332 ELECTRICAL METER.'i 

through 90° from its previous phase. If MN is turned throuj 
an angle 6, other than 90°, the electromotive force induced in 
it will be due to the resultant flux due to both coils AA' and BB'. 




This flux rotates, as has been shown in Article 72, and is equal to the 
maximum flux due to one coil. The phase of the electromotive 
force induced in coil MN ia thus, likewise, shifted by an angle 0. 




Any power-factor from 1 to can thus easily be obtained by 
merely shifting the secondary with reference to the primary. 
The connections of a three-phase, variable-phase transformer 



OBTAINING DIFFERENT POWER-FACTORS 333 

are shown in Fig. 279, and the complete transformer as manu- 
factured by the General Electric Co. is shown in Fig. 280. 

296. Ammeter Method of Measuring Power-factors. — For 
the want of a better name, the author, having devised the two 



Am 






Am 




Am 



Fia. 281. 



following methods, has decided to call them "Ammeter Methods." 
The reason for this is that at most only two ammeters, and with 
the use of a polyphase switchboard, only one ammeter is necessary 
for an approximate determination of the power-factor. 

In plants using quarter-phase — com- 
monly called two-phase — or three-phase 
generators, the methods will undoubt- 
edly prove useful and acciu-ate enough 
for commercial purposes. 

296. Ammeter Method on Two-phase 
Circuits. — ^The connections for testing 
the watt-hour meter on a two-phase 
three- wire circuit are shown in Fig. 281. 
The series coil of the watt-hour meter 
carries the vector sum of the two-phase 
currents. When the voltage coil of the 
watt-hour meter is connected as in- 
dicated in the diagram, the power- 
factor is the cosine of the angle between 
the series current and pressure across 

mains 1 and 2. Thus in Fig. 282 let 0E\ represent the voltage be- 
tween mains 1 and 2, and OE^^ the voltage between mains 2 and 3. 
Since the load is supposed to be non-inductive, 0/iand O/2 may be 
considered as representing the currents in the separate phases. 




Fig. 282. 



334 



ELECTRICAL METERS 



The current in main 2 is the vector sum of O/i and Ot^&ad 
therefore, represented by 0/.' The power-factor of the load 
registered by the watt-hour meter, when connected as indicated 
in Fig. 281, is cos 8, where 9 is the angle between OEi and 01. 
The value of S is determined from the relative values of the cur- 
rents in lamp banks Li and tj. That is, if Ii is the current in 
load Li, and It the current in load Lj, the power-factor is equal to 

cos » - (j^r+'T^iya 

and hence, can be determined from the readings of two ammeters, 
one placed in main 1 and the other in main 3. Since, (/j' + /»^)^ 
= /, the current in the series coil of watt-hour meter, an ammeter 
placed in main 2 will indicate (Zi* -|- /j')^ of /. The power-factor 

then reduces to 



When h = 0, the total load is on Li; I, = I, and cos fl = 1. 
When Ii = 0, the total load is on Lt, and cos 6 = y =0. 




Hence, by adjusting the load between Li and L2, any power- 
factor between and 1 can be approximately determined. 
According to the foregoing discussion, two ammeters are needed; 
later it will be shown how the connections may be made ao that 
one ammeter will suffice. 

In case the generator is not wound for three-wire connection, 
which the foregoing method presupposes, a three-wire circuit 
can be obtained by connecting two transformers, as shown in 
Fig. 283. The primary circuits of the transformers are connected 

' To be exact the current in main 2 should be repteaented by dotted line 
Olt. The value of the power-factor will be the same ia either caae. 



OBTAINING DIFFERENT POWER-FACTORS 335 



to the separate phases of the generators and the secondaries are 
interconnected as shown. 

297. Ammeter Method on Three-phase Circuits. — When three- 
phase alternators are available, the same general plan may be 



•u- 



•u 



^ 



L 




Fig. 284. 

followed. When the series coil of the meter to be tested is 
connected to the middle wire, as indicated in Fig. 284, and the 
pressure coil across Ei, the power-factor is 

/% _ -ly Iz'~ I2 is ~" I2 

^^ " ^ (/a« -h 12/3 + Is^)^ "" 2/ 



60"' y 




FiQ. 285. 

where /, I2, and Iz are currents in middle and outside wires, 
respectively. 

When the potential circuit is connected across £$, the power- 
factor is 

2/3 + I2 27, +/, 



cos ^ = 3^ 



(/2* + I2IZ + Iz')^ 



21 



336 ELECTRICAL METERS 

These formulas can be derived as follows: 

Assuming the time-phase displacements of the electromotive 
forces of the three-phase generator to be 120**, Fig. 286 is a vector 
diagram of the quantities involved. From this diagram it is 
plainly evident that both the magnitude and time phase of / 
with reference to Ei depend upon the relative magnitudes of 
It and /s. 

Let $ be the angle between I and -Bi, then the angle between 1 9 
and El is 60** when the load is non-inductive. Hence, 

cos e = cos (7 + 60) 

= yi cos 7 — MV§ sin 7. 

From the triangle whose sides are /, /2, and Iz, we get 

7s:/2 : : sin (60 — t) : sin 7, 

whence sin 7 = M/. ^f^-^jj^^^rj^ 

. - . 2/3 + 72 

and COS7 = li (7.« + 7,7, + i^- 

Substituting these values in the expression for cos and reducing, 
we get, 

But (/s« + hh + 1 2')^ = / 

hence, cos ^ = H y — -' 

When /2 = /«, or when both phases are equally loaded, cos ^ = 0. 
When It = 0, /« = /, and cos ^ = 0.5; and when Iz = 0, /a = 
— 1, and cos 6 = —0.5. Hence, by such a connection the 
power-factor can be varied between —0.5 and +0.5. 

By a similar process of reasoning it can be shown that when 
the pressure coil is connected across Ez, the power-factor is 

/, 1.^ 2/8 + /2 2/8 + /« 

COS^ = M(J^2+J^J3 + J^2)« = —27— 

When I2 = 0, Zs = /, and cos ^ = 1. 

When h = 0, cos 6 = 0.5. That is, when all the load is on Lz 
the power-factor is 1, and when all the load is on Li the power- 
factor is 0.5. 

The advantage of this method lies in the ease with which both 
the connections and calculations can be made. The ordinary 
ammeter — voltmeter — wattmeter method necessitates three in- 



OBTAINING DIFFERENT POWER-FACTORS 337 

Btruments, and it is a well-known fact that at low power-factors 
the inductance of the pressure coil of the wattmeter introduces 
errors which are proportional to sin d. This error, due to the 
inductance of the pressure coil, may be as great as that due to 
the unbalancing of the pressures in the method under consid- 
eration. The fact that one ammeter is su£Scient, makes this 
method especially advantageous for small power plants whose 
supply of instruments is limited. 

In order to use only one ammeter, the polyphase switchboard, 
shown in Fig. 252 may be used. The three mains are connected 
to binding posts 1, 2, 3, and the three load terminals to posts 1', 2', 
and 3', while the ammeter is connected to leads indicated. This 
connection is shown in Fig. 286. An examination of the dia- 




FiG. 286. 



gram will show that when the three-pole, and three single-pole 
switches are closed, the ammeter will register no current. When, 
however, both double-pole, double-throw switches are closed to 
the left and single-pole switch C is opened, the ammeter will 
give the current in one lamp bank. An examination of the 
diagram will show the operations necessary to obtain in succes- 
sion the currents in the other lamp bank and in the middle wire. 
It has been shown by experiment that for the purpose of watt- 
hour meter testing the method is accurate enough for commercial 
purposes, and in fact the results obtained by the ammeter method 
are just as accurate as the three-instrument method unless 
accurately calibrated instruments of proper range are available. 
The adjustable load must be non-inductive. 



CHAPTER XXI 

SPECIAL TESTS OF ALTERNATING-CURRENT WATT- 
HOUR METERS 

298. Test for Quarter-phasing. — Aa pointed out in Article 184, 
the displacement between the magnetic field due to the current 
coil and that due to the voltage coil must be 90° for accurate 
registration on inductive load. One of the first tests to be made 
on a single-phase meter is to determine whether this relation 
exists. 

Since no torque should be exerted upon the rotating disk when 
the current lags or leads by an angle of 90°, in order to determine 




Fig. 287. 

whether the meter ia properly quarter-phased, the absence of 
torque under proper conditions is the criterion of the test. In 
making the test, connect the current coil to one phase of a quarter^ 
phase circuit and the voltage coil to the other phase. A suitable 
method of making these connections is shown in Fig. 287. The 
exact phase difference is calculated from the readings of the 
ammeter, voltmeter, and wattmeter, thus, 
watts 



TESTS OF WATT-HOUR METERS 



339 



If the quarter-phase relation exists, the wattmeter reading will 
be zero if corrections are made for resistance, hysteresis, and eddy- 
current losses. Any inaccuracy in the wattmeter will, however, 
vitiate the result. Accurate measurements of ,alternatirig-cur- 
rent power in circuits of low power-factors require special methods 
and apparatus. 

299. Test of Single-phase Meter on Non-inductive Load. — ^For 
non-inductive load test, connect the meter as shown in Fig. 288. 
It must be remembered that the connections shown are diagram- 



A.C. Supply , 




Fig. 288. 

matic only. For any particular make of meter, the connections 
will have to conform to the diagrams and directions sent out by 
the makers. 

The voltage during the test should be constant, and the time 
of a definite number of revolutions of the disk determined by the 
aid of an accurate stop watch. It is more accurate to count a 
definite number of revolutions than to count the revolutions 
during a definite time, as the fraction of a second is more easily 
determined than the fraction of a revolution. The per cent 
accuracy is then determined by 

^ ^ 100 X Xi2 

Per cent accuracy = y >< ^^^^^ 

where X, 72, and T have the significance already explained. The 
non-inductive load test is to be made at various percentages of 
load, but with the constant voltage. Then repeat the test with 
both an increase and decrease in voltage of 15 to 20 per cent, 
but the same loads as before. That is, first increase the voltage by 
20 per cent above the rated voltage and ascertain the accuracy on 
10, 50, 100, and 125 per cent of load. Second, decrease the 
voltage by 20 per cent and ascertain the accuracy at the previ- 
ously mentioned fractions of load. When the accuracy for the 
various voltages and loads has been determined, curves should 
be plotted from the data, the per cent of load being plotted 
horizontally and the percentage of accuracy vertically. 



ELECTRICAL METERS 



EXAMPLE 



T«Bt No. S. — Test of aingle-phsse matt-hour meter. 

Apparatju. — Fort Wayoe 110-volt, 60-cycle, 5-amp. watt-hour meter. 

Weston wattmeter No. 4,123. 

Lamp bank. 

Stop watch No. A. 

Temperature 21=0. 









Table 


vm 






P««nt 


No revo- 


Time 


Meter 


Correct 


Peroenlsge 


Remarlis 


iMUl 


lutioDB 




wattt 


«.». 


ade>,r«y 


10 


2 


32.7 


55.0 


55.0 


100.0 




25 


8 


52.4 


137.5 


137.5 


100.0 




60 


12 


39.6 


273.4 


275.0 


99:5 


Voltage con- 


7fi 


16 


35.1 


408.4 


412.5 


99.0 


Btant at 110 


100 


20 


33.4 


540.5 


550.0 


98.3 


volta. 


125 


25 


33.5 


673.7 


687.5 


98.0 


Curve, Fig. 289a. 



































































-1 


^^ 
































' 




—, 


i^ 


^ 






! 


„ 


to 


w 


10 


°e>- 


tn"' 


e/L 


cod 


w 


loa 


■lO 


"" 




1 
































V 
























t 




\ 


S 






















i^ 








^-^ 


^^^ 


















^ 












e^^ 


■icrc 


\o 


9D 


100 


•m 


-^B 




































V 




























\ 


















^ 












\ 


^ 










^ 


^ 












rfe 


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« 




IT^ 


S^ 


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90 


100 


<m 


liO 





TESTS OF WATT-HOUR METERS 



341 



300. Test of Siugle-phAse Watt-hour Meter on InductiTe Load, 
— For an inductive load test, any of the methods for varying the 
poweii^factoc previously discussed may be used. If the station 
13 provided with a three-phase generator, the three-phase am- 
meter method is perhaps the most convenient. A diagram of 
connections for a test board as described by Mr. H. B. Taylor in 
the Electric Journal for November, 1906, is shown in Fig, 290. 




gP|q PO^^ oifff OPj» 



Fig. 290. 

This diagram is for a three-phase circuit and both non-inductive 
and inductive load tests can readily be made by the aid of a board 
or table wired as here shown. The three-phase terminals are 
indicated by A, B, and C. At the left is indicated a potential 
regulator by means of which gradual changes in secondary 
voltage from maximum in one direction to maximum in the 
other direction can be obtained. It may also serve as a phase 
shifter, depending on whether the primary is connected to the 
same phase as the meter or to another phase. In the lower left- 
hand corner ia shown a small transformer with taps, connected 
to the potential circuit. The series auto-transformer shown at 
the bottom of the diagram is put in simply to economize in energy 
in testing heavy current meters. This transformer is cut in or 
out by means of the plug switches and is used only when the our- 



342 



ELECTRICAL METERS 



rent is above 10 amp. The lamp board is connected between the 
switches as indicated. When the load is all on one lamp board 
and the potential circuit is connected to the wires supplying the 
lamps, the conditions are the same as on any single-phase circuit. 
Thus, when the lamps are connected to A and B, and the poten- 
tial plug is inserted at A' and B\ the test may be made on prac- 
tically unity power-factor. Transferring the plug to B'C gives 
about zero power-factor. The power-factor will not necessarily 
be exactly zero, but near enough for commercial practice. For 
inductive load test, the load is divided between the two lamp 
boards, and the shunt is connected to outside mains. When the 
load is evenly divided between the two lamp boards, the power- 
factor is 0. Changing the load on either lamp board changes the 
power-factor, as previously explained. 

EXAMPLE 

Test No. 6. — Test of watt-hour meter on inductive load. 
Apparatus. — Same as in Test No. 5. 

Weston ammeter. 

Weston voltmeter. 
Temperature, 

Table IX 
Part I 



Volts 


Amperes 


Watts 


Power* 

factor, 

per cent 


No. 
revolu- 
tions 


Time, 
sec- 
onds 


Meter 
watts 


Per cent 
accuracy 


Remarks 


110 
110 
110 
110 
110 


10.20 
8.18 
4.10 
2.72 
2.05 


225 
225 
225 
225 
225 


20 
25 
50 
75 
100 


12 
12 

12 
12 
12 


46.7 
47.5 
48.2 
48.5 
48.7 


230.6 
227.5 
244.0 
223.0 
222.7 


102.5 

101.0 

99.5 

99.1 

99.0 


Load con- 
stant, vary, 
ing powers 
factor. 

Curve, Fig. 289b, 



Part II 



Volts 


Amperes 


Watts 


Power- 
factor, 
per cent 


No. 
revolu- 
tions 


Time, 
sec- 
onds 


Meter 
watts 


Per cent 
accuracy 

101.5 

100.0 

98.0 

97.8 

98.5 


Remarks 


110 
110 
110 
110 
110 


7.5 
7.5 
7.5 
7.6 
7.5 


165.0 
206.2 
412.6 
618.6 
826.0 


20 
26 
60 
76 
100 


6 

12 
22 
30 
44 


32.4 
52.4 
49.0 
44.6 

48.7 


167.5 
206.0 
403.7 
604.9 
813.0 


Current conn 

< 

stant. 
Curve. Fig. 289c, 



TESTS OF WATT-HOUR METERS 



343 



The power-factor had comparatively little effect on the accu- 
racy of this particular meter, but this is not always the case. The 
curve of Fig. 291 shows what variations in the percentage of ac- 
curacy are possible when the meter is not properly adjusted. 




£0 



40 



40 



SO 

Fig. 291. 



301. Testing with Standard Test Meten — The connections for 
testing a two-wire meter by means of a standard test meter are 
shown in Fig. 292. This method of testing is fast superseding 
the indicating instrument method. The operation of testing 
with a standard test meter is very simple and consists merely in 
the determination of the number of rotations of the moving ele- 
ment of the test meter corresponding to a definite number of 
rotations of the tested meter. 

To faciUtate the work, some companies equip the test meter 
with an electrical contact which closes a circuit through a tele- 
phone receiver, every rotation giving a click. When this method 
is used, observations are made by what is called an "eye and ear 
method. " The operator observes the rotations and fractions of 
a rotation of tested meter corresponding to a whole number of 
rotations of the disk of the test meter, noting the latter by the aid 
of the telephone receiver. 

In some cases, arrangements are made for starting and stopping 
the test meter at the instant the spot on the disk of the tested 
meter passes the observation window in the case. This starting 



S44 



ELECTRICAL METERS 



or stopping may be accoinpliahed by opening the volt^e coil of 
the teat meter, or by short-circuiting Us current coil. Instead of 
stopping the disk, the moving element may be caused to pick up 
and drop the hand through the agency of a little magnetic clutch. 
The chief advantages of the test meter have been pointed out. 
It evidently eliminates the use of stop watches, which are always 
troublesome in meter testing; it minimizes the effect of voltage 
fluctuations; and reduces the work of calculation to a minimum. 



Ampere Switi 




When a test meter is used whose constant is not the same as 
that of the service meter tested, the two meters will not make the 
same number of rotations. To facilitate the conversion of the 
number of rotations of the test meter to the equivalent of those of 
the service meter, Table X has been prepared. The table con- 
tains the constants of the meters most commonly used. 

The table is used as follows: 

Suppose a Westinghouse 5-amp. test meter is used to check a 
Fort Wayne service meter of the same capacity. If both meters 
are for 110-volt circuits, the constants arc }4 watt-hour and J^ 
watt-hour respectively. Opposite the test-meter constant J^ and 
under the service meter 0.25 we find 7.5, which means that for 
every ten rotations of the service meter the test meter should 
make 7.5 rotations. 



TESTS OF WATT 'HOUR METERS 345 

If a meter is used whose constant is not found in the table, the 
conversion can be made as follows: 

Let Ki = test-meter constant, 

K2 = service-meter constant. 

Then 72 = ^^ X 10 

where R = number of rotations of the standard corresponding to 
ten rotations of the service meter. The percentage of accuracy 
is then calculated as follows: 

Count a definite number of revolutions of the service meter, 
and from Table X find the number of rotations the standard 
should have made in the same time. The ratio of the number 
of rotations the test meter should have made to the actual 
number it did make will give the percentage of accuracy. 

EXAMPLE 

A 50-amp., 110-volt, type C, General Electric meter waa tested with a 6- 
to 100-amp. Duncan test meter. The service meter made 20 rotations 
while the test meter made 15; what is the percentage of accuracy of the 
service meter? The constant of the Duncan test meter is 2.5 and that of the 
service meter 2; hence, opposite 2.5 and under 2 is found the figure 8. The 
test meter should have made 16 rotations, but as it made only 15 the per- 
centage of accuracy is 1^5 = 106.6. 

302. Testing of Polyphase Meters. — Since polyphase meters 
are simply a combination of two single-phase meters, they may 
be tested as single-phase meters, each phase being tested sepa- 
rately. Both potential coils must, however, be connected to the 
circuit during the test. A diagram of connections is shown in Fig. 
293. It will be noticed that the current is passed through only 
one series coil at a time. This is accomplished by changing the 
connections of the three-point switch. When one circuit of the 
watt-hour meter is fully loaded, the rotating element makes one- 
half the normal number of revolutions. Pass through the circuit 
a given number of watts which must be kept constant while read- 
ings are being taken. Time the number of revolutions of the 
disk with a stop watch, and compute the percentage of accu- 
racy in the same manner as in testing single-phase meters. The 
proper constants to be used will depend upon the make of meter 
as previously pointed out. When the percentage of accuracy of 
one circuit has been determined, load the other circuit and repeat 
the test. 



346 



ELECTRICAL METERS 



Another method of testing polyphase naeters consists in con- 
necting the current coils in series, and the potential coils in paral- 
lel. An objection to this method is the inability to determine 
any unbalancing of one of the circuits. Should the meter be 
found to be inaccurate, and be adjusted when unbalanced, the 
meter will give inaccurate results when connected to polyphase 
circuits. 

While conducting tests in accordance with either method, care 
should be exercised not to reverse either of the potential circuits 
when connected in parallel. If the series connection of current 
coils is used, the connections of one of the circuits should be re- 



Lcod 



Line 



m 

^vcision 
Wattmeter 



Ttfree Roint 3\^itch^ , 

rD/ypho3e 

\V\ibttnjeter 




Fig. 293. 

versed in order that the action of both coils may be in the same 
direction. 

On account of the inconvenience mentioned and the liability 
of inaccurate results, it is preferable to test each circuit sepa- 
rately, the potential circuits remaining connected in parallel, or, if 
the test is made on polyphase circuit, the potentials may be left 
connected to the same phase as in service. 

303. Test for Interference of the Two Metering Elements. — 
By means of a long series of tests the Electrical Laboratories 
found that various makes of meters differed considerably with 
respect to the electromagnetic interaction of the two elements of 
polyphase, watt-hour meters. In some makes the interference 
was so small that careful tests failed to detect it. In other makes 
the interference was so large that serious errors might, under 
certain conditions, be introduced by it. As a result of these 
investigations the following specifications for the test of indepen- 
dence of elements has been incorporated in the Meter Code of the 
National Electric Light Association. 

Element A of the meter under test is connected to phase I of a 
two-phase circuit and a certain current is sent through its current 



^^^H 


^^^^^^^H 




.125 


^.2 


.2. 


.3 


8 


10 


lOf I2i 


X3J 


15 


16 { 20 


25 


26f 


30 


33i 4 


i 


■o 


i« 


«) 


»4 


























.2 


B.M 




ll.S 


It i 
























.25 


i.O 


8.0 


ID 


12 1 
























.3 


4. IB 




S.3I 


ID < 
























i 


3.78 


s.o 


7.8 


B.O . 
























A 


S.U 


S,0 


S.ZS 


7.5 
























.5 


!.i 


*.o 


S-0 


s.o : 
























.6 


J.08 






3.0 
























t 


l.SB 


3.0 


3.7 


«.t 
























i 


1.87 


2.«7 


3.33 


4.0 
























I 


i.aa 


I.O 


l.S 


3.0 ' 
























« '* 


1,00 


IB 


2.0 


3.4 { 
























S 1* 




l.S 


l.ST 


l.!5 
























I 1* 






I.IT 


S.0 


























1 2 








l.S 


40 
























§ 2» 










M 


« 






















g 2| 










») 


37.8 


10 




















g 3 










i».7 


33.3 


IB. 6 


41. M 


















S- 3* 










34 


30 


32 


37.5 


40 
















° 3.75J 








21,3 


2B.a 


3S 


4 


33.3 


36 




40 














i * 1 








JO 


at 


26 


B 


31.3 


33 


3 37.8 


40 












fi = 










1« 


30 


31 


3 


28 


30 




30 


33 


40 










5 6 










13.3 


■ «.• 


17 


77 


20.8 


=3 




36 


38.S 


3.33 


11,8 








^ 6| 










13.0 


18.0 


la 





1S.8 


20 




33.4 


34 


30 


37.6 


40 






7* 










10. (S 


13.33 


■4 


22 


IB.BS 




77 


SO 


31.33 


2B.B8 


33.33 


3S.8S 


40 




8 










ID 


12,8 


13 


33 


18. B2 




ee 


18 78 


30 


28 


31.35 


33.33 


37.6 


41. B6 


10 










8.0 




10 


«B 


12.8 




33 


IS 


IS 


30 


26 


28.18 


M 


33.33 40 


■ lot 












11.3S 


10 




11.73 




8 


14.0(1 


18.0 


1B.7B 


33.44 


36 


38.13 


31.28 37 


■ 










e.i 


a.Q 


8 


S3 


ID 




«9 


13 


13.8 


18.0 


30 


31.33 


34 


26. Bd 32 


r i3i 










fl.O 


7.8 


8 





S.37 






11.28 


12.0 


18.0 


13.78 


30 


22.8 


26 30 


15 










6.33 


«.U 


7 


11 


8.33 




as 


10 


10. BB 


13.33 


1B.B8 


17.77 


30 


33,33 U 


16 










6.0 


B.2B 


6 


BB 


7.81 




33 


2.37 


10 


13.6 


18.63 


18. B8 


18.76 


30.83 26 


20 










4.0 


8.0 


6 


33 


t.ai 




BB 


7.« 


8.0 


10 


13.6 


13.33 


18 


IB. IB 30 


25 










3.2 


4.0 


* 


M 


6.0 




33 


D.O 


8.4 


s.o 


10 


10.88 


la 


13.33 18 


26t 










3.0 


3,76 


4 





t.«g 







6.83 


8.0 


7.8 


9.37 


10 


11.38 


13.6 18 


30 










a.M 


3,33 


3 


68 


4.ie 




44 


6.0 


6.K 


8.U 


8.33 


s.es 


10 


11.11 13 


831 










a.4 


3.0 


3 


3 


3.76 







4.6 


4.B 


8.0 


7.S 


3.0 


8.0 


10 13. 


' « 












3.6 


» 


M 


tI36 




33 


3.78 


4.0 


6,0 


8.2t 


8.88 


7.6 


S.U <0 


\ 


^■'"'■"'"™" '"" 








^H 


^H 


^1 


^H 


■ 


■ 


^H 


■ 




^H 


^M 




^M 


^H 


^H 


^^^ 



TESTS OF WATT-HOUR METERS 



347 



coil. The voltage coil of element B is also connected to phase I 
and accuracy readings are taken with the current in the volatge 
coil of B direct and reversed. Next the voltage coil of B is con- 
nected to phase II and similar readings are taken. Finally, with 
the voltage coil of element B disconnected, a current equal in 
value to the current passing through current coil of element A, is 
sent through the current coil of element B. The current through 
element B is first taken from phase I and then from phase II, and 
in each case both direct- and reverse-current readings are taken 
and compared. Tests are to be made with both light and full- 
load currents. Under any given set of conditions the diflFerence 
between the direct and reversed readings must not exceed 1 per 



Ckimp 



Y r. 





MeUr 
Shaft 



Fig. 294. 

cent. In case a meter shows a greater correction than this it 
must be tested on a polyphase circuit with the direction of rota- 
tion on each phase given, so that in installing the meter the same 
direction may be preserved. If the variation in direct and re- 
versed readings is not over 1 per cent, the meter may be tested 
on a single-phase circuit, the current coils being connected in 
series and the potential coils in parallel. 

304. Test to Determine Torque. — As previously pointed out, 
other things being equal, the watt-hour meter whose torque- 
weight ratio of moving element is the largest, is the best meter; 
hence, a knowledge of the torque is essential. Fig. 294 shows a 
so-called torque balance, an instrument for determining this 
quantity. As shown in the diagram, the instrument consists of 



348 ELECTRICAL METERS 

two arms at right angles to each other, balanced on a knife edge 
C. With the instrument is provided a clamp to which is attached 
a light extension rod EN. In operation, the arm EN is securely 
clamped to the shaft of the meter, and connected by the link to 
the vertical arm of the balance. Normally, the weight G overbal- 
ances the arm H, and the pointer swings to the right. When the 
meter is loaded, the torque exerted by the disk pulls the pointer 
back to 0. The load necessary to secure balance is measured on 
an indicating wattmeter, and the torque in gram-centimeters is 
calculated from the weight G and the levers (?C, CF, and EN thus: 

Let w = weight of G in grams, 

/ = the pull along link L, 
and let T = torque of meter. 

Then T = fX EN 

and fXYC=-wX CG. 

Eliminating /, we get 

T __ EN 

wXCG~ YC 
ENXwXCG 

^ - YC 

When ly is in grams and the other quantities are in centimeters, 
the above expression gives the torque in gram-centimeters direct. 
The rods Y and EN are provided with several loops, and two 
weights are also supplied to permit the use of the balance for 
measuring a wide range of torques. By accurately weighing the 
moving elements, the torque-weight ratio is obtained by dividing 
the torque by the weight. Also the torque per watt of load may 
readily be obtained from the calculated torque and the reading of 
the indicating wattmeter. 

Another device for measuring the torque of electrical instru- 
ments has been devised by Dr. Agnew of the Bureau of Standards 
and is illustrated in Fig. 295. As the figure clearly shows, it 
operates on the pendulum principle, the characteristic feature 
being scale S on a concave spherical surface of 1-meter radius 
turned from a brass casting. The bob D is supported from an 
adjustable arm so arranged that the point of support P is at the 
center of the sphere of which the scale S is the surface. The silk 
fiber supporting the bob is wound on a friction pin A and passes 
through a V-shaped notch in the end of the adjustable brass strip 



TESTS OF WATT-HOUR METERS 



349 



B. The whole instrument is mounted on an ordinary clamp 
stand, the tripod of which is fitted with leveling screws. 

The graduations of the scale S consist of 153 concentric circles, 
the distance between successive circles being so spaced as to give 
the tangents of the angles of deflection directly. In milli- 
meters the distance be- 
tween circles is 1,000 X 
tangent of angle of de- 
flection. The bob consists 
of a small hollow brass 
cyUnder with a fine sewing 
needle passed through it 
perpendicular to the axis, 
as shown in Fig. 296. 

The silk fiber, by which 
the horizontal force to be 
measured is transmitted to 
the bob, is attached to the 
needle and passes out along 
the axis of the hollow cyl- 
inder. The point of at- 
tachment is made at the 
center of mass of the bob 




ac 



la 



Fig. 295. 



Fig. 296. 



which is adjusted to 0.5 gram. For changing the range of the 
instrument, concentric cylinders, each cut in halves, are made 
to fit snugly over the inner cylinder as indicated in Fig. 296. 

In measuring the torque of a deflection instrument a horizontal 
thread, one end of which is connected at D, Fig. 295, is fastened 
to the pointer of the meter at a convenient distance from the pivot, 
the torque balance adjusted to the proper height, and the deflec- 

35 



350 ELECTRICAL METERS 

tion instrument moved horizontally until the desired deflection 
is obtained. The torque is then given by 

Torque T =- I X mg X 0.001 X d 

where I = distance from pivot to point of attachment of silk fiber 
on pointer, mg is weight of bob, and d is the number of divisions 
on scale S. 

In measuring the torque of a watt-hour meter it is necessary only 
to attach the thread to the edge of the disk, apply the current and 
voltage to the meter, and allow the meter to deflect as far as it 
will. The calculations for torque may then be made as above. 
The horizontal thread must be kept tangent to the disk, if this is 
done the distance I equals the radius of the disk. 

Tests made show that the torque of alternating-current watt- 
hour meters ranges from 3.06 to 7.74 gram-cm. 

306, Test of Influence of Friction. — In connection with the 
foregoing test, the influence of friction upon the torque may be 
advantageously determined. First adjust the friction compensa- 
tion so that the meter is just balanced at no load. To secure this, 
the compensation should be just sufficient to cause the meter to 
creep at no load when slightly jarred. When the compensation 
has been properly adjusted, full load is applied and speed deter- 
mined. Then the compensating coil is disconnected and the 
speed is again determined at the same load. The so-called "fric- 
tion-torque ratio'' is the ratio of the decrease in speed with com- 
pensating coil disconnected to the speed with coil in circuit. Thus 
a decrease of 5 per cent in speed would mean a ratio of 1:20. 
The smaller this ratio, the less the influence of friction, and from 
this view point, the better the meter. 

306, Test to Determine Influence of Stray Field. — For this 
test, mount the meter in such a way that current-carrying con- 
ductors may be conveniently brought near. 

First, test the meter under conditions making impossible the 
existence of an external magnetic field. Having determined the 
accuracy under these conditions, place a conductor carrying a 
current in various positions. Direct-current meters should be 
tested under the influence of a direct-current field, and alternat- 
ing-current meters under the influence of alternating-current 
fields of the same frequency and in phase with the current in the 
meter. Run the conductor in a horizontal position back of the 
meter at a distance of 15 in. from the axis of the moving element. 



TESTS OF WATT-HOUR METERS 351 

Pass a current equal to twice the capacity of the meter through 
the conductor, and determine the iaccuracy of the meter at 100 
per cent load. Change the position of the conductor, and repeat 
the test. 

For determining the influence of a stray field on the accuracy of 
alternating-current meters, the meter committee of the National 
Electric Light Association recommends the following: 

"The meter to be tested shall be subjected to an alternating 
stray field of the same frequency as that of the testing current, 
and produced by a straight conductor six (6) feet long, with re- 
turn leads arranged to form a rectangle six (6) feet square, lying 
in a plane parallel to the switchboard. A current of fifty (50) 
amperes in phase with the voltage applied to the meter shall be 
passed through this conductor.'' 

Separate tests are to be made when the stray field conductor is 
placed successively in the following positions: 

1. "Behind the meter in a horizontal position at the level of 
the moving element and at a distance of fifteen (15) inches from 
the axis of the moving element. 

2. "Directly behind the center line of the meter, in a vertical 
position and at a distance of fifteen (15) inches from the axis of 
the moving element. 

3. "Vertically, at the same distance in front of the switch- 
board as the axis of the element and at a distance of fifteen (15) 
inches to the right or left of the meter center line, the return leads 
being so arranged that the loop which they form does not sur- 
round or include the meter." 

In connection with the foregoing, tests may be made to deter- 
mine the minimum distance which should be maintained between 
meters when in service. To do this, first determine the accuracy 
of two meters on 5 and 10 per cent loads. Test each meter sep- 
arately when there is no load on the other meter. Maintain 
a constant load of 100 per cent on one meter and determine the 
accuracy of the other meter at various distances apart. In 
varying the distances, always move the meter having the con- 
stant load. From the data thus obtained, the distance at which 
the accuracy of the meter is within permissible limits, can readily 
be determined. 

307, Test to Determine Loss in Potential Coil. — ^To determine 
this loss, two methods are available; it can be measured directly 
or computed from the resistance and voltage. The method of 



k 



352 ELECTRICAL METERS ^H 

measurement will perhaps be the most convenient for alternating- 
current meters, while for direct-current meters, the method of 
calculation will give more accurate results. 

To measure these losses, connect the potential coils of several 
meters of the same rated voltage in parallel and, if the meters are 
for direct-current circuits, measure the total current and voltage 
applied. The energy lost will be equal to the product of current 
and applied voltage, which divided by the number of meters will 
give the average loss per meter. 

On account of the low power-factor of the voltage circuit of 
alternating-current meters it is preferable to measure the resist- 
ance of the coil and calculate the loss by 

Watt loss = PR 

where / is the voltage-coil current and R the coil resistance. If 
a low-reading wattmeter is available, this may be used, providing 
proper corrections are made for its inaccuracy on low power-fac- 
tors. If the resistance of the voltage coil is not known, it can be 
mcEtsured in a variety of ways. When direct current is available, 
it can l>e measured by the drop of potential method which will 
necessitate a milliammeter and a high -resistance voltmeter. 

The loss in current coil can be calculated more accurately than 
measured. First, the resistance of the coil must be accurately 
measured, ajid then the loss at any current will be given by 

Watts loss = 7'fl as above. 

Since the resistance of the current coO is small, special precautions 
must be taken in its measurement. The drop of potential method 
may also be used, but in this case the voltage drop will be small, 
and hence, a comparatively high-resistance millivoltmeter will be 
necessary. The current can be measured by an accurate amme- 
ter of proper range. 

308. Test for Proper Comiections.~To connect a single-phase 
meter properly to a circuit is a comparatively simple process. 
When, however, it is desired to connect a polyphase meter, the 
likelihood or probability of securing a proper connection is much 
less. The difficulty encountered will depend somewhat upon the 
coil connections within the meter. As is evident from Figs. 190 
and 191, the polyphase meter consists of two metering elements 
each containing one current and one voltage coil. The ends of 
each coil may be connected to a separate terminal or the coils may 



TESTS OF WATT-HOUR METERS 353 

be interconnected. If the former system of connections is em- 
ployed, there will be eight terminals to be connected to the three- 
wire circuit. Under these conditions there are theoretically 
possible 192 different connections some of which are very improb- 
able and only four of which are correct. The usual method of 
checking the connections is to open the current or voltage circuit 
of first one element, and then the other and to note the direction 
of rotation in each case. If the power-factor of the load is above 
0.5, the torque on each element is in the same direction when the 
meter is properly connected, hence under these conditions, the 
direction of rotation of the meter is a criterion of the correctness 
of the connections. It is not an absolute criterion, however, for 
certain incorrect connections will also cause rotation of the mov- 
able element in the right direction when this procedure is followed 
and the power-factor isaboveO.5 and below 1. Theopeningof the 
voltage or current circuits of each element alternately can be re- 
lied upon as a correct check upon the correctness of the connec- 
tions only when the power-factor of the load is unity. 

A more reliable method of determing whether a meter is prop- 
erly connected is to interchange the voltage-coil connections of 
the two elements. For this check the load must be balanced or 
nearly so. The reasons for and character of this check will be 
readily understood from Fig. 191 which shows diagrammatically 
a polyphase meter properly connected to a three-wire circuit. 
When connected as shown, the torque on the movable element is 
directly proportional to the power as shown in Article 199. If, 
however, the connections of the voltage coils to mains 1 and 2 
be interchanged, we will have the following result for the torque: 

T = i\e2 — i\ei 

and the average torque must be av. T = av. {i\e2 — t'2ei). On 
balanced load the average of i\e2 must equal the average of i'^i\ 
hence, the average torque is zero, and the meter stands still. If 
the meter is improperly connected, an interchange of the connec- 
tions of the voltage coils will not reduce the torque to zero, and 
hence this method of checking the connections of a polyphase 
meter gives reliable results. The only objectionable feature is 
the necessity of a balanced load.^ 

^See KouwENHovEN, "A Method of Determining the Correctness of 
Polyphase Wattmeter Connections," Proceedings A.I,E.E., February, 1916. 

36 



CHAPTER XXII 

INSTRUMENT ERRORS 

309. Sources of Error. — So far, very little has been said in a 
systematic way about errors to which measuring instruments 
are liable, although some of the most important sources of error 
have been pointed out. The following discussion is adapted 
from a bulletin on "Testing of Electrical Measuring Instru- 
ments/' issued by the Bureau of Standards, and from other 
sources, and is the result of many investigations and tests. 

An important matter in connection with the use of electrical 
instruments, is the question of sources of error and the best 
means of securing a required degree of accuracy from a given set 
of instruments. It may be said in the beginning that in very 
many cases the user underestimates the errors and overestimates 
the accuracy of the result. This is partly due, in many cases, 
to the lack of means for checking the results obtained; as there 
is no check, inaccurate results are passed without suspicion of 
their inaccuracy, and the maker's representations as to accuracy, 
which are sometimes much exaggerated, are accepted as correct 
for an unlimited time after the maker's test and for all conditions 
of use. Portable instruments are often used in places subject 
to strong magnetic stray fields or extreme temperatures; sub- 
sequent comparison with other instruments in the testing room 
may show that the working instruments have small errors, while 
their performance under unfavorable conditions may have been 
5 per cent or more in error. 

In all physical measurements, to attain a relatively high degree 
of accuracy, care must be exercised to distinguish between at 
least three possible sources of error. These are: 

1. Inherent errors of the instrument. 

2. Errors due to the method of measurement. 

3. Errors of observation. 

310. Inherent Errors. — Inherent errors are those due to im- 
perfections of materials, limitations of accuracy in construction, 
physical conditions determined by quantities measured, etc. 
In short, the properties of materials used and the inevitable 

37 355 



350 



l-UJCVTHICM, MICTKUS 



itiaccuracicB of conBtruction ituLkc il imposHtble to cotiflbnict a 
perfect nicaKuring instrument. Inherent errors cannot be 
entirely eliminated although by improved and refined methods 
of construction, and by a knowledge of their preaence, their 
influtmco may be rodut'ed. 

311. Inherent Temperature Errors.— Among inherent errors 
may first bo mentioned thoBo due to the effect of change in the 
temperature of the various parts of tho instrument. Taking, 
for example, a voltmeter of the permanent-magnet raoving-coil 
type; if it reads correctly at a given point at a certain tempera- 
ture, it will, in general, show a small error at any other tempera- 
ture. An increase in temperature of the working parts of an 
instrument has three effects: a decrease in tho strength of tho 
magnet, which tends to reduce the reading at any given voltage; 
an increase in the resistance of the moving coil which also tends 
to reduce tho reading; and a third effect is the weakening of 
the controlling spring, which, to some extent, compensates the 
other two. The temperature coefficient of the spring is about 
0,04 per cent per degree Centigrade; that of the magnet is not 
BO definite. The resultant temperature coefficient of the instru- 
ment is quite small, as a rule. The question of making such an 
instrument practically free from temperature error is then re- 
latively simple as it is only necessary to have a low value of tho 
resistance temperature coefficient of the circuit. This is accom- 
plished by making the moving coil of low resistance, usually of 
copper, and mounting in series with it an external resistance of 
manganin whoso resistance temperature coefficient is negligible 
within the working temperature range of the instrument. Thus, 
if the value of tho external series resistance is ten times the 
resistance of the coil, tho resistance temperature coefficient of both 
will be reduced to one-tenth. The higher the series manganin 
resistance, the lower the resulting temperature coefficient. It 
is thus seen that where a voltmeter has low and high ranges, a 
greater inaccuracy due to temperature changes is to be expected 
on the lower ranges. If a low-range voltmeter is to have a low 
temperature coefficient, tho moving coil must be constructed with 
few turns and have a very low rcfiistance. 

So far, it has been assumed that the temperature within the 
instrument is uniform. This would be the case if no source of 
heat existed within the instrument. Most instruments, however, 
contain sources of heat. Unequal heating is, therefore, possible, 



INSTRUMENT ERRORS 357 

and some error will result from this cause. When, as in alter- 
nating-current voltmeters and wattmeters, a large portion of the 
resistance is so-called dead resistance in series with the working 
element, this heat-producing resistance should be partitioned 
off from the working system and properly ventilated. Unless 
this is done, the instrument cannot be left in circuit for any 
length of time without error. 

An important instance of large errors through unequal heating 
within the instrument is found in connection with the permanent- 
magnet moving-coil ammeter with internal copper shunt. In 
this instrument the moving coil of copper is connected to the 
terminals of a copper shunt within the instrument case. The 
temperature coefficient of the moving coil used alone as an 
ammeter is quite small, and, as changes of room temperature 
will not alter the relative values of current in moving coil and 
shunt, such an instrument would seem at first sight to be almost 
an ideal one. The performance of the low-range instruments is 
quite good. The performance of the higher-range instruments is 
not very satisfactory and they are suitable only for rough work. 
In general, it may be said that up to about 25 amp., well-made 
instruments of this type will give fairly good service.; for cur- 
rents above that they should not be used for accurate work. 
The use of manganin for precision shunts is now recognized as 
the best practice. For large ciurents, the shunt should be 
separate from the instrument. In practice, it is desirable to 
keep down the weight of ammeter shunts as well as the waste 
of power in them. To fulfill these conditions, milivoltmeters 
are made to give full-scale reading for very low voltages across 
the terminals. A very common value of this voltage is 50 
millivolts, where the instruments are intended for switchboard 
use. As the shunts are usually made of a material of a low 
temperature coefficient, while the millivoltmeter circuit consists 
largely of copper, the error due to varying room temperature 
may be considerable. When the instrument is intended for 
commercial switchboard use, this effect of room temperature is 
of no great moment; for precision work in the laboratory, or in 
the testing of direct-current watt-hour meters, the tempera- 
ture errors above referred to become quite objectionable. To 
remedy this, most makers manufacture a line of millivoltmeters 
which have added to copper coil a manganin resistance which 
has from four to nine times the resistance of the copper coil. 



L 



358 ELECTRICAL METERS 

This cute down the temperature coefficient of the instrument, 
but requires a higher drop across the shunt, namely, from 150 
to 200 millivolts at full load. 

Aside from the errors due to heating, changes of several per 
cent in the resistance are caused by the method of bolting the 
copper bar to the shunt. To overcome this difficulty, the 
terminal blocks should be made longer, so as to make the lines 
of current flow more nearly parallel at the junction of terminal 
and resistance metal, near which junction the potential terminals 
should be located. The same result may be attained by con- 
stricting the section of the terminal block considerably between 
the current and potential terminals. 

For precision ammeter shunts, the most satisfactory material 
is manganin, and the best makers are adopting it in spite of 
some additional trouble involved in the manufacture of the 
shunts. 

The influence of temperature upon the electromagnetic (soft- 
iron) ammeter, with spring control, is to lower the permeability 
of the iron, and also to reduce the elasticity of the spring. Since 
the effect on the spring just about neutralizes the effect on the 
soft-iron core, the ammeter is very nearly independent of ordinary 
temperature changes. 

In the clectrodynamometer type of instrument, a tempera- 
ture change affects mainly the spring. Such instruments will 
read too low at temperatures below that at which they are 
calibrated, the temperature correction being about 0.04 per cent 
per degree Centigrade. This assumes that the potential or 
shunt circuits contain so small a percentage of copper that their 
change in resistance with temperature does not sensibly affect 
the result. For ordinary ranges of voltage, this is the case. 

In the soft-iron voltmeter the temperature coefficient depends 
mainly upon the ratio of the resistance of the copper coil to the 
total resistance of the instrument. This ratio is a question of 
design, depending upon the range of the instrument and the 
amount of power required for its operation. The temperature 
coefficient of well-made voltmeters of this type, for the usual 
commercial voltages, is quite small, and for practical work need 
not be taken into account, except in extreme cases. 

Much data on the physical characteristics and performance 
of the voltmeters and ammeters whose correction curves are 
shown on pages 281 and 294 were determined by Fitch and Huber 



INSTRUMENT ERRORS 



359 



at the Bureau of Standards and are given in the following 
tables: 

Table XI. — Performance op Voltmeters 



Voltmeter 



B 



D 



£ 



H 



Resistance (ohms) 

Watts at 150 volts 

Per cent change from stand- 
ing 1 hr. at 150 volt8> 

Per cent change from revers- 
ing a stray field of 4 gausses. 

Damping. Time in seconds 
to come to rest after closing 
on 120 volts 

Mechanical balance. Maxi- 
mum deviation of index, per 
cent of full scale* 

Insulation resistance between 
coil and case, in megohms 

Temperature coeflScient. Per 
cent change per degree C*. . . 



12.450 


16,180 


18.400 


7,540 


12,350 


14,380 


16,760 


1.81 


1.39 


1.22 


2.00 


1.82 


1.56 


1.34 


-0.2 


-0.2 


-0.1 


-0.1 


-0.3 


0.0 


+0.1 


0.8 


2.2 


1.5 


1.1 


2.5 


2.3 


1.2 


0.8 


4.8 


2.1 


1.2 


4.6 


2.4 


2.8 


0.0 


0.4 


0.2 


0.1 


0.3 


0.1 


0.1 


>75 


15 


37 


>75 


75 


>75 


25 


-0.01 


-0.03 


-0.03 


-0.02 


-0.02 


-0.01 


+0.02 



14,190 
1.58 

-0.2 

1.7 



3.7 



0.1 



>75 



-0.01 



1 The minus sign indicates that less voltage was required at the end of the period. 

> In this test the instrument is turned at different angles. 

* The minus sign indicates that less voltage was required at the higher temperature. 

It will be observed that the effect of temperature upon the 
indications of the ammeters is much greater than upon the 
indications of the voltmeters. 

The temperature error of watt-hour meters is the resultant 
of the effects of temperature changes on the several parts of the 
meter, namely: 

1. Effect on voltage circuit. 

2. Effect on series circuit. 

3. Effect on retarding disk. 

4. Effect on retarding magnets. 

5. Effect on frame of the meter. 

6. Effect on lubricant. 

The accuracy of the electrodynamometer-type watt-hour meter 
is affected primarily by the resultant of the first four effects. 
Any change in the temperature of the voltage and compensating 
coils and retarding disk produces a like change in the resistance 
of the coils and disk. Thus, when the temperature increases, 
the resistance increases. This result decreases the voltage-coil 
current and eddy currents in the disk and, hence, the driving and 
retarding torques are both decreased. As these two effects are 



360 



ELECTRICAL METERS 



Table XII. — Performance op Ammeters 



Ammeter 



Resistance of millivoltmeter 

(ohms) 

Shunts: 

Millivolts at full load 

Watts loss at full load 

Temperature rise in plates 

at full load *C 

Temperature rise in lugs 

at full load *C 

Thermal e.m.f. after 1 hr. at 

full load, millivolts 

Total change of resistance 

from 26'» to 60*0. (per 

oent)i 

Per cent, change from stand- 
ing deflected at full load 

Per cent change from revers-, 
ing a stray field of 4 gausses- 
Damping. Time in seconds 
to come to rest after closing 

circuit on 160 amp 

Mechanical balance. Maxi- 
mum deviation of index, 

per cent of full scale.* 

Insulation resistance between 

case and coil, in megohms. . . . 

Temperature coefficient. Per 

cent change per degree C.*.. . 



1.3 


3.7 


2.1 


0.9 


2.0 


1.3 


4.8 


50 


74 


60 


49 


70 


50 


61 


10.0 


14.8 


12.0 


9.8 


14.0 


10.0 


12.2 


53 


73 


69 


38 


70 


66 


62 


40 


59 


58 


20 


45 


58 


50 


0.0 


0.7 


0.0 


0.0 


0.4 


0.3 


0.1 


+0.5 


+0.1 


+ 0.2 


+0.1 


+0.4 


0.0 


+0.1 


-0.5 


-1.2 


-0.9 


-0.1 


-1.6 


-0.4 


-0.3 


0.7 


1.5 


1.4 


1.1 


3.5 


1.6 


0.8 


1.1 


2.0 


1.6 


1.4 


5.8 


2.1 


2 4 


0.9 


0.7 


0.7 


0.4 


0.6 


0.6 


0.8 


75 

• 


75 


37 


75 


>75 


>75 


9 


+0.11 


+0.08 


+ 0.09 


+ 0.15 


+0.15 


+0.32 


+ 0.28 



3.2 

07 
10.4 

82 

43 



0.1 



+0.1 



-0.6 



1.0 



2.4 



0.7 



75 



* The plus sign indicates an increase in resistance with rise of temperature. 

* The minus sign indicates that less current was required at the end of the period. 

* In thb test the instrument is turned at different angles. 

* The plus sign indicates that more current was required at the higher temperature 
for the same indication. 



in a measure compensating, theoretically, the two circuits may 
be designed so as to neutralize the temperature effects of each 
other; actually this is not realized in practice. 

The heating of the series coil is not negligible as was determined 
by Fitch and Huber.^ The influence of heating the current coil 
on the accuracy of fine electrodynamometer-type watt-hour 
meters is shown in Fig. 297. 

A change in temperature of the retarding magnets changes 
their magnetic properties, and also changes the length of the air 
gap. The combined effect is to reduce the flux with increase in 
temperature. 

^ Fitch and Huber, "Study of American Direct-current Watt-hour 
Meters," Bulletin of the Bureau of Standards, vol. 10. 



INSTRUMENT ERRORS 



361 



If we define the temperature coefficient of the meter as the 
per cent change in accuracy per degree change in temperature, 
the temperature coefficient of the meter is the resultant of the 
temperature coefficients of the several parts. As the retarding 
torque is proportional to the square of the flux between the poles 



J 



1^0 
1.000 
0.980 

LDIO 
LOOO 
0,900 

1X10 
1.000 
0.900 

LOIO 
1.000 

0.990 

um 

LOOO 
OMO 

um 

LOOO 
0J90 




z:c — 



B 



D 



K 




40 00 80 100 
Per Cent Fall Load 

Fia. 297. 



lao 



140 100 



of the drag magnets, the resulting per cent change in the torque 
is twice the per cent change in the flux causing it. Hence, the 
temperature coefficient of the magnets must be doubled in calcu- 
lating the meter coefficient. Table XIII gives the temperature 
coefficients of six direct-current watt-hour meters.^ 

» Tables XIII, XIV, XV, XVI, and XVII are taken from Fitch amd 
Ruber's paper referred to above. 



362 



ELECTRICAL METERS 



Table XIII. — Temperature Coefficients (Per Cent per Degree C.) 



Watt-hour meter 



B 



D 



£ 



Potential circuit . 

Disk 

Magnets 

Algebraic sum^.. 
Meter 



+0.17 
+0.39 
-0.03 
+0.28 
+0.26 



+0.35 
+0.38 
-0.01 
+0.05 
+0.10 



+0.41 
+0.39 
-0.01 
0.00 
+0.10 



+0.30 
+0.40 
-0.01 
+0.12 
+0.12 



+0.41 
+0.37 
-0.02 
0.00 
+0.07 



+0.38 
+0.38 
-0.03 
+0.06 
+0.11 



1 In taking the sums, the coefficients of magnets were doubled and the sign reversed for 
both potential circuit and magnet coefficients. 




-20 



20 40 60 80 100 

Temperature in Degrees Fahrenheit 

Fig. 298. 



120 



140 



The effect of a cyclic change of temperature on the accuracy 
of five different makes of direct-current watt-hour meters was 
recently made by Royce and Andrew at the Electrical Labors- 



INSTRUMENT ERRORS 



363 



tories of the University of Wisconsin. Typical curves showing 
the changes in accuracy with changes in temperature, are given 
in Fig. 298. 

The characteristics of the other meters tested are similar 
although they differ in magnitude. 

The effect of temperature changes on induction meters is less 
than upon the electrodynamometer type. This is mainly due 
to the fact that both the driving and retarding forces operate 




-20 20 40 60 80 100 

Temperature in Degrees Fahrenheit 

Fig. 299. 



upon the same disk. The error in induction meters is about 1 
per cent per 10°C. This will vary somewhat with the design 
of the meter and the absolute temperature. Typical curves for 
the effect of cyclic changes of temperature are shown in Fig. 
299.1 

312. Inherent Errors Due to Time and Use. — Other errors, 
to which most instruments are liable, are due to changes 
in the properties of the materials of which the instruments are 
made, with time and use. In spite of the labor which has been 

^ B. E. Miller, Electrical World, Sept. 18, 1915. 



364 ELECTRICAL METERS 

expended on making permanent magnets and the investigations 
concerning their properties, individual magnets ci the best 
makes will occasionally show changes with time. When the 
instrument is new, it may, for a time increase in strength; later, 
it is more likely to decrease. Controlling springs also show sli^t 
changes with time. If the effect of the weakening of the magnet 
is offset by the weakening of the springs in a direct-current 
instrument, the accuracy is unchanged. 

When direct-current instruments are used in the nei^borhood 
of dynamos or motors, or in other locations subject to strong 
stray iBelds, as, for example, near conductors carrying heavy 
currents, their indications will be considerably affected at the 
time of use, and in addition permanent changes may occur in 
the permanent magnets. Stray fields are liable to be found in 
the neighborhood of switchboard instruments and hence these 
should be shielded from them. The iron case very generally used 
for such instruments affords considerable protection, but, in 
addition, it is advisable to keep heavy currents well away from 
the instruments, and, as a further precaution, important instru- 
ments that are permanently attached to the switchboard, should 
be checked in position, under working conditions. Care must 
be taken that the portable instruments used in this checking 
are in a location not exposed to stray fields; if this is impossible, 
the mean of two readings should be taken; for the second reading, 
the instrument is turned 180° from its first position. The magni- 
tudes of these errors are given in Tables XI and XII for ammeters 
and voltmeters and in Table XIV for direct-current watt-hour 
meters. 

313. Inherent Mechanical Errors. — Among the most common 
sources of error may be mentioned friction, defective preformance 
of springs, scale marking, and lack of balance of moving coil. 
The friction of pivots on a good indicating instrument should 
not be noticeable, unless it is old or has been roughly used. The 
friction of the pen on recording instruments is the main cause of 
inaccuracy of these instruments. It is evident that friction can- 
not be entirely eliminated, and hence, the problem is to have a 
spring strong enough to cause the coil to take up its proper 
position irrespective of friction. If the spring is strong, the 
torque for a full-scale deflection will also have to be high. Ac- 
cording to one writer, this torque expressed in gram-centimeters 
should not be less than one-sixth the weight of the coil in grams; 



INSTRUMENT ERRORS 



365 



Table XIV. — Performance op Watt-hour Meters 



Watt-hour meter 



B 



E 



Rated full-load r.p.m 

Per cent difference in balance of current 

elements: 

No. 1 

No. 2 

No. 3 

Per cent change from reversing stray 

field of 1 gauss at full load 

Per cent change from removing covers: 

Heating! 

Magnetic 

Per cent change from reversing polarity: 

50 per cent load 

100 per cent load 

Polarity marked 

Range of light-load adjustment, per cent. 

Range of full-load adjustment, per cent.. 

Per cent change of full-load rate by maxi- 
mum change of light-load adjustment. . 

Per cent change of light-load rate by 
maximum change of full-load adjust- 
ment 

Per cent change from short-circuit on 120 
volts 

Maximum amperes on 120-volt short- 
circuit 

Per cent change by short-circuit on 240 
volts 

Maximum amperes on 240-volt short- 
circuit 

Full-load back e.m.f. in volts 

Starting current, in amperes: 

No. 1 

No. 2 

No. 3 

Creeping voltage, in volts: 

No. 1 

No. 2 ■ 

No. 3 



33.0 


36.7 


45.8 


1.1 


5.1 


0.4 


3.2 


1.5 


1.0 


4.2 


3.6 


0.8 


2.2 


2.2 


2.3 


+0.3 


+0.1 


+0.6 


+0.2 


0.0 


-0.4 


0.8 


0.6 


0.5 


0.5 


3 


0.2 


Yes 


Yes 


No 


4.6 


5 6 


13.8 


86 


165 


68 


0.5 


0.3 


0.7 


85 


154 


66 


2.5 


2.9 


1.1 


240 


260 


260 


34.0 


11.6 


5.6 


400 


400 


430 


0.13 


0.13 


0.19 


0.06 


0.02 


0.04 


0.07 


0.06 


0.05 


0.07 


(«) 


0.03 


130 


120 


130 


130 


130 


130 


130 


100 


130 



27.5 



0.0 

0.0 
0.0 

2.9 
1.9 
No 
4.6 
35 

-1.5 



38 

2.3 

>500 

0.0 

730 
0.0001 



0.02 



160 
260 
180 



45.8 



0.6 
0.0 
0.8 

2.6 

+0.7 
-0.3 

0.9 

0.4 

Yes 

22.0 

92 

1.5 



104 

1.9 
270 

4.7 

440 
0.17 

0.09 
0.07 
0.08 

130 
130 
130 



55. 



2.6 
3.2 
0.3 

2.7 

0.0 
0.0 

0.5 

0.2 

Yes 

12.2 

65 

1.1 



65 

-2.2 

340 

-3.4 

560 
0.07 

0.08 
0.04 
0.11 

130 
130 
130 



1 The plus sign indicates an increase in speed. 

> Where no figure is given of the starting current it indicates creeping on voltage only. 

this weight includes that of springs, index, etc. Another author 
gives a minimum value considerably lower, namely, one-twen- 
tieth. Both authorities assume a deflection of about 90°, this 
being nearly the full-scale deflection for direct-current indicat- 
ing instruments. It is desirable to keep the ratio of torque to 
weight as high as possible in all electrical measuring instruments. 
It should be noted, however, that an instrument with a very 
high torque may really be a poor instrument, if the high torque 
is obtained by using an excessively heavy moving system. 



366 



ELECTRICAL METERS 



The most important factor affecting the accuracy of inte- 
grating meters is friction of brushes, bearings, and registering 
mechanism. If this friction were constant, any errors intro- 
duced by it could be compensated, but since it is an extremely 
variable factor, under favorable conditions the error due to it 
may be appreciable. Tightening the brushes on a commutator 
meter may cause a 10 per cent error on a 10 per cent load. To 
reduce the effect of friction to a minimum, the meter should 
operate at a comparatively low speed and the ratio of driving 
torque to weight of moving element should be high. Hig^-speed 
and heavy-moving elements increase friction. 



Table XV. — Constants op the Coils 



Watt-bour meter 


A 


B 


C 


D« 


E 


F 


RMbUnM of potentUI 
etreuit in ohm*: 

Multiplier 

SUrting ooiL 


3.060 

230 

2.300 


1.340 

12 

1.290 


1,790 
930 




1.710 
980 




Armftture. . x x ....... . 


1.360 






ToUL 


5.010 


2,040 


2,720 


5.290 


2.690 


4.580 






PotentLal-eireuit watU. . . 

Current element: Resist- 

ftneet obmc 


2.2 

0.260 
0.5 

70 


4.0 

0.230 

5.7 

85 


4.4 

0.230 
5.7 

75 


9.2 
0.002 


4.5 
210 


2.0 
0.100 


Watts loM. fuli load 

Flux density full load. 
(auatfM 


2 i 5.2 

1 

70 


2.5 
85 






1 


1 





>Rat«d voltac« of meter D was 220; of the others, 110. 



Table XVI. — Constants of Moving Elements 



Watt*hour meter 



B 



Torque in oentimeter-crama 

Weight in grama 

Ratio of torque to weight 

Diameter of commutator, centimeter 

Number of commutator segments 

Thickness of disk« centimeter.* 

Diameter of disk« centimeter 

Voltage drop across armature with 1 10 volts 

on potential circuit 

Brush p r M s ure, grams 



7.47 


14.31 


98.4 


156.2 


0.076 


0.002 


0.265 


0.465 


3 


8 


0.115 


0.150 


11.40 


13.35 


45.1 


53.8 


0.24 


0.57 



16.69 
101.8 





8 
0. 



164 
240 

065 



12.66 

37.6 
1.50 



3.92 


1 
14.92 


7.2 


96.1 


0.545 


0.155 


• » • • 


0.240 


• • • • 


8 


0.090 


0.005 


10.18 


12.70 


• • • • 


40.1 


• » • • 


1.80 



2.85 
97.4 
0.090 
0.196 
3 

0.115 
8.54 

32.7 
0.34 



INSTRUMENT ERRORS 



367 



1'able XVII. — Constants of Magnets 
[The dimensions are given in centimeters and the flux densities in g&nmeB.] 



Watt-hour meter 



B 



D 



£ 



Number of magnets 
Steel: 

Length 

CrossHsection 

Air gap: 

Length, 

CrossHsection .... 

K« 

Total flux 



2 


2 


4 


2 


4 


19.4 


26.2 


23.2 


18.1 


24.0 


2.2 


2.0 


1.4 


2.2 


1.4 


0.28 


0.36 


0.24 


0.29 


0.25 


5.3 


6.8 


4.4 


3.1 


4.4 


167 


247 


304 


88 


302 


9,700 


14,400 


7,300 8,100 


7,300 



13.3 
2.6 

Adjustable 
2.5 



1,300* 



1 Taken with 2.5-min. air gap. 

s K is the ratio of the length of the manegt to its cross-section divided by the ratio of the 
air gap to its cross-section. 

314. Defective Performance of Springs. — An indicating instru- 
ment whose pointer stands exactly at zero with no current flowing, 
will not always indicate zero after use on full load. If the full 
load is on for only a moment, the pointer will usually return to 
zero within the limit of reading. If full-scale deflection be main- 
tained for an hour or so, it will probably be found that the pointer 
does not return exactly to zero when the circuit is broken; if the 
full-scale deflection lasts several hours, the discrepancy will be 
still greater. This zero shift is only temporary, and gradually 
disappears. The amount of this zero shift varies in different 
classes of instruments, and in different instruments of the same 
class. In first-class voltmeters it should be just noticeable; 
in millivoltmeters, as a rule, it is considerably greater, although 
occasionally a millivoltmeter will show very good performance in 
this respect. The inaccuracy due to zero shift is most marked 
if the instrument is used for a small deflection soon after it has 
sustained a large deflection for a considerable length of time. 
The reason for the poorer performance of millivoltmeters lies in 
the necessity of using springs whose electrical properties approach 
those of copper. For voltmeters no such limitations exist, and 
the springs may be made of bronze whose mechanical properties 
are Ixjst suited for the purpose irrespective of electrical resistance. 
The design of a spring determines its performance, as well as the 
material of which it is made; the shape, length, and thickness 
determine its elastic limit when made of a given material. 



368 



ELECTRICAL METERS 



In discussing controlling eprings, it was stated that the torque 
is proportional to the angle or distance through which it has been 
distorted. This proportionality is not exact, and any measure- 
ments based upon the exactness of the assumption may lead to 
errors of 1 per cent or more. This fact is brought out more 
clearly in Fig. 300, which shows some calibration curves of several 
Siemen's dynamometers and a precision instrument. These 
curves are duo to Bradshaw. The error in deflection is plotted 
vertically and the actual deflection horizontally. Thus, when 



















/ 




















/ 




















'/ 






















/ 
































• 




^ 




,"~ 




_ 


^ 






-~> 


5 


\: 




— 


"^ 


\ 


^ 


s. 




-^ 


o 


\ 






/ 






\ 












V 


/ 










M 
























s 



























50 )oo 150 zoo iso 

Division* 
FiQ. 300. 

the deflection on the precision instrument is 150, the instrument 
whose curve is marked 1 reads two divisions too high. At 50 
the reading is 1.5 divisions too low, which shows that the torque 
of the spring does not follow exactly the assumed law. In the 
ordinary direct-reading instruments this variation does not 
appear if the scale has been properly graduated. However, if 
by accident the spring should be distorted or bent out of its 
original shape, the scale will no longer be correct, even though 
by shifting the spring holder the pointer be brought back to 
zero. 

From the foregoing, it is evident that a first-class instrument 
should have a scale graduated for that particular instrument. 
It is not necessary to determine every division by exact test, 



INSTRUMENT ERRORS 369 

especially on instruments for commercial use. It is usually con- 
sidered sufficient to determine, say ten or fifteen points, and fill 
in the intermediate points, preferably by some mechanical 
method. 

Any change in the relative position of the working parts of an 
instrument will affect its calibration. Thus, the simple removal 
and replacement of the pole pieces of a direct-current instrument 
— in fact, even the tightening of the screws that hold the pole 
pieces — will affect the distribution of the magnetic flux so that a 
scale, which fitted before the operation, will now show appreci- 
able errors. Any accident, and mechanical change or adjust- 
ment of an instrument should be followed by a test. Some 
makers claim for their portable direct-current instruments a 
possible accuracy of 0.1 scale division. No such accuracy need 
be expected in the average instrument. 

316. Errors Due to Balancing. — When a portable instrument 
is held in different positions when not connected to a circuit, it 
will be observed that the pointer will not remain at the zero 
position. This deviation is due to imperfect balancing of the 
moving parts of the instrument. A portable direct-current 
voltmeter examined in this way will show a deviation of not more 
than a few tenths of a scale division if in good balance; milli- 
voltmeters, wattmeters, and alternating-current instruments, all 
of which usually have a smaller ratio of torque to weight of mov- 
ing parts than the direct-current voltmeter, may show devia- 
tions as great as one division. Most portable instruments are 
intended to be used on a level support in a horizontal position, 
and to avoid errors on account of imperfect balancing they should 
be used and tested in that position. All other instruments should 
be tested in the position in which they are to be used. 

316. Errors of Use. — In addition to the foregoing inherent 
errors of construction, there are what may be called inherent 
errors of use. The instrument may be used under circumstances 
such that errors in the result are inevitable. One of the most 
common sources of error of this kind is due to stray magnetic 
fields either from other instruments, or conductors carrying 
heavy currents. Even the proximity of unmagnetized masses of 
iron may influence the readings. The effect of stray field depends 
upon the nature of the field, and the design of the instrument. 
The influence of a direct-current field is constant so long as the 
current is constant, and varies with the ciu'rent. Its effect upon 



370 ELECTRICAL METERS 

a direct-current moving-coil instrument may be obtained by 
reading the instrument in a given position, quickly turning it 
through an angle of 180^ and reading it again. One-half the 
sum of the readings will be the true reading. So long as the 
stray field remains constant, the error may be determined as 
above and may be allowed for by a percentage correction for 
readings on any part of the scale, the instrument remaining in a 
fixed position. 

The effect of the stray field is to change the strength of the 
field of the magnets of the instrument; the distribution of the 
field is not perceptibly changed. The resulting deflection of the 
instrument may then be considered as proportional to the 
product of the current in the moving coil and composite field. 

Thus let H = original magnet field 

let H' = component of stray field parallel to magnet 

field 
and / = current in moving coil of instrument. 

Then the reading of the instrument in one position may be 
written 

R^ K{IH -\' IW), 

With the instrument turned through an angle of 180® the eflFect 
of the stray field will be opposite to that in the former case, hence, 

i2' = JS: (IH - IW). 

Adding the two deflections or readings we get 

(R + jBO = 2KIH 

whence « = KIHj the true reading. 

Subtracting the two readings the difference is 

R-R' = 2KIH' 

or ^-X^' = ^^H' 

the effect or change in reading due to stray field. The percentage 
error is then 

R- R' 

2 ^ KIH ' 

R + R' KIH 

2 
R- R' H' 



INSTRUMENT ERRORS 371 

This shows that so long as H' remains constant, the error is a 
constant percentage of the true reading. 

Since, in most cases it is necessary to calculate the true reading 
from the indication of the instrument, it is better to give the 
error as a per cent of the instrument indication. This can 
readily be done as follows: 

^—^ = KIH' 

or change in true reading due to influence of stray field. If R 
is the indication of the instrument in the original position, the 
percentage error of R is 

R - R' 

2 ^ KIH' ^ H' 
R KI{H + H') H + H' 

and is also constant. When this percentage error has once been 
determined, it may be applied for obtaining the true reading at 
other indications of the instrument. The true reading will be 
equal to 

«(' ± ^) 

the plus sign being used when the actual indication of the instru- 
ment is less than the true reading, and the minus sign when the 
conditions are the reverse. With instruments of the electro- 
dynamometer type the case is different. Since the deflection in 
this type of instrument is due to the reaction of the fields in two 
coils, a position of the instrument can be found such that the 
stray field produces no effect for a given reading of the instru- 
ment; that is, at a given position of the moving coil the stray 
field exerts no torque upon the moving coil. At any other posi- 
tion of the moving coil the stray field will have some effect, and 
this effect will vary with the deflection. Even weak fields, such 
as that of the earth, have appreciable effects, and the usual 
method of avoiding error in the test of such instruments, consists 
in measuring with standard instruments the current, voltage, or 
power required to bring the pointer of the instrument under test 
to a given point on the scale; the direction of current is then 
reversed, and a second measurement made with the same reading 
of the instrument under test. The arithmetical mean of the two 
readings of the standard instruments will give the correct value 

38 



372 ELECTRICAL METERS 

of the quantity measured, and what should be indicated by the 
instrument under test were no external field present. 

When such instruments are used on alternating currents, the 
constant stray fields will have no effect. Here the trouble is 
more likely to come from heavy alternating currents of the same, 
or nearly the same, frequency as those of the quantity being 
measured. Errors due to this cause may best be avoided by 
twisting the leads together in such a way that the inductive 
effect of the current is eliminated or at least very much weakened. 
If other sources of stray field are supposed to exist, the instru- 
ment may be turned through an angle of 180° and the effect 
determined, as explained above. 

A strong magnetic field, due to an alternating current, is liable 
to partially demagnetize the permanent magnet and cause the 
instrument to read low permanently unless repaired. Unless the 
field is strong enough to cause this partial demagnetization it will 
have no effect whatever upon the reading. Instruments of the 
electrodynamometer type are sometimes made astatic to avoid 
the errors due to stray field. This is accomplished by construct- 
ing the instrument with two moving coils which are so connected 
that a stray field produces equal and opposing torques on the two 
coils. If the stray field is the same at the two coils, no error is 
produced. It is not safe, however, to assume that such instru- 
ments may be used without error in close proximity to heavy 
currents, as both theory and experiment show that appreciable 
errors may result. The same precautions should be taken with 
astatic instruments as with those of ordinary form. 

The hot-wire and electrostatic instruments are not affected to 
any appreciable extent by stray fields, as their action is not based 
on magnetic reaction. Induction instruments are also free from 
serious error from the influence of stray fields, since their air gap 
is small and their fields quite strong. 

317. Electrostatic Effect. — The electrostatic attraction or re- 
pulsion between the moving parts of an instrument and some sta- 
tionary part may cause appreciable errors. Rubbing the cover- 
glass with a handkerchief, cloth, or even the hand will often 
cause the pointer to have an initial deflection. The remedy 
for this consists in breathing upon the glass, the moisture of the 
breath causing the charge to disappear. 

In calibrating indicating wattmeters by means of two separate 
sources of electromotive force, a similar effect is likely to be 



INSTRUMENT ERRORS 



373 



experienced. When the potential applied to the fixed coil is 
much different from that applied to the moving coil, an electro- 
static force is exerted between the two, and an appreciable error 
in the reading may result, 

318. Contact Errors. — Still another source of error is the lack 
of good contact. This may be the fault of the individual con- 
necting the instrument to the circuit, or it may be due to faulty 
construction. Millivoltmeter readings are especially liable to be 
erroneous due to this cause. A millivoltmeter ia usually con- 
nected to the shunt by two leads, and in most instruments now 
in use this involves four contacts in the instrument circuit, two 
at the shunt and two at the binding posts. As the resistance of 
the instrument is only a few ohms, a corroded or dirty terminal 
or binding-post surface may introduce errors which may amount 
to several per cent. Binding posts and lead terminals of all 
precision instruments should be nickel-plated to avoid corrosion. 
The use of any substance which is liable to corrode the contacts 
should not be permitted in either the construction or use of the 
instrument. Soft-rubber tubing contains sulphur which will 
corrode copper, and for that reason should be avoided in instru- 
ment construction. 

319. Errors Due to Thermo-electromotive Forces. — In ordinary 
"station shunts" some errors are due to thermo-electric effects. 
That is, the heating of the junction of the resistance metal to 
the terminal block sets up thermo-electric currents which may be 
quite appreciable. 

Errors due to thermo-electric effect may be observed by allow- 
ing the current to flow until the shunt has assumed working 
temperature. On breaking the circuit, the millivoltmeter will 
show a small current flowing under the action of thermal-electro- 
motive forces. This may be distinguished from zero shift by 
opening the millivoltmeter circuit. 

A bad contact at one end of an ammeter shunt, or even the use 
of too small a current cable at one end of the shunt, will cause that 
end to be heated more than the other. With many shunts now 
in use, this will cause considerable error from thermal-electro- 
motive forces. For accurate work the shunts should be placed 
in oil and the temperature equalized by constant stirring. 
Some provision for cooling and constant stirring of the oil must 
be made when large currents are used unless it is arranged to 
short-circuit the shunt terminals for most of the time. 



374 



ELECTRICAL METERS 



320. Errors Due to Combination of Instruments. — The amount 
of energy consumed by the ordinary electrical measuring instru- 
ments is small, and may be neglected when the instruments are 
used in commercial practice. When, however, the instruments 
themselves are being tested, and for accurate measurements, it 
is necessary to know what errors may be introduced by neglect- 




LrtLi 



Fig. 301. 

ing these losses. Some arrangements of instruments introduce 
larger errors than others, and also the percentage error with the 
same arrangement may be higher in one case than in another, 
depending upon the characteristics and ranges of instruments 
used. When a wattmeter, ammeter, and a voltmeter are used, 




Fig. 302. 



the instruments may be connected in several ways, two of which 
are indicated in Figs. 301 and 302. In Fig. 301 the ammeter and 
voltmeter are both connected between the wattmeter and load. 
When such a connection is used, the current indicated by the 
ammeter is less than the current passing through the current coil 
of the wattmeter. If the wattmeter is being tested, the product 



INSTRUMENT ERRORS 375 

of current and pressure, / X -B, is too low; and if power consump- 
tion of load is being determined, the wattmeter indication is too 
high. The excess in current is plainly that flowing through the 
voltmeter and pressure coil of the wattmeter. If the wattmeter 

is properly compensated, no correction need be made for its pres- 

E^ 
sure coil current. The voltmeter correction will be -»■» where 

E is the load pressure and R the resistance of voltmeter coil. 

When the connections of Fig. 302 are used, the wattmeter 
indication should equal /JB, but this is greater than the power 
consumption of load. 

In the combined use of the three instruments the best method 
of connection will depend somewhat upon the conditions of test. 
The instruments should be so connected that if corrections are 
necessary they can easily be made. 

321. Errors Due to Voltage and Current Transformers. — 
In order that excessive errors may not be introduced in the 
measurement of electrical quantities when instrument trans- 
formers are used, it is necessary to know the ratio of transfor- 
mation and phase relation between primary and secondary 
currents. In current transformers, the ratio of transformation 
must be known in connection with the ammeter and leads with 
which it is to be used. Slight phase shifting due to the fact that 
primary and secondary quantities are not exactly in opposition, 
introduces no errors in current and voltage measurements. In 
connection with the measurement of power, it is necessary to 
consider the phase displacement, and make the necessary 
corrections. A more complete discussion of instrument trans- 
formers is given in Chapter XXIII. 

322. Errors Due to Frequency and Wave Form. — ^The errors 
due to changes in frequency, and those due to deviations of the 
current and electromotive-force waves from a true sine wave 
will differ with th6 type of instrument. The reading of all in- 
struments that contain iron in their operating elements, unless ac- 
curately compensated, will be influenced by changes in frequency. 
Many modem instruments can now be obtained in which the 
compensation makes them practically free from this error. It 
is a good plan, nevertheless, to test a meter at the frequency on 
which it is to be used. The inductance of the meter coils is 
primarily responsible for frequency errors. The mathematical 
expression for this error in meters whose coils are connected as 



376 ELECTRICAL METERS 

diagrammatically indicated in Fig. 566, may be determined as 
follows: 

Let jBo = resistance of shunt, 

Lo = self-inductance of shunt, 
R\ = resistance of movable-coil circuit, 
Li = self-inductance of movable-coil circuit, 
M = mutual inductance of movable and fixed coils. 
This varies with the position of the coils. 
Let / = effective current in fixed coil, 

/i = effective current in movable coil, 
E = pressure across the shunt, 

0) = 27r/. 

Then, by using the notation of the complex quantity, which in 
this instance is perhaps the more simple, we have: 

E = IiRi + ja)LiIi + JG)MI 

where j represents \/— 1, wLi/i and cjMI are components of 

pressure 90° out of phase with 7. 
This gives 

^ Jg - ja>MI 

^' Ri+jwLi' 

But 

E 
lo = Ti — ; — ^— F" = current through shunt 
Ro + j<aLo 

and 



Ri + j(i)Li Ro + jo)Lo 

Solving this for E we have: 

g _ I[(Ri + jo>Li)(Ro + jo^Lo) + jwMjRo + ja>Lo)] 
Ro + jo)Lo + Ri + j<aLi 

Substituting this value of E in the expression for /i and reducing, 
we get: 

I[Ro{Ri + fio) + co«(Li +Lo) (Lo - M) +ia) (fii +fio) (Lo - Jf ) ~ fio(Li +Lo)l 

(«i+i^o)*+««(Li + Lo)« 

This expression consists of a rational term and an imaginary 
term. The rational part 

I[Ro{Ro + Ri) + i^KLi + Lo)(Lo - M)] 
(Ri + Roy + a)2(Li + Lo)' 



INSTRUMENT ERRORS 



377 



is the component of /i in phase with /, and hence it is that part 
of Ji which produces a torque. The torque due to / and this 
component of 7i is: 

. KP[RoiRo + Ri) + <o'(Li + Lo)(Lo - M) ] 
(Ro + iJi)* + u,\Lo + Li)« 

,(Lo + Li) (Lo-M) 



T = 



= KI\ 



Ro 



1 + 0)' 



{Rq + Ri) Rq 



1 + 0) 



, (Lo + Lir 



Ro -j- Ri 

' ^'''\Ro + Riy 

In order to reduce this to simpler form, let: 

Lo + Li 



Then 



Ro "H Ri 
Lo- M 

Rq 



= T 



= r«. 



T = KIK 



fto rl + <oT X To 



iL 1 + wT« J 



= /C2«. 



i2o + i?iL 1 + w"! 

Ro K'Pu^T(To- T) 



Ro + /2i 
K' = K 



1 + w«r* 

i2o 



Rl -(- ito 



i2o 



But KP B — i — BT is the torque when the coils are non-inductive, 
iCo -r i^i 

or it is the torque that a direct current of I amp. would produce. 
Call this torque ro. Then: 



r = To + 



1 + 0)2^2 



The effective alternating current is proportional to the square 
root of r; we then have: 



Vr = -Wro + 



K'Po3^T{To - T) 



1 + 0)2X2 

Vr - Vro = [to + f+^f^ -J - VTo. 

Hence per cent error 



= 10o:^^^^;J^« = 100 



I TO H 



Vro 

100 a)2r(ro - T) 

2(1 + 0)2^2) 



1 + o>^T^ 
Vto 



- 100 



, approximately. 



378 ELECTRICAL METERS 

Example. — A shunted dynamometer ammeter has the following ocm- 

stants:^ 

Ri = 4: ohms, 

L = 0.03 X 10-» henrys, 

To = - 5.36 X l0-», 

T = 0.75 X 10-», 

« = 2t X 100. 

Here per cent error = 

J^ X 100 X (2t X 100)« X 0.75 X lO"* X 6.11 X 10"* 

1 + (2t X 100)2(0.75 X 10-*) « 
_ _ 2t' X 0.75 X 6.11 X 10-* 

1 + 4t* X 0.5625 X 10-« 
= 0.09 of 1 per cent, low, approximately. 

The effect of wave form upon the reading of any instrument 
will depend to a considerable extent upon the relation between 
the actuating force and current causing it. This relation in most 
alternating-current instruments is expressed by : 

r = KP 

and the influence of Wave form upon the readings of such meters 
may be investigated as follows: 

As shown in Article 55 an alternating-current wave may be ex- 
pressed by a series of sine and cosine functions. As the current 
supplied by commercial alternators contains no even harmonics, 
the practical current wave may be expressed by: 

i = Ai sin X + AzsinSx + . . . A» sin n x 
+ Bi cos X + Bz cos 3x + ... Bn cos n x 

Where n is an odd number, and e may be expressed by a similar 
series. 

In an instrument whose impelling force is proportional to the 
square of the current we have: 

T = Ki^ = K[Ai sin x + A3 sin 3x + , . . + An sin n x 

+ B\ cos X -{- Bz cos 3x + ... + Bn cos n xY, 
and average torque 

= A'ri^..i„. + ^.3i.3x+...+A.sin„« 

+ Bi cos X -\- Bz cos 3x + ... + Bn cos n x^dx. 
Squaring the quantity within the brackets this becomes: 

- \Ai^ sin2 ^^a: + ( Az'' sin^ ^xdx + . . . + Mn^ sin^ n xdx 

TT L Jo Jo Jo 

+ I Bi^ cos2 xdx + I Bz^cosz^xdx + . , , + i B\ cos^ n dx\ 
* See RisDALE, loc, cit. 



INSTRUMENT ERRORS 379 

plus the integral of a series of terms of the following form: 
AnAm sin nx sin mxdx, AnBm sin nx cos mxdx and BnBm, cos nx 
sin mxdx. The integrals of these terms between the limits of 
zero and t reduce to zero and we have left as the average torque: 

av. r = - I Ai2 sin2 xdx + | Az^sm^3xdx+ . . . + I ^n^sin^ 
^ L Jo Jo Jo 

n xdx + I Bi^ cos^ xdx + I ^3^ cos ^Sa^x + . . . 
Jo Jo 



+ 
K 



I Bn^ cos^ n xdx 



= 7 [^^1' + 1^3^+ . . . Ia„^ + |Bi* + |58^ + . . . + |b»*] 
= ^L^ + _+...+_ + _ + _+...+ _j. 



But 

Ai^ + Bi« Ji« 

2 — ^T' 

^8^ + g»^ ^ Js^^ etc. 
2 2 ' ' 

yl„« + B„2 /„" 

2~ T' 

where 7i, J3, etc., In, are the maximum values of the fundamental, 
and harmonics, respectively. The average torque is thus pro- 
portional to: 

7i2 r 2 7 2 



2 ' 2 ' ••' ' 2 
and 



= /i' + ¥ 



2 7 2 

+ ... +^ 



where I is the reading of the instrument if an ammeter. If the 
instrument is a voltmeter, it can be shown by a similar process 
of analysis that: 

fE^ ^ EJ 

V 2 ^ 2 ^ ^ 2 

This shows that in ammeters and voltmeters of the electrodyna- 
mometer type the torque is the sum of the independent torques 
of the component harmonics, and that these torques do not 
interact with each other to produce a torque. This is an im- 
portant result and simplifies considerably the analysis of the 



380 ELECTRICAL METERS 

problem of the influence of wave form upon the errors of electro- 
dynamometer instruments. 

In a preceding discussion it was shown that the percentage 
error in a two-circuit electrodynamometer ammeter is given with 
close approximation by: 

^ ^ 100 o>^T{To - T) 

Per cent error = _^^-^_^^,^, 

when measuring a current whose wave form is a sine curve. If 
the current measured contains harmonics, each harmonic will 
produce its own torque and its own error. The resultant error 
will then consist of a series of terms of which the above is a type. 
The torque due to the first harmonic or fundamental is: 



r l + a)^rx To i 



Similarly, the torque due to the third harmonic is: 



rz ^s ^ L 1 ^ (3a>)«r« J 
and in general 

r„ i„ TV ^ J nWr« J' 



+ 
The total torque is equal to the sum of these, hence: 



4' L i + nwr» J 



n 



where 2) nieans the sum of all terms obtained by substituting 

1 
1, 3, 5, 7, etc., for n, depending upon the number of harmonics 

present, or 

n 

But 2^1 ^'In would be the torque were the coils non-inductive, 

1 
or it is the torque due to direct current of the same value. 

Hence: 

r - TO + 2,^/» L 1 + n*a,«r« J 



V T — V To . . U>-J \t. — J. ) -^ _ 

"^ » ^ 1 + n^w^r* 



Vr 



- 1 



INSTRUMENT ERRORS 381 

and per cent error = 

100 <^nTo_- T) ^ n^K* aoDroximatelv 
-2 -J, 2; 1 + n«««r«' approximately. 

1 

If the form of the current wave is known, the per cent error, 
due to wave form, can be readily calculated. 

Wave-form Errors in Dynamometer Voltmeters. — ^The coils of 
an electrodynamometer voltmeter are invariably connected 
in series, hence it is a comparatively simple matter to derive an 
expression for frequency and wave-form errors. If L is the self- 
inductance of the coils, and M the mutual inductance, which 
varies with the position of the coils, then the effective value of 
the current through the instrument, due to a sine wave of electro- 
motive force, is: 

Vr^ + w2(L + My 

where R is the total resistance of the instrument. The torque 
due to the first harmonic or fundamental is, then: 

E^ 
n = KP = K 

Similarly, for the nth harmonic the torque is: 

En' 



n^K 



R^ + n^o>\L + My 



and 



A E 2 



R^ + n^o}\L + My 

= IT V ^' - ^ V gnn^^co^L + My] 



^ iga 52 ^ ^2 + n^^^\L + M)' 

K ^ 
But p2 ^ Ef? is the torque due to a constant electromotive 

force. Hence: 



a)2(L + M)2g A nmn^ 



w \AJ ~y srjL J X&. ^-\ lb xvf 

r = To 



i?« ^R* + n^<a\L + M)* 



382 ELECTRICAL METERS 

Per cent error 



^r n*En* 1 

2 « ^^ A [ftT+ „,„,(£, qr-jj/yij, approximately. 

1 



2 



When n is 1, this reduces to: 

^ , 100 oy\L + My 

Per cent error = -^ /e> + ^»(l + My 

EXAMPLE 

An electrodynamomctcr voltmeter has the following conBtantf? 

R - 2,000 ohms, 
L - 102 millihenrys, 
ilf - 3 millihenrys maximum. 

Calculate the per cent error in the reading of the instrument when used 
on a circuit whoso frequency is 133M cycles. 

SolviUm, — 

,, ^ 100 (oKL + My 

Per cent error = -^ rT:^ oi^il + ilf )« 

■f X 4.« X -7^ X 0.105. 



2,000^ + ^V></^^ 0.106. 
- 0.1 of 1 per cent, approximately. 

Wave-form Errors in Ekdrodynamometer WaUmeters. — The 
error due to the self-inductance of the potential coil when both 
electromotive force and current waves are simple sine curves has 
been discussed in Article 112. It remains to investigate briefly 
the influence of upper harmonics. 

If power is measured in a circuit in which the electromotive- 
force wave is a simple sine wave, and the current wave is com- 
posite, we may express the wave forms as follows: 

e = Em sin o)t 

i = Iim sin {cot + 6) + I%m sin (3wi + jS) + /»mSin (6«i + 7), etc. 
and ei = EnJim sin (at sin {(at + B) + EnJzm sin (at 

sin (3a>< + ff) + EnJim sin (at sin {5(at + 7), etc. 

and average ef = - I EnJim sin (at sin {(at + B) + -- I EmJtm 

irjo ^ Jo 

sin (at sin {3(at + B) + - I EnJtm sin (a t sin {5(at + 7), etc. 



INSTRUMENT ERRORS ' 383 

depending upon the number of harmonics in the current wave 

The integral of the first term is plainly — ^ • — -^ cos 6. The 

integrals of the second and subsequent terms all reduce to zero 
as can easily be shown. Hence, the average torque of the watt- 
meter is proportional to the product of the effective value of the 
electromotive force by the effective value of the fundamental 
of the current curve. The indication of an electrodynamometer 
wattmeter is thus independent of the upper harmonics when 
either the electromotive force or current is simple harmonic. 

If both the electromotive force and current waves contain 
upper harmonics, then the resultant torque is proportional to the 
sum of the products obtained by multiplying the effective value 
of each electromotive force harmonic by the effective value of 
the current harmonic of the same frequency and by the cosine 
of the phase difference, or, in mathematical symbols: 

r = Kei = K ^^ cos e + K^^!^ cos ^s +, . . . 



E I 

A -z: cos Bi, 



This relation can be demonstrated mathematically, but a long 
analysis is not necessary, for if the first harmonic of the electro- 
motive-force wave does not produce a torque with the upper 
harmonics of the current wave, it follows that any upper harmonic 
of the electromotive-force wave will not produce a torque with 
any harmonic of the current curve except the one of the same 
frequency. Hence, the conclusion is obvious. The error due 
to upper harmonics when self-inductance alone is considered 
may be derived as follows: 



n 



= K^EnlnWos^ an COS On + sin an COS an sin On] 



1 

n n 



= K^Enln cos On + K^EnIn[&m an sin (On — ttn)] 



ELECTRICAL METERS 



Per cent error = 



. I 

^EJ„ cos fl„ 



[sina.BinCB.-o.)) 
_ ^ lOO^r ^g_,_ "„ (,i„ ,. _ „„;r COB ..). 

JeJ.cosS. ' 

Where 3" is the time constant of the instrument circuit, $„ 
is the phase difference between the nth electromotive force and 
current harmonics. When the shape of the current and voltage 
curves and the constants of the instrument are l^nown, the per 
cent error may be calculated. 

Induction watt-hour meters are considerably affected by fre- 
quency and wave form; a 5 per cent variation in frequency 
may cause from 1 to 2 per cent error on one-halE load. A certain 
meter registered correctly on a current from one generator but 
showed a 15 per cent error on current of same frequency but 
different wave form supplied by another generator. 

313. Errors of Observation. — The errors due to reading are 
very variable and depend upon two factors, one upon the con- 
struction of the instrument, and the other upon the skill and 
care of the observer. For accurate readings, the pointer should 
be constructed with a flattened end, the plane of the pointer being 
perpendicular to the scale, under which should be mounted a 
mirror. The reading is then made by closing one eye and with 
the other noting that the pointer ia exactly over its reflection 
from the mirror. In this way errors due to parallax are easily 
avoided. 

In any series of measurements of the same physical quantity, 
we find that the results differ slightly one from another owing to 
imperfections in the instruments, or errors in making observa- 
tions. Errors of observation are likely to be positive as often 
as negative, and, if a sufficient number of readings are taken, may 
in the long run, be considered as having little influence upon the 
result. The greater the number of individual observations, the 
less likely will the mean of the individual observations deviate 
very far from the correct value. The conditions, and degree 
of accuracy desired, will in each case determine the number of 
readings to be taken. 



CHAPTER XXIII 
mSTRITMENT TRANSFORMERS 

324. Defimtioiis. — Instrument transformers are transformers 
specially designed to be used in connection with alternating-cur- 
rent meters. They are of two kinds: current, and voltage or 
potential transformers, sometimes designated as series and shunt 
transformers, respectively. The first designation is based on 
the quantity transformed, and the second upon the manner of 
the transformer's connection to the circuit. The names current 
and voltage transformers are preferable and will be used in the 
following discussion. 

326. Reasons for Use. — ^There are two main reasons for using 
transformers m connection with alternating-current instru- 
ments. The first has already been pointed out, namely, that it 
is impractical to construct meters of sufficient capacity to 
measure directly very large currents or pressures. Another 
important reason is that their use makes it possible to measure 
high voltages by means of instnunents which can be properly 
insulated without difficulty and great expense. 

326. General Theory. — ^An extended and complete theory of 
instrument transformers is beyond the scope of this text. Only 
so much is given as will give the reader some imderstanding of 
the influence of the constants of the transformer upon the read- 
ings of the instruments connected to it, and the errors resulting 
from the interactions of the transformer and instrument constants. 
In its simplest form the instrument transformer consists of an 
iron core upon which are wound two distinct or separate coils, as 
shown in Fig. 303. In this respect it is exactly like the ordinary 
power transformer, but as it is used with precision instruments, 
it is designed and constructed with more care and refinement. 

327. Current Transformer. — From a purely mechanical view- 
point, there is little difference between the current transformer 
and the common power transformer; nevertheless, electrically 
they have somewhat different characteristics. In the ordinary 
power transformer the primary current changes with, and de- 
pends upon the secondary current. In the current transformer, 
however, the effect of the secondary current upon the primary 

385 



386 



ELECTRICAL METERS 



current is negligible. The primary or main current is determined 
by the constants of the load circuit, and within practical limits 
is entirely independent of the current in the secondary circuit. 

The function of the current transformer is to supply current 
to a secondary circuit of constant relative value and having con- 
stant phase relation with respect to the current in the primary. 
There are thus two quantities upon the constancy of which 
depends the accuracy of meters connected to the secondary 
circuit: namely, the ratio of the primary to the secondary cur- 
rent, and the phase difference between them. 




Hi 




Fia. 303. 

The readings of ammeters and voltmeters are affected only by 
variations in the ratio of transformation; the indications of power- 
factor meters and synchroscopes are affected only by variations 
in the phase relation; but power and energy meters are affected 
by changes in both the ratio of transformation and in the phase 
angle. 

The ratio of transformation, and phase angle depend upon cer- 
tain constants of the transformer, constants of the piimary or 
load circuit, and constants of the secondary or meter circuit. 
These constants are designated in Fig. 303 as follows: 

R, X = resistance and reactance of load circuit respectively, 
ri, Xi = resistance and reactance of primary winding of 

transformer. 
r2, X2 = resistance and reactance of secondary winding of 
transformer, 
r, x = resistance and reactance of meter circuit. 
The influence of these quantities upon the ratio of trans- 
formation and phase angle will be more readily understood from 



INSTRUMENT TRANSFORMERS 



387 



a consideration of Fig. 304 in which /i and I2 are drawn in length 
proportional to the ampere-turns in the primary and secondary 
circuit. No attempt is made to show actual values, hence the 
vector diagram is merely illustrative. 

Let E, the pressure across the load circuit, be taken as the 
reference vector. Then /i, the primary current, will lag behind 




Fig. 304. 

E by an angle By where cos ^ is the power-factor of the load. This 
primary current sets up a magnetomotive force and magnetic 
flux in phase with it. This flux is nearly neutralized by the 
secondary current /2. Some flux must nevertheless be developed 
in order to induce an electromotive force in the secondary cir- 
cuit of suflScient magnitude to force the secondary current through 
it. This flux as well as the current to which it is due is the re- 
sultant of 7i and I2. Let this flux be represented by $ and the 
exciting current by /«. The fluctuating flux $ will induce ah 
electromotive force in both the primary and secondary circuits. 
These two electromotive forces will be in phase and will lag 90** 
behind $. The induced secondary voltage is represented by 
jB2. The applied electromotive force, which neutralizes the in- 
duced electromotive force in the primary is represented by Ei, 
opposite in phase with reference to E2. The terminal secondary 
pressure of the transformer is the vector difference between Et 
and the impedance drop in the secondary circuit. This terminal 

pressure is represented by E2. In a well-designed current trans- 
99 



388 ELECTRICAL METERS 

former Et^ is practically iti phase with Et', that ia, the reactance 
of the secondary of the transformer is inappreciable. The 
secondary current 1% will 1^ behind £«' by an angle a which 13 

determined by tan a = -' 

If the transformer has an appreciable core loss, the exciting 
current /, may be considered as the resultant of two components, 
/„ the magnetizing component, and /» the enet^ component. 







. 


















j: 




\j 
























^^ 


^~- 












5 100 




— 










— _, 
























— 



XrUlX. LOAD 

Fio. 305. 

The ratio of 7i to It and the angle are the quantities which 

affect the accuracy of a meter operated by the transformer. An 

examination of the diagram shows that these quantities vary 







\ 






















\ 


\ 
























-\ 


















^ 


^ 




■~~^ 






■ — 


— 





11 






^ 






































4 











w 





X PUU. UOAO sec AMP9. 

FiQ. 306. 
with the core loss of the transformer, the impedance of the 
secondary circuit including that of the meter circuit, and the 
ampere-turns for which the transformer is designed. 

Fig. 305 shows some typical ratio-current curves for current 
transformers, the ordinates being the ratios of the primary to the 
secondary current expressed in j)er cent of nominal ratio, while 
the abscissae are the secondary current expressed as a per cent 
of full load. 

In 1%. 306 are typical curves showing the variations in phase 



INSTRUMENT TRANSFORMERS 389 

angle with secondary load. It will be observed that both the 
ratio of transformation and phase angle approach a constant 
value near full load. 

328. Potential or Voltage Transformer. — ^The general principles 
of the potential transformer are the same as those of the current 
transformer. The principal difference between the two types of 
transformers is in the manner of their connection to the circuit. 
The primary current in the current transformer is determined 
by the condition of the main or load circuit, the primary electro- 
motive force being merely the impedance drop across the trans- 
former. In the voltage transformer, the primary electromotive 
force is determined by the conditions of the main circuit, while 
the primary current resulting is determined by the electromotive 
force applied and the impedance of the transformer. Thus the 
vector diagram of Fig. 304 may, with certain modifications, be 

applied to the potential transformer. If E\ is the applied elec- 

E\ 
tromotive force the ratio of transformation will be rv" which is 

.e.,. ^ „he. .. ana .....»...„ or .J: .e PH. 

mary .^d »co„dary winding; and th. phaae angle i. th, angle, 

7, between the vector E\ reversed and E\. These two quan- 
tities are also of importance in power and energy measurements. 

329. Influence of Transformer Constants in Power Measure- 
ments. — The influence of the transformer constants upon power 
measurements is the same as upon energy measurements and ac- 
cordingly only the former will be discussed. To understand the 
effect of the ratio of transformation and phase angle upon the 
reading of a wattmeter let us briefly consider Figs. 307 and 308, 
the first of which shows a wattmeter connected to a power 
circuit through transformers and the second is a vector diagram 
illustrating the phase relations between the quantities involved. 
Both the secondary current and voltage are shown as leading the 
corresponding quantities in the primary circuit. From this dia- 
gram it is evident that the correct reading of the wattmeter, 
assuming it to be direct reading, is 

Power = /i El cos 6 

= RER1I2E2 cos 6. 
But the actual reading of the wattmeter is 

Reading = R'eR'iI2E2 cos (^ - /3 + 7). 
If jS and 7 are lagging their signs must be reversed. 



390 



ELECTRICAL METERS 



In the above expressions R'e and /?'/ are the actual ratios of 
transformations which to give the true power should be Rb and Rf. 
Due to the phase angles P and y and to inaccurate ratios of trans- 
formation, the per cent error is 

RBR1I2E2 cos d - R'gR'iIiEiCos (e-p+y) 



Per cent error =100 



= 100 



[1 -^-^ 
L R 



RBR1E2I2 cos e 

R'eR'i cos (^ - j8 + 7) 



f/2/ 



cos 



] 



Generator 



Current 
MMOOftOQ/i 




TbLood 



Tmnsftrnh r 




Wcfttmetigr 



Fig. 307. 



Re kwr-s^^/ Z \ 





Fig. 308. 

If the ratios of transformation are correct, that is if R'e = Re 
and 72'/ = Ri, the resulting error is due to phase angle alone. 

330. Variation of Error with Power-factor. — The per cent error 
due to the phase angle of the transformer increases rapidly as 
the power-factor of the main load decreases. 
This may be shown as follows: 
Let X = per cent error. 

cos (e — p + y) 



Then a; = 100 - lOOkekj 



cos $ 



INSTRUMENT TRANSFORMERS 391 

and the rate of change of x with respeot-to 6 is 

dx ^^^ , , [- s in (e — P+y) cos d + cos (d — P+y) sin 

cos2 6 
sin f^ - (^ - /3 + 7)] 



- = - 100 A fc r - Sin (g - j3+7) cos g + cos (g ~ j3+ 7) sin g l 

5^ ^ ^ L cos^ e J 



= lOOkski 



= lOOkeki 



cos2 ^ 
sin (/3 ~ 7) 

C0S2 ^ 



5-c 
With a fixed fi and 7 the value of tt evidently increases rapidly 

ou 

with a decrease in cos 6, or with an increase in 6. To a reader 

unacquainted with the calculus, a numerical example may be 

more intelligible. 

EXAMPLE 

Given /3 — 7 = 3°. Calculate the per cent error in the wattmeter read- 
ing at power-factors of 0.1, 0.5 and 0.9. 

Solution, — 

Assume A^K^/ = 1. 
When cos ^ = 0.10, d = 84** 16'. 
When cos B = 0.50, d = 60**. 
When cos B = 0.90, d = 25° 50'. 

Then per cent, error = 100 

*^ cos 6 

100 cos (84° 15^ - 3°) 

"" ^"" 0.1 

= 52.12 per cent when cos e = 0.1. 

Likewise when the power-factor is 0.5 the per cent error is found to be 8.9 per 
cent and when the power-factor is 0*9, the error is only 2.4 per cent; that is, 
in so far as the error depends upon phase angle it increases with a decrease 
in the power-factor. 

331. Variation of Error with Phase Angle. — Assuming the 
power-factor of the load to remain constant, it is of interest to 
determine the variation in the per cent error with variations in 
phase angle of the transformers. Let jS — 7 = 0, and represent 
the per cent error by y, then 

^ cos d 

and 

by ^ 100 sin {e-(t>) 
8<l> cos d 

which shows that the rate of change in the per cent error due to 



392 ELECTRICAL METERS 

changes in is not constant, but depends both upon d and ^. 
When ^ = 0, or nearly zero, we may write without appreciable 
error, 

77 = 100 sin 0. 

As <^ is small in well-designed transformers, -^ varies as sin ^. 

For changes of from to 4^, sin ^ changes from to 0.07, 
or within these limits the graph between y and ^ is practically a 

straight line. When $ is near ^ the expression for — becomes 

Z 6fp 

by 100 cos </> . X 1 

5^ ^ "^T approximately, 

and again for changes in 4> from to 4° the change in -r: is only 

about 0.004, hence at low power-factors the graph between y 
and 4> deviates less from a straight line than at high power-factors. 

If then a chart is prepared on which are drawn lines showing 
the relation between per cent error and phase angle, this chart 
may be used to determine the per cent error of any other power- 
factor and phase angle. Such a chart is shown in Fig. 309. In 
the foregoing discussion = /3 — 7. If only a current trans- 
former is used, the same principles still apply as will be evident 
by letting 7 = 0. 

SS2. Testing Instrument Transfonners. — Many different meth- 
ods have been devised for measuring the phase angle and ratio 
of transformation of instrument transformers. Some of the 
methods are very elaborate and hardly suitable for commercial 
practice. Only two of the more simple methods will be described 
in this text. 

333. Watt-hour Meter and Standard Transformer Method.' — 
The fundamental principle of this method consists in comparing 
the effect of the phase angle and ratio of the transformer on the 
registration of a watt-hour meter with the like effect of the 
known constants of another transformer. The necessary appara- 
tus consists of two identical induction watt-hour meters, a trans- 
former, whose constants are known, of the same range as the 
transformer to be tested, an auxiliary load circuit, and two 
double-pole double-throw switches. A diagram of connections for 

^ Db. p. Q. Agnbw, BttUetin Bureau of Standards, voL 11, p. 347. 



INSTRUMENT TBRNSFOBMERS 393 

testing a potential transformer is shown in Fig. 310. The two 
current coils of the watt-hour meters are connected in series and 
the voltage coils are connected through the two switches to the 
secondaries of the transformers whose primaries are connected 
across a voltage supply circuit. 



" 








/ 














/ 












/ 












,/ 


























/ 












^ 






.,/ 






,/ 








" 










f/ 






/ 






/- 








// 






1 




'1 






/ 








/ 




i/ 




^ 


'/ 






/ 


















•f/ 






,y 




7 
















P 




^/ 






^,. 




1 




/ 




/ 




.•^ 






y_ 




1 








/ 




1 




/ 




y 


— 


/ 










/ 




-^ 




*r 


/ 




/ 






/ 


/ 




/ 




^y 








/ 




/ 


/ 


/ 


/ 


1 






f,* 


/- 






, 


. 




/ 


/ 




/- 


r 


f 


r 






1 


/ 


/ 


/ 


/ 




1S1 


,«» 




< 






/ 


/ 


^ 


X 


?2! 


i*s-i- 




■^ 


"- 




\///^. 


^y 




^ 










3 


_^ 




r 




- 


- 






g£ 










U 







PluM* Angla 
Fia. 300. 
The connections for testing current transformers are very 
similar as is shown in Fig, 311. 

334. Test for Ratio of Transformation, Watt-hour Meter 
Method. — The test for the ratio of transformation consists in first 
connecting the voltage coil of meter A to A\, and of meter fi to B% 



394 



ELECTRICAL METERS 



and carefully noting the number of rotations of the meter disks in 
a definite time interval. The connections are then shifted from 
A 1 to A 2 and from B2 to Bi and again the number of rotations 
in a given time is observed. From the known constants of the 
standard transformer, the load circuit, and the number of rota- 



1 




1 0OOOOQ_, 






.000000. 
















TRANS i 


^ 


-* - < 


TRAIMM. 






At 




AM 








O 

Bi 


• 


o 

BM 
















• 




sQfiQtU 
00 


*■■■■ 


UflJUL 

00 


] 


MX. CURRENT SUPPiy ^'^^^'^ MBTCR B 00^ 



Fia. 310. 

tions of the watt-hour meters the constants of the transformer 
under. test are determined. Let transformer 1 be the standard 
transformer, and transformer 2 be the one whose constants are 
to be determined. Also: 



wmrn — 

TRANS J ' — I 



TT^nnnnr 




7RAN3Z 








^ ^RAfl^BRB, 



AUX 
YOLTABB 
BUPPLf 

Fia. 311. 



let 72 1 and R^ 

ai and a2 

Ua and n'ji 



ratio of transformers 1 and 2 respectively, 
phase angles of transformers, 
number of rotations of meter A when con- 
nected to Ai and A% respectively, 



INSTRUMENT TRANSFORMERS 395 

no and n'a = the number of rotations of meter B when 

connected to Bi and B2 respectively, 
Pa and pa = percentage of accuracy of meters A and 5, 
k = energy constant of the watt-hour meters. 

Then in tia rotations, meter A will register kn^ watt-hr. The 
actual energy that has passed is lEi cos (6 + ai) when $ is the 
power-factor of the load. 

Hence kriA = PaIEi cos {6 + ai) 

and 

Pa cos (^ + ai) 

But RJEi cos ^ is the power in terms of the primary pressure, 
and current in auxiliary circuit; multiplying both sides of the 
above equation by Ri cos 6 we get, 

riARik cos 6 



RJEi cos e = 



Pa cos {e + ai) 



In exactly the same way we have 

— - — 77r~r — \ for the actual power in terms of the constants 
Pa cos {d + a2) ^ 

of meter A and transformer 2. 
The corresponding expressions for meter B are 

Rinak cos 6 , R^n'sk cos 

and 



Pb cos {B + ai) Pb cos (^+a2) 

As each of these expressions is the actual power, they must be 
equal; hence equating simultaneous readings, we have, 

riARik cos 6 v/BR^k cos B 

Pa cos ifi + ai) "" Pb COS {6 + a2) 
and 

n'ARJk cos g riBR i k cos ^ 

Pa cos (^ + ^2) "" 7>ir cos {6 + ai) 

Dividing the equations term by term we get, 

Ua Ri cos {0 + a^) _ n^ B2COS {B + qi) 
n'x -B2 cos {6 + ai) "" Ub R\ cos (^ + a^) 
Whence 

/22^ WAn/r cos^ {6 + "2) 



/?i* n'xn'fi cos2 {e + ai) 
and 



R^ = fiiA/ ^/'*^? approximately, 



396 ELECTRICAL METERS 

for "Z~(n~T — \ is practically unity at unity power-factor, that 

is when ^ = 0. n^, nsj ti'a and n's are the numbers of rotations 
of the watt-hour meters at unity power-factor. 

Since p^, p^, and k do not appear in the result, the ratio is 
independent of these quantities, and the accuracy of the method 
can be increased by increasing the speed of the watt-hour meters. 
This can be done by shunting the retarding magnets. 

336. Test for Phase Angle, Watt-hour Meter Method.— It has 
already been shown that the effect of phase angle upon the ac- 
curacy of meter readings is much greater at low power-factors 
than at high power-factors. At high power-factors the influence 
of the ratio with reference to accuracy predominates. Upon 
this fact is based the method of determining the phase angle. 
If the readings of the watt-hour meters are taken as before, but 
at low power-factors we have 

R^ __ r '^atib 1 COS' (e + a2) 
Ri^ "" Ln'^n'/rJ COS* (6 + ai) 
whence 

cos (^ + a2) = p- -— — cos(^ + ai). 

The subscript 6 means that n^, n^, u^a and u'b are readings at 
power-factor cos 6 and 6 is large. 

■^ = a/ / f where n^, n^, ti'a and n'a are the readings 

at unity power-factor. Since all the quantities in the right-hand 
member of the above expression are known, a2 can be calculated. 
In commenting upon this method. Dr. Agnew, its author, 
says: 

''It is important that the ratio and the phase angle of the standard 
transformer, whether of the current or voltage type, be determined 
under actual working conditions of load, including the meter. Multiple 
range transformers are very convenient as standards and good trans- 
formers have very accurately the same constants for the different 
series-parallel arrangement of coils. If the no-load ratio of a voltage 
transformer is required, it may be obtained very closely by adding a 
second or duplicate meter as load, and then extrapolating to the no- 
load condition. 

While the present method has neither the high precision nor ele- 
gance of the null laboratory methods, it has ample accuracy for com- 



INSTRUMENT TRANSFORMERS 397 

mercial requirements, it is independent of ordinary line fluctuations, 
and no specialized apparatus is required." 

The equation 

R^ _ nAiiB cos^ (^ + «2) 
Ri^ "" nAtiB cos2 [0 + ^^) 

can be transformed so that instead of calculating a2 by trigo- 
nometry, it may be obtained from the chart, Rg. 309. To do 
this we must find the per cent error due to phase angle. Trans- 
forming the above equation we have 

cos (6 + 02) __ R2 y/n^nB 

cos {B + a^ ■" fii y/ UaUb 

and 



(cos B + a2) _ _ R2 y/uAUB __ 
(cos ^ + ai) "" Ri y/'W^ 

and per cent error = 

ioo pQs«? + a2) . 1] ^ 100 fe:^^S - ll 

Lcos(^+ai) J L^i V nxUB J 

Let ^ + ai = 

Then 100 V"^ ^^ + ^"^ ~ "^^^ - ll = 100 [^l^^W _ 1 

If a three-phase circuit is used, and the auxihary circuit be 
taken from one phase and the pressure from another phase, 
cos <^ becomes the power factor under which the watt-hour 
meters operate when connected to the standard transformer. 
a2 — ai is the difference in power-factor under which the 
meters operate when connected to transformer 2. The left 
hand member of the above expression is the per cent error due 
to this difference in phase at a power-factor cos 0. The right 
hand member contains known quantities only and can thus 
be evaluated. R2 and R\ are the ratios of transformation at 
the particular load, n^, n^, n^', Ub are the rotations of the 
meters at power-factor cos B, Substituting and reducing we 
get the per cent error by the aid of which a2 — ai can be read 
off the chart. For example, if cos is .5 and the per cent error 
is 8, we find that where the horizontal line corresponding to 8 
per cent error crosses the 50 per cent power-factor corresponds 



398 ELECTRICAL METERS 

to a phase angle of 2^ 40'. This is aj — ai. As ai is known then 
a2 is at once obtained. 

336. Ratio hy Wattmeter and Standard Transformer Method* 
— ^A practical method of determining the ratio of potential trans- 
formers consists in connecting the secondary of the transformer, 
whose ratio is known, in opposition to the secondary of the trans- 
former whose ratio is desired, while the primary circuits are con- 
nected in parallel, and measuring the difference in the seccmdary 
voltages as indicated in Fig. 312. If the standard and trans- 
former under test have the same nominal ratio, the difference 
between the secondary voltages will be small, hence to measure 
this difference its effect must be enhanced. This is accomplished 
by sending a current from an auxiliary source through the current 
coil of a low-range wattmeter while the voltage coil is energized 
by the difference in the secondary voltages of the transformers. 
The desired ratio of transformation may then be calculated 
from the reading of the wattmeter, the auxiliary current, primary 
voltage and the ratio of the standard transformer, thus: 

let E = primary voltage, 
/ = auxiliary current, 
Ri = ratio of standard, 
Ri = ratio of transformer imder test, 
ai = phase angle of standard transformer, 
a2 = pha^ angle of transformer under test, . 
6 = phase difference between current and pres- 
sure in wattmeter circuit. 

Since ai and a2 are very small, and Ri is nearly equal to Rt, B 
will be approximately zero when the auxiliary circuit is non- 
inductive and the connections are as indicated in Fig. 312. The 
wattmeter reading is then, with close approximation, 

\R2 Ry 

whence 

tt2 = 



RiW + IE 

If the secondary voltages of the two transformers are equal, 

W = 
and 

R2 = Ri' 



INSTRUMENT TRANSFORMERS 



399 



To determine whether RiW is positive or negative, that is whether 
Rt is less or greater than 72 1, it is merely necessary to connect a 
non-inductive load, L, to the secondary of the transformer under 
test. The effect of such a load is to increase the ratio of trans- 
formation or decrease the secondary voltage. If the deflection 




Fia. 312. 

of the wattmeter is up scale when there is no load on the secondary, 
and if the addition of such a load increases the deflection, then at 
no load 7?2 is greater than 7?i and vice versa, 

337. Phase Angle by Wattmeter Method. — To determine the 
phase angle of a potential transformer by means of a wattmeter 




-^c 



Fia. 313. 

and standard transformer the two transformers are connected as 
in Fig. 312, but the auxiliary current is taken from the other 
phase of a two-phase circuit. Before proceeding with the test 
the ratio of the transformers should be made equal by loading, 



400 ELECTRICAL METERS 

with a non-inductive load, the transfonner with the lower ratio. 
The current taken by this load should be measured. If the load 
must be applied to the standard transformer, the phase angle of 
this transformer corresponding to the secondary current may 
then be obtained from curves plotted showing the relation be- 
tween phase angle and secondary current. 

Diagram Fig. 313 shows the phase relations, exaggerated, of 
the several quantities involved. From this diagram it is evident 
that the wattmeter reading is 

W = Ed cos e. 



But 



and 



E^ = 2Ei sin ""' "*' 



02+ Oi\ 
V = *> ' 



Hence 



W = 2EiI COS — 2 — s*^ I — 2 — / 
= EJ [sin a2 — sin ai] 



and 



^ W 

sm a2 = sm ai ± 



EJ 

As all the quantities on the right-hand side are known, as can be 
calculated. 

EXAMPLE 

Given ai = 20 minutes, Ei =110 volts, 
7=5 amp., and W= 1.5 watts. 
Calculate at. 
Solution. — 

W 
Sin at = sin ai ± tt-,* 

Ell 

ai = 20', sin ai = 0.00582. 

W = 1.5 watts. 

7 = 5 amp. 

^i = 110 volts. 



Hence 



Therefore 



W 1.5 

= 0.00272. 



EJ 5 X 110 



sin a, = 0.00582 ± 0.00272 
= 0.0031 or 0.00854 
and ai -> 11 minutes, or 29 minutes. 



INSTRUMENT TRANSFORMERS 401 

It remains to determine which value of a2 is* correct. To deter- 
mine this a non-inductive load is connected to the secondary of 
the transformer under test. If the deflection of the wattmeter is 
increased it shows that a2 is greater than aj and the second value 
must be taken. If the introduction of the non-inductive load 
reduces the wattmeter reading, a2 is less than aj. 

If a two-phase circuit is not available, a three-phase to two- 
phase arrangement of power transformers may be used, or the 
current for the series coil of the wattmeter may be taken from 
another phase of a three-phase circuit. The reading of the 
wattmeter under this condition will be 

W = 2EiI sm — 2 — ^^s (30 s — ) ' 

or 

W = 2EiI sm — 2 — ^^s (150° ^ ) * 

according to which of the two other phases the auxiliary circuit 
is connected. 

When reduced, both these expressions give the same numerical 
value, namely, 

W = jBi7[0.866 (sin a2 — sin aj) — 0.5 (cos a2 — cos ai)]. 

But as the difference between cos Qf2 and cos ai is negligible we 
have 

W = 0.866^1/ (sin a2 - sin ai) 

and 

I.IGTT , . 
sm at = p J — h sm ai 

as before.^ 

338. Potential Transformer Comparator Voltmeter. — To facili- 
tate rapid and accurate tests of potential transformers, the Weston 
Electrical Instrument Co., has recently placed on the market a 
voltmeter which takes the place of the wattmeter in the test de- 
scribed in the foregoing section. The instrument is a voltmeter 
of the electrodynamometer type, the field coils of which are 
separately excited from a source of constant voltage. The scale 
is therefore practically uniform which permits more accurate 
reading. As the operation of the instrument in testing is exactly 

' Other methods of testing instrument transformers can be found in 
^'Electrical Meterman's Handbook," Transactions of the American Instir 
iute of Electrical Engir^ersj and other technical publications. 



ELECTRICAL METERS 



the same as that of the wattmeter already described, no further 
discussion is necessary. 




The instrument has three ranges; 250-0-250, 25-025, and 
2.5-02.5 volta, with the zero in the middle. The field coil cir- 
cuit is provided with a plug switch so arranged that it may be 



INSTRUMENT TRANSFORMERS 403 

supplied from any voltage from 95 to 125 volts in steps of 5 
volts. The lowest range scale is divided into 0.05-volt divisions. 
In testing a transformer having a 110-volt secondary, each 
division, therefore, represents less than 0.05 of 1 per cent, diflfer- 
ence in the ratio. The complete instnmaent is shown in Fig. 314. 
Phase angle may also be determined by the aid of this voltmeter 
in exactly the same way as with the wattmeter described above. 
The instrument itself will not introduce any phase error as the 
two circuits are compensated for phase angle so that if both 
circuits are connected to the same source of electromotive force 
the currents in the two circuits will be exactly in phase. A 
diagram of connections is shown in Fig. 315. 



40 



INDEX 

Numbers refer to pages. 



Alternating currents, 47 

average value, 61 

definition, 47 

effective value, 54 

generation of, 47 

instantaneous value, 53 

law of fluctuation of current and 
pressure, 49 

maximum value, 54 

root — ^mean square value, 64 

sine wave of, 50 
A.C. and d.c. ammeters and volt- 
meters, 286 

a.c. indicate effective values, 
286 

calibration of a.c. ammeters, 288 

ventilation of, 288 
Alternation, 53 
Ammeter method of measuring 

power-factor, 333 

advantages of, 337 

on three-phase circuits, 335 

on two-phase circuits, 333 

theory of, 334 

use of polyphase-switch board, 
337 
Ammeters, 32 

ampere balance, 91 

Bristol recording, 149 

electrodynamometer tjrpe, 83, 
84 

General Electric inclined coil, 37 

General Electric recording, 164 

hot-wire, 105 

induction type, 75 

method of connecting to circuit, 
32 

movable coil, permanent mag- 
net type, 40 



Ammeters, movable core type, 36 

ranges of, 33 

recording, 149, 154 

shunts for, 33 

thermo-ammeter, 106 

uses of, 32 

Westinghouse induction type, 
76,77 

Westinghouse plunger type, 36 

Westinghouse recording, 169, 
162 

Weston soft iron type, 38 
Ammeters, testing of, 278 

calibration curve, 279 

calibration of a.c, 288 

comparison of, 278 

correction curves, 279, 280 

potentiometer method, 284, 
285 

standard resistance and volt- 
meter method, 282 
Ampere-hour meters, 241 

Bastian meter, 241 

electromagnetic type, 241 

Sangamo, 242 

test of, 324 

theory of, 241, 242 
Apparatus for instrument testing, 
264 

galvanometer, 265 

lamp bank, 276 

low voltage transformer, 314. 

phase-shifting transformer, 330 

portable sortage battery, 313 

potentiometers, 265, 270 

special load box, 312, 315 

standard cell, 264 
resistances, 274 

variable resistance, 275 

water rheostat, 277 
Arago's discovery, 65 



405 



406 



INDEX 



Armature, watt-hour meter, 183 
cylindrical, 183 
spherical, 183 
three coil, 183 
Attraction of induced and inducing 
currents, 28 
of permanent magnets, 28 
Average value of an alternating 
current, 54 



B 



Balance, Kelvin's ampere, 91 
Balance of meter elements, 190, 205 

test for, 323 
Bases of energy rates, 238 
Bastian ampere-hour meter, 245 
Bearings, watt-hour meter, 184 

ball, 185 

pivot, 185 
Bristol meters, 149 

ammeter, 149 

voltmeter, 150, 152, 153 

wattmeter, 151 
Brooks deflection potentiometer, 270 
Brushes, watt-hour meter, 181 



C 



Calibration curve for ammeters, 279 
Calibration of ammeters, 282 

of a.c. ammeters, 288 

of millivoltmeters, 284 

of shunts, 285 
Capacity, electrical, 21 

definition, 22 

effect of, 56 

farrad, 22 
Carbon plate rheostat, 275 
Cell, standard, 264 
Checking tests, 263 
Circuits, 61 

poljrphase, 61 
quarter-phase, 62 
three-phase, 62 

single-phase, 61 
Classes of meters, 26 

basis of classification, 26 



Coefficient, temperature coefficient 
of resistance, 16 
of inductance, 21 
negative temperature coeffi- 
cient, 16 
positive temperature coefficient, 
16 
Columbia induction watt-hour meter, 
205 
light load compensation, 216 
Combination of instruments, errors, 

374 
Comparison of d.c. voltmeters, 290 
Compensation, for frequency, 76 

for temperature effect, 81 
Compensating coil for wattmeter, 1 16 
Complaint tests, 309 
Commutator, watt-hour meter, 182 
Connection of polyphase meter, 352 
Constants, meter, 309 

determination of experiment- 
ally, 315 
effect of temperature on, 316 
Controlling forces, 28 

attraction of gravity, 28 
attraction of induced and in- 
ducing currents, 28 
attraction of permanent mag- 
nets, 28 
mechanical friction of rotating 

fan, 28 
resisting force of spring, 28 
torsion of filament, 28 
Contact errors, 373 
Correction, curve for ammeters, 279 
factor for wattmeters, 117 
for power loss in wattmeters, 
114 
Coulomb, 19 

Creeping of watt-hour meters, 180 
Current, 17 

electrical, 17 

practical electromagnet unit of 

current, 17 
unit current, 17 
water, 17 

current and voltage in three- 
phase circuits, 63 
Cycle, 53 



INDEX 



407 



D 



Damping, 42 

electromagnetic, 43 

mechanical, 42 

of electrostatic voltmeter, 101 

of hot-wire instruments, 105 

of induction ammeters, 82 

of recording meters, 161 
Defective performance of springs, 367 
Deflection type potentiometer, 270 

theory of, 269 
Delta connected circuits, 63, 228, 220 
Demand indicators, 247 

graphic, 259 

induction type, 248 

mechanical type, 254 

thermal type, 247 

time lag, 250 

use of, 252 
Difiference between d.c. and a.c. am- 
meters and voltmeters, 286 
Direct acting recording meters, 148 

Bristol, 149 

Esterline, 157 

General Electric, 154 

Pen, 156 
Duncan induction watt-hour meter, 
206 

E 

Earth's magnetic field, influence oft 

95,369 
Eddy currents in rotating disk, 65 
Effect of inductance, 55 
Effective value of alternating cur- 
rent, 54 
Electric current, 17 

analogy for, 17 

definition, 17 

unit of, 17 
Electrical quantities that are meas- 
urable, 26 
Electrical units, practical, 14 

ampere, 14, 24 

coulomb, 14, 24 

farad, 14, 25 

henry, 14, 25 

joule, 14, 24 



Electrical units, kilowatt, 24 

kilowatt-hour, 25 

ohm, 15, 24 

volt, 15, 24 

watt, 15, 24 
Electrodynamic instruments, 26, 83 
Electrodynamometer ammeter, 83 

relation between current and 
deflection, 84 

shunted, 85 
Electrodynamometer ammeter and 
voltmeter on a.c. circuits, 
287 

frequency enfors, 287 

limitations of, 287 

use for calibrating a.c. meters, 
288 
Electrodynamometer power-factor 
meter, 128 

coils of, 132 
Electrodynamometer type synchro- 
scope, 143 

Weston, 143 
Electrodynamometer type watt- 
hour meter, 170 

armature, 183 

bearings, 184 

brushes, 181 

Columbia, 174 

commutator, 182 

compensation for friction, 178 

creeping, 180 

Duncan, 174, 176 

General Electric, 173, 175 

jewels, 185 

on a.c. circuits, 187 

Westinghouse, 172 
Electrodynamometer voltmeter, 87 

advantages, 96 

ampere balance, 91 

construction, 89 

disadvantages, 96 

effect of inductance upon, 88 

General Electric, 90 

non-uniformity of scale, 91 

reading, 91 

Roller-Smith, 90 

Westinghouse, 90, 94 

Weston, 90 



408 



INDEX 



Electrbdynamometer wattmeter, 109 

compensation for power con- 
sumed in meter, 114 

General Electric, 113 

relation between torque and 
power, 110 

Roller-Smith, 90 

theory of, 110 

Westinghouse, 112 

Weston, 110, 113 

Weston polyphase, 114 

test of, 294 
Electrolytic ampere-hour meter, 242 
Electrolytic ampere-hour meter, 
242 

Bastian, 245 

Edison, 245 
Electrolytic conduction, 12 

electrochemical equivalents, 13 

electrolytes, 13 

Faraday's laws, 13 
Electromagnet, 8 

flux density in, 10 

iron cores of, 10 

magnetic field in, 9 
Electromagnetic ampere-hour meter, 
241 

Sangamo, 242 
Electromagnetic instruments, 26 

definition, 26 

induction type, 26 

movable coil permanent magnet 
type, 26, 40 

movable core type, 26, 36 
Electromotive force, 18 

analogy for, 18 

definition, 18 

how generated, 18 

of self induction, 22 

value of, 18 

volt, 18 
Electrostatic errors, 372 
Electrostatic meters, 27 

advantages, 102 
Electrostatic voltmeter, 97 

advantages, 102 

damping, 101 

Hartmann & Braun, 102 

insulation, 101 



Electrostatic voltmeter, multicellu. 
lar, 99 
theory of, 97 
Westinghouse, 99 
Energy, 1 

comparison between electrical 

and mechanical, 2 
conservation, 2 
conversion of potential into 

kinetic, 1 
definition, 1 
electrical, 2, 19 
kinetic, 1 
loss of, 23 
potential, 1 

similar expressions for electrical 
and mechanical, 3 
Errors, meter, 355 
Equation for ampere balance, 91 



Factor, correction for wattmeters, 

119 
Faraday's laws, 13 
Flux density in electromagnet, 10 
Force between parallel electric wires, 

11 
Force exerted upon an electric wire 
in a magnetic field, 10 

direction of force, 11 
Fort Wayne Electric Works, 204 

double lagging of meters, 219 

induction watt-hour meter, 204 

light load compensation, 213 

polyphase meter, 224 
Frequency, 53 

compensation for effect of, 76 

errors due to, 375 

influence of, 81,217 
Frequency-meters, 134 

Campbell, 136 

Hartmann & Braun, 136 

induction type, 138 

movable core type, 140 

polarized reeds, 138 

recording, 163 

resonance type, 135 

testing, 300 



INDEX 



409 



Friction of supports, 30 

compensation for on electro- 
dynamometer watt-hour 
meter, 178 
induction watt-hour meter, 213 
mercury watt-hour meters, 193, 

195 
resilient support, 31 
test for influence of, 350 
Full-load adjustment on induction 
watt-hour meter, 208 
mercury watt-hour meter, 195 



G 



Galvanometer, 265 
General Electric meters, 37 

ammeters, 37 

ampere demand indicator, 247 

light load compensation, 213 

pen, 156 

prepayment meter, 236 

recording meters, 154 

single-phase watt-hour meter, 
197 

voltmeters, 86 

watt-demand indicator, 249 

watt-hour meters, 173, 197 

wattmeters, 113 
Graphic meters, 148 
Gravity control, 29, 175 
Groups of measuring instruments, 26 

electrodynamic, 26 

electromagnetic, 26 

electrostatic, 26 

thermal, 27 



H 



Heat effect of electric current, 14 
Henry, 21 

Hot-wire instrument, 102 
ammeter, 105 
advantages, 106 
use of shunts with, 105 
damping, 105 
voltmeter, 102 
advantages, 106 
Hartmann & Braun, 103 



Hot-wire instruments influence, of 
stray field, 106 
influence of wave form, 106 
Roller-Smith, 104 
theory of, 102 



Induction, 19 

coeflicient of, 21 
effect of, 55, 88 
electromotive force of, 21 
henry, 21 

mutual induction, 21 
principle, 65 
self induction, 21 
Induction ammeters and voltmeters, 
75 
influence of frequency on, 81 
influence of temperature on, 81 
relation between current and 
torque, 79 
Induction type frequency meter, 138 
theory, 138 
Westinghouse, 138 
Induction type wattmeter, 120 
Induction type watt-hour meter, 
196 
balance of metering elements, 

205, 231 
double lagging, 219 
effect of over lagging, 213 
effect of under lagging, 213 
effect of power-factor, 232 
four-wire polyphase, 229 
full-load adjustment, 208 
improper connections of poly- 
phase meters, 233 
influence of frequency, 217 
interference of elements, 231 
lagging, 207, 212 
light load compensation, 213 
parts of General Electric meter, 

197 
phases, difference between vol- 
tage coil and series currents, 
200, 212 
polyphase meters, 224 
practical construction, 202 



410 



INDEX 



Induction type watt-hour meter, 
pressure element of Columbia 

meter, 204 
relation between torque and 

power, 210 
shifting magnetic field, 201 
single-phase meters on poly- 
phase circuits, 220 
. theory of operation, 198 
three-wire meters, 220 
Induction type wattmeters, 120 
influence of inductance on, 117 
lagging, 123 
operation of Westinghouse 

meter, 121 
relation between torque and 

power, 121 
scale, 125 
theory, 120 
Influence, of earth's magnetic field, 
95, 353 
of wave form on hot-wire me- 
ters, 104 
Inherent errors, 355 
Inquiry tests, 309 
Installation tests, 308 
Instantaneous value of alternating 

current, 53 
Instrument testing, 263 
Instrument transformers, 385 
current transformer, 385 
general theory, 385 
influence of transformer con- 
stants, 389 
phase angle, 386 
potential or voltage trans- 
former, 389 
ratio of transformer, 386 
reasons for use, 385 
variation of error with power- 
factor, 390 
variation of error with phase 
angle, 391 
Integrating meters, definition, 169 
ampere-hour, 241 
watt-hour, 169 



Jewels, 185 



Joule, 19 



K 



Kelvin balance, 91 

as ammeter, 91 

as voltmeter, 93 

disadvantages of, 96 

equation for, 94 

recording meters, 159 
Kilowatt-hour, 25 
Kmds of tests, 263, 310 

checking tests, 263 

complaint tests, 309 

inquiry tests, 309 

installation tests, 308 

periodic tests, 308 

repair tests, 309 

re-tests, 309 

shop tests, 308 

special tests, 309 

standardization tests, 263 



Lagging induction wattmeters, 123 
by secondary winding in mag- 

metic circuit, 124 
by shunting series coil, 124 
Lagging watt-hour meters, 187 
double-lagging, 219 
efifect of overlagging, 213 
effect of underlagging, 214 
induction meters, 213 
shunting series coil, 188 
Lamp bank resistance, 276 
Law of magnetic circuit, 10 
Leeds & Northrup potentiometer, 268 
Light load compensation on induc- 
tion watt-hour meters, 214 
flux shunting method, 216 
unbalanced shifting-field 
method, 214 
Loading watt-hour meters, 312 
consumer's load, 312 
low voltage transformer, 314, 
portable lamp bank, 312 
portable storage battery, 206 
special load box, 312 



INDEX 



411 



Loss in pressure coil, test for, 351 



M 



Magnetic circuit, law of, 1 

relation between flux, m.m.f., 
and reluctance, 10 
Magnetic field, 4 

air-gap, 6 

arrangement of magnetic lines 
between poles, 5 

conventional statement in re- 
gard to magnetic lines, 4 

force exerted upon a wire, 10 

magnetic flux, flux density, 4, 6 

method of representing field, 6 

methods of exploring, 3 

properties of, 4 

relation between tension and 
flux density in, 6 

revolving, 68 

rotating, 68 

seat of force of attraction and 
repulsion, 5 

shifting, 201 

strength of field, 6 
Magnetic field around a wire carry- 
ing a current, 6, 7 

direction of, 7 

field of circular coil, 7 

rule for determining direction, 7 

strength of magnetic field in 
. solenoid, 8 
Magnetic shielding, 30 
Magnetism, 3 

definition of magnetic bodies, 3 

permanent magnet, how to 
make, 3 
Magnetizing force, m.m.f. of sole- 
noid, 10 
Magnetomotive force, 4 
Magnets, watt-hour meter, 186 
Manganin, 16 

temperature coefficient, 16 
Maximum demand indicators, 247 

ampere demand indicator, 247 

graphic, 259 

mechanical type, 254 

time lag, 250 



Maximum demand indicators, watt 

demand indicator, 249 
Maximum value of alternating cur- 
rent, 54 
Measurable electrical quantities, 26 
Mechanical, errors, 364 

friction of rotating fan control, 
28 

type demand indicator, 254 
operation, 255 
Mercury watt-hour meter, 192 

compensation for friction, 196 

for d.c. circuits, 192 

full-load adjustment, 195 
Meter constants, 309 

table of, 318 
Meter errors, 355 

contact errors, 373 

defective performance of 
springs, 367 

due to balancing, 369 

due to combination of instru- 
ments, 374 

due to frequency and wave 
form, 375, 378 

due to thermo-electromotive 
forces, 373 

due to time and use, 369 

due to transformers, 375, 390 

effect of stray field, 369 

electrostatic effect, 372 

errors of use, 369 

inherent, 355 

mechanical errors, 364 

of observation, 384 

sources of, 355 

temperature, 359 
Meter testing, 263 

ammeters a.c., 288 

ammeters d.c, 278 

ampere-hour meter, 324 

apparatus for testing, 264 

frequency meters, 300 

general, 263 

kinds of tests, 263 

percentage of accuracy, 321 

polyphase power-factor meter, 
299 

recording meters, 301 



412 



INDEX 



Meter testing, single-phase power- 
factor meter, 298 
voltmeters d.c, 290 
watt-hour meters, 303 
wattmeters, dynamometer type, 
294 
Mil system, 15 

circular mil, 15 
mil, 15 

square mil, 15 
Movable-coil permanent magnet 

type, 40 
Movable core type ammeters and 

voltmeters, 36 
Movable core type frequency meter, 
140 
theory, 141 
Weston, 140 
Movable core type synchroscope, 145 
Lincoln type, 146 
Westinghouse, 145 
Multipliers for voltmeters, 35 



O 



Ohm, 14, 24 
Ohm> law, 22 



Percentage of accuracy, 320 
definition, 320 
test for, 321 
Percentage error due to inductance 

of wattmeter, 117, 382 
Period, definition, 53 
Periodic tests, 308 
Phase angle, 60 
difference, 57 
analogy for, 57 
Polyphase circuits, 61 
Polyphase, power-factor meter, 132 
switchboard, 337 
watt-hour meters, 224 
balance of elements, 231 
diagrams of connections, 226 
difference between four-wire 
and three-wire meters, 229 
effect of power-factor on, 232 
four-wire meters, 229 
improper connections, 233 



Polyphase, watt-hour meters, inter- 
ference of elements, 231, 346 
relation of torque to power on 

Y-connected loads, 227 
relation of torque to power on 

A-connected loads, 228 
testing, 299 
Potentiometers, 266 
deflection type, 270 
Leeds & Northrup, 268 
slide-wire type, 266 
theory of, 269 
Power, definition, 19 
horse power, 19 
in a.c. circuits, 58 
in d.c. circuits, 58 
loss, 24 
watt, 19 
Power-factor, definition, 60, 127 
determination of by ammeter, 
voltmeter, and wattmeter, 
127 
effect of on operation of poly- 
phase watt-hour meters, 232 
effect of on wattmeters, 117 
Power-factor meters, 128 

analytical proof of principles, 129 

electrodynamometer type, 128 

movable core type, 133 

recording, 163 

polyphase, 132 

principles, 129 

testing, polyphase, 299 . 

single-phase, 298 
Westinghouse, 133 
Weston, 131 
Power-factor, methods for obtaining, 
325 
ammeter or unbalanced load 

method, 333 
phase-shifting transformer meth- 
od, 326 
reactance coil method, 325 
two generator method, 329 
two resistance method, 328 
two transformer method, 326 
Power measuring instruments, 109 
Prepayment watt-hour meters, 236 
operation of, 237 
prepayment attachment, 235 



INDEX 



413 



Pressure drop in d.c. circuits, 23 
Proper connection of polyphase 

meter, 352 
Pull of solenoid on iron core, 39 



Q 



Quantity of electricity, 18 

Coulomb, 19 
Quarter-phase or two-phase circuit, 
61 



R 



Range of instruments, 33 

of ammeters and voltmeters, 33, 
34 

of wattmeters, 119 
Rates, bases for, 238 
Reactance method of changing 

power-factor, 325 
Reaction between shifting field and 

induced currents, 76 
Recording or graphic meters, 148 

Bristol ammeter, 149 

damping, 161^ 

definition, 148 

direct acting, 148 

disadvantages, 149, 166 

Esterline, 156 

General Electrjc, 154 

relay type, 158 

Sangamo, 164 

testing, 301 

Westinghouse, 159, 162 
Registering mechanism, 187 
Relation between current and torque 
of induction-ammeters, 79 
Relay type of recording meters, 158 

construction, 158 

damping, 161 

frequency meter, 162 

general principles, 158 

operation, 160 

power-factor meter, 163 

right line pen motion, 166 

sensibility, 162 

Westinghouse voltmeter, 159 
Reluctance, 10 



Repair tests, 309 
Resistance, 14 

analogy for resistance, 14 
the ohm, 15 

change with temperature, 16 

lamp bank, 276 

resistaiice of mil-foot, 16 

standard, 267 

variable, 275 

water, 277 
Resistance method of changing 

power-factor, 328 
Resisting force of springs, 28 
Re-tests, 309 
Revolvmg magnetic field, 68, 72 

how produced, 72 

speed of, 74 
Rheostat, 275 

carbon, 275 

water, 277 
Rollinson's load box, 314 
Rotating magnetic field, 68 

produced by equal component 
field, 68 

produced by unequal compo- 
nent fields, 70 
Rotating standard or test meter, 303^ 

Duncan, 304 

General Electric, 305 
Root-mean-square value, 54 



S 



Sangamo ampere-hour meter, 242 
Sangamo watt-hour meter, 191, 205 
Sangamo graphic meters, 164 
for d.c. circuits, 192 
friction compensation, 195 
full-load adjustment, 195 
Scale, lack of uniformity, 29 

on electrodynamometer amme- 
ters and voltmeters, 91, 92 
on electrodynamometer watt- 
meters, 112 
on gravity control meters, 29, 

30, 38 
on hot-wire meters, 103 
on induction ammeters, 82 
on induction wattmeters, 125 



414 



INDEX 



Scale, on permanent magnet mov- 
able coil meters, 46 
Sensibility of recording meters, 162 
Series transformer principle, 77 
Shifting magnetic field, 73, 201 
Shop tests, 308 
Shunted watt-hour meter, 176 
Shunts for ammeters, 33 
Sine wave of alternating current and 

pressure, 50 
Single-phase circuits, 61 
watt-hour meters, 196 
on polyphase circuits, 220 
test for quarter phasing, 338 
test on inductive load, 341 
test on non-inductive load, 

339 
test with standard test meter, 
43 
three-wire meters, 220 
Solenoid, 8 

magnetic field in, 8, 9 
magnetizing force, m.m.f. of, 10 
Special tests, 309 » 

Speed of revolving field, 74 
Standard cell, 264 
Standardization tests, 263 
Standard resistances, 267 
Stray magnetic field, test for, 351 
correction for, 370 
errors, 369 
Summary of electric and magnetic 

principles, 24 
Summation of power, 172 
Switchboard polyphase, 337 
Synchronizing, 142 
lamps, 142 
principles, 142 
Synchroscopes, 142 

electrodynamometer type, 143 
movable core type, 145 
speed of rotation, 147 
Westinghouse, 145 
Weston, 143 



Table of watt-hour meter constants, 
318 



Temperature, coefficient of resist- 
ance, 16 
errors due to, 356 
influence on induction amme- 
ters, 81 
on resistance, 16 
Testing instruments, 263 
ammeters a.c., 288 
ammeters d.c, 278 
calibration curve, 279, 281 
checking tests, 263 
frequency meters, 300 
kinds of tests, 263 
proper connection, 352 
polyphase power-factor meter, 

299 
recording meters, 301 
single-phase power-factor meter, 

298 
standardization tests, 263 
voltmeters a.c, 292 

d.c, 290 
watt-hour meters, 303 
wattmeter dynamometer type, 
294 
Tests of a.c watt-hour meters, 338 
diagram of testing board, 341 
influence of power-factor, 343 
single-phase meter on inductive 
load, 341 
on non-inductive load, 339 
test for quarter-phasing, 338 
testing polyphase meters, 345 
with standard test meter, 
343 
Thermal instruments, 28 
Thermo-ammeter, 106 
theory of, 106 
use in testing, 288 
Therm o-electromotive forces, 373 
Three-phase circuits, 62 

current and voltage in Y-con- 
nected, 63 
in A-connected, 64 
Three-wire d-c watt-hour meters, 
189 
on balanced load, 189 
on unbalanced load, 190 
test of, 322, 323 



INDEX 



415 



Three-wire single-phase watt-hour 
meters, 220 
on balanced load, 221 
on unbalanced load, 223 
voltage coil connections, 221, 224 
Time lag of demand indicators, 250 
curve for, 252 
theory of, 250 
Torque, 347 

balance, 347, 348, 349 
test for, 347 
Torque exerted by a magnetic field 
upon a rectangular coil, 44 
Torque of induction watt-hour 
meters, 210 
of four-wire polyphase meters, 

229 
of polyphase meters on Y-con- 

nected systems, 227 
on A-connected systems, 228 
Torsion of filament, 28 
Transformer method of varying 

power-factor, 326 
Transformer testing, 392 

potential transformer-compara- 
tor voltmeter, 401 
test for phase angle, 396, 399 
test for ratio of transformation, 

393, 398 
watt-hour meter method, 392 
wattmeter method, 39$ 
Two-phase or quarter-phase circuit, 

61 
Two-rate meters, 239 

U 

Unbalanced load method of varying 

power-factor, 333 
Use of ammeters, 32 

of constants in testing, 310 

of voltmeters, 32 



Vector diagram for series transfor- 
mer, 78, 387 

Ventilation of a.c. voltmeters, 288 

Voltmeters, 32 

calibration curve, 293 
comparison of d.c, 290 



Voltmeters, correction curves, 295 

electrodynamometer type, 87 

electrostatic, 97 

hot-wire, 102 

induction type, 75 

method of connecting to circuit, 
32 

movable coil permanent mag- 
net type, 40 
core type, 36 

multipliers, 34 

potentiometer method, 291 

range of, 34 

testing of a.c. meters, 292 

uses of, 32 

ventilation of a.c, 288 

Westinghouse induction type, 
76,79 
Voltmeters, recording, 151, 162 

Bristol, 151 

Esterline, 156 

General Electric, 156 

Westinghouse, 162 



W 



Water-rheostat, 277 
Watt, 19 

Watt-hour, 19, 109 
Watt-hour meters, 169 

armature, 183 

bearings, 184 

brushes, 181 

commutating type, 171 

commutator, 182 

compensation for friction, 178 

counter torque, 171 

creeping, 180 

electrodynamometer type, 170 
on a.c. currents, 186, 188 
with iron, 177 
without iron, 170 

friction compensation, 178 

induction type, 196 

jewels, 185 

lagging, 187, 209 

large current capacity, 174 

magnets, 186 

mercury type, 192 



416 



INDEX 



Watt-hour meters, polyphase, 224 
prepayment, 235 
registering mechanism, 186 
shunted, 176 
single-phase, 220 
summation of power, 172 
theory of, 169 
three-wire d.c, 189 
two-rate, 239 

Watt-hour meter constants, 310 
determination of, experiment- 
ally, 316 
dial constant, 309 
Duncan meter constant, 311 
effect of temperature, 316 
Fort Wayne meter constant, 311 
General Electric meter con- 
stant, 311 
table of meter constants, 318 
test constant, 309 
use of constants in testing, 310 
watt-hour constant, 310 
watt-minute constant, 310 
watt-second constant, 310 
Westinghouse meter constant, 
311 

Watt-hour meter testing, 303 
constants, 310 
influence of friction, 350 
influence of stray field, 350 
loss in pressure coil, 351 
methods of loading, 312 
rotating standard or test meter, 

303 
test of polyphase, 345 
test of single-phase, 339 

Wattmeters, 109 

compensation for power con- 
sumed in meter, 114 
correction curve, 297 
correction factor, 117, 382 
electrodynamometer type, 109, 

110 
induction type, 120, 121 
mercury type, 125 

Wattmeters, influence of inductance 
of voltage coil, 117 
method of connecting to circuit, 
110 



Wattmeters, range of, 119 

recording, 148 to 168 

scale, 125 

standard watt-dynamometer, 
297 

test of, 295 
Wave form, errors due to, 378 
Westinghouse 

ammeter, induction type, 76, 77 

ammeter, movable coil type, 41 

ammeter, plunger type, 36 

demand indicator, 252 

frequency meter, 138 

power-factor meter, 133 

recording meters, 145 

synchroscope, 145 

voltmeter electrodynamometer 
type, 90 

voltmeter induction type, 77 

watt-hour meter, electrodyna- 
mometer type, 172 

wattmeter electrodynamometer 
type, 112 
Westinghouse wattmeter, induction 

type, 121 
Westinghouse induction watt-hour 
meter, 203 

light-load compensation, 214 
Westinghouse recording meters, 162 

ammeters, 162 

frequency meters, 162 

voltmeters, 162 
Weston 

dynamometer voltmeter, 90 

frequency meter, 141, 142 

multipliers, 35 

power-factor meter, 131 

shunts, 35 

soft iron voltmeter, 38 

standard cell, 264 

synchroscope, 143 

wattmeter, 113 
Wire gauge, 16 
Wright demand indicator, 247 



Y-connected system, 63, 64, 227» 
229 



SFP 1 4 1920