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Full text of "Exercises in electrical engineering : for the use of second year students in universities and technical colleges"

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Class ' 


Exercises in 
Electrical Engineering 



T. MATHER, W H . SCH., F.R.S., M.I.E.E. 


G. W. O. HOWE, WH. SCH., M.Sc., M.I.E.E, 




[A I! rights reserved} 


A CONSIDERABLE time having elapsed since the publication of 
a collection of exercises in electrical engineering, the present 
moment seems opportune for carrying out a plan which has 
often been suggested, namely, the collection and publication 
of a selection of the questions set in recent years in the 
second-year exercise classes and examinations at the Central 
Technical College. The questions have been revised where 
necessary, and classified and graded for publication. It is 
hoped that they may be found useful in the second-year work 
of other colleges and institutions of university rank. 

To get a thorough grasp of the matter dealt with in 
lectures, it is absolutely essential that students work out for 
themselves numerous exercises on the subjects under consider- 
ation. If exercise classes are held, these should not be of the 
nature of examinations, but the students should be encouraged 
to discuss the questions with the lecturer and even with each 

From a perusal of the exercises it will be seen that their 
object is to cultivate familiarity with, and an exact working 
knowledge of, fundamental principles rather than a superficial 
knowledge of modern electrical practice. 

Answers to the numerical examples have been added at the 
end of the book so that the students may have a check on 
their work. It is desirable, of course, for the pupils' own 



benefit that a question should be worked out carefully before 
the answer given in the book is consulted. 

Our best thanks are due and are hereby tendered to Mr. 
F. B. Meade and Mr. J. C. Hutton, of the Central Technical 
College, for much assistance in copying and working out many 
of the questions. 


G. W. 0. HOWE. 

Sept., 1910. 


I. 1-38. 

















































INDUCTION ....... 13 

INSTRUMENTS . . . . . . .18 





INDUCTANCE ....... 38 




TRANSFORMERS . . . . . . . 47 











1. If a current of 1 ampere deposits 4~ grammes of 
silver in one hour, find the amount of silver deposited by a 
million coulombs. 

2. If a current of 5 amperes be taken from 110 volt mains, 
find the quantity of electricity passing per hour. 

3. If the agreement with an Electric Supply Company is 
to the effect that 4rf. shall be charged per Board of Trade 
unit, how can the amount of the bill be ascertained from 
readings of a coulomb meter ? 

$. What exactly is meant by a " quantity of electricity " ? 
Compare the industrial value of a quantity of electricity at 
the potential of the earth with a quantity of coal-gas at 
atmospheric pressure. 

5. Calculate the relation between the British Thermal 
Unit and the Board of Trade Unit. 

6. What will be the cost of heating a quart of water to 
the boiling-point in an electrical kettle, if the efficiency be 
80 per cent, and the cost of electrical energy 2d. per B.O.T. 


7. Calculate the cost of heating 10 Ibs. of water from 
60 F. to the boiling-point by means of electrical energy 
at one penny per unit. Assume that the apparatus has an 
efficiency of 90 per cent. (Mechanical equivalent of heat = 
778 foot-pounds per pound degree Fahrenheit.) 

8. The average for 1905 in one of the largest and most 
economical power stations in the world was 2'38 Ibs. of coal 
per K.W.-hour generated. The average calorific value of the 
coal was 12,368 B.Th.U. per Ib. Find the overall efficiency, 
and state approximately how the losses would be distributed 
between the boilers, engines, and dynamos. 

9. If a suction-gas plant on full load test burns f Ib. of 
anthracite (15,000 B.Th.U. per Ib.) per B.H.P.-hour, what 
is the overall efficiency of the producer and engine ? 

10. If the British Thermal Unit is equivalent to 778 ft. - 
Ibs., find the relation between the horse-power-hour and the 
calorie. What amount of coal must be burnt in a modern 
power station to supply 10 carbon filament lamps of 16 c.p. 
for four hours ? Assume what you consider suitable 

11. Describe any method of converting thermal energy 
directly into electrical energy. Why has the method 
described not been generally adopted on a large scale ? 

12. Calculate the relation between the B.O.T. unit, the 
horse-power-hour, and the foot-pound. 

13. If a reservoir 150 feet above the turbine house 
contains 100,000 tons of water, what is the value of the 
energy thus stored at one penny per Board of Trade unit ? 

1$. Find the cost of hoisting 100 tons 80 feet by means 
of an electric motor, if the price of energy is l^d. per unit. 
The combined efficiency of motor and gearing may be taken 
as 60 per cent. 

15. Find the brake horse-power of p a motor to lift 4 tons 


a height of 500 feet in 2 minutes, if the efficiency of the 
motor is 90 per cent, and that of the gear 80 per cent. 
What will the operation cost if the price of energy is 2d. per 
unit ? 

16. A centrifugal pump lifts 85 gallons of water per 
minute against a head of 35 feet. The motor takes a current 
of 10 amperes at 200 volts. Find the overall efficiency of 
the set. 

17. A crane is required to hoist 10 cwts. 50 feet in 15 
seconds. The efficiency of the hoisting gear, excluding the 
motor, is 70 per cent., while that of the motor alone is 85 per 
cent. Find (a) the B.H.P. of the motor, and (#) the cost of 
hoisting, per ton, if the price of energy is one penny per 

18. What must be the brake horse-power of a motor to 
hoist a ton 200 feet in one minute ? Find the cost of each 
operation if the price of electrical energy is one penny per 
unit. Assume suitable efficiencies. 

19. Find the cost of hoisting 4 tons 100 feet in 5 minutes 
by means of an electric crane, if energy cost one penny per 
kilowatt-hour. Efficiency of motor 90 per cent., efficiency of 
gear 80 per cent. 

20. G-ive definitions of a watt, a joule, and a Board of 
Trade unit. What instruments would you employ to measure 
(a) the power supplied to an electric circuit, (b) the energy 
supplied to an electric circuit ? 

21. If 4 yards 6 inches of No. 20 copper wire (diam. = 
0*036") has a resistance of ~ ohm, what is the resistance 
between the opposite faces of a cube of copper of 1 cm. 
edge ? 

22. Find the specific resistance of mercury from the 
practical definition of the ohm. 

23. Find the resistance between the brushes of a two-pole 


armature wound with 1000 feet of wire 2 mm. diameter. The 
specific resistance of warm copper may be taken as 2 x 10~ 6 
ohms per cm. cube. 

25. Three resistance coils are connected in parallel. 
A P.D. of 10 volts sends a total current of 5 amperes through 
them. If two of them are known to be 5 ohm coils, what is 
the resistance of the third ? 

25. A cylindrical coil has an inner diameter of 2 cms., an 
outer diameter of 3 cms., and a length of 4 cms. : find its 
resistance if a P.D. of 2 volts is necessary to produce 300 
ampere-turns. (Assume that one-half of the available space 
is occupied by copper, the remainder by insulation and air 
spaces, and that the specific resistance of copper is I'l microhms 
per cm. cube.) 

26. The shunt dynamo in Fig. 1 produces a P.D. of 105 
volts between the brushes. The main conductors have a 
resistance throughout of 5 ^ ohm per yard, and at ab, cd, and 
ef there are 10 sixteen candle-power lamps in parallel, each 


< - - 20 yds. x 20 yds - - Xr - -20 yds - -> 

FIG. 1. 

of which absorbs 60 watts when the P.D. between its 
terminals is 100 volts. Calculate what is the actual P.D. 
between the terminals of each of the three sets of lamps 

27. A dynamo having an E.M.F. of 250 volts and an 
armature resistance of 0'25 ohm is charging a battery of 
accumulators with a back E.M.F. of 220 volts and a resistance 
of 0-1 ohm through a regulating resistance of 0'25 ohm. Find 
the P.D. between the various points of the circuit, and also 


the power wasted and usefully employed in both dynamo and 


28. Two coils are connected in parallel and a P.D. of 
100 volts applied to the terminals. The total current 
taken is 15 amperes, and the power dissipated in one of 
the coils is 500 watts. What is the resistance of the other 

29. Compare the power, and also the energy, given to a 
circuit in the following cases : 

(a) A continuous current of 12 amperes flowing at a 

P.D. of 100 volts for Ij hours ; 
() A continuous current of 8 amperes flowing at a P.D. 

of 200 volts for f hour. 

30. Power is electrically transmitted by means of a given 
current generator of fixed E.M.F. and resistance, through a 
pair of given conductors to a coil of wire used for warming 
water. Calculate (1) what should be the resistance of this 
coil so that the water may be heated most rapidly ; and (2) 
what should be the resistance of the coil so that f of the 
total energy developed by the generator may appear as heat 
in the water. 

31. The resistance of the field winding of a dynamo is 
50 ohms at 15 C. After running for several hours, the current 
in the field winding is found to be 2 amperes when the P.D. 
between its terminals is 114 volts. What is the average 
temperature throughout the winding ? 

32. A coil of copper wire having a resistance, when cold, 
of 50 ohms, is subjected to two distinct heating tests ; in the 
first test a constant P.D. of 100 volts is maintained across it, 
whereas in the second test the current is maintained constant 
at 2 amperes. Will the final temperatures differ ? if so, why ? 

33. A resistance is required to carry a certain current and 
to dissipate a certain amount of power without exceeding a 


specified temperature rise. If rnade of copper, 100 feet would 
be required with a diameter of ^". Find the length and 
diameter of German silver wire to answer the same purpose, 
if the conditions as to emissivity and cooling are the same 
in each case. The specific resistance of G.S. is 15 times 
that of copper. 


1. Two bar magnets are placed in line with their north 
poles facing each other at a distance of 10 cms. If the 
strength of each pole is 10 units, find the strength of the 
magnetic field at a point midway between them. 

2. Three bar magnets are arranged so that their north 
poles lie on the corners of an equilateral triangle of 6 inches 
side, while their south poles are so far away that they may 
be neglected. The strengths of the poles are 100, 200, and 
300 units respectively. Find the force acting on the pole of 
100 units. 

3. Define what is meant by the temporary magnetic induc- 
tion, the residual magnetic induction, and the coercive force 
of a piece of iron. Discuss the relative values of these three 
quantities for soft iron and hard steel. 

$. What is meant by magnetomotive force, and how is it 
related to electromotive force ? Write out the equation for 
the magnetic flux, which corresponds to Ohm's Law for the 
electric circuit. 

5. What analogies exist between a magnetic and an electric 
circuit ? How would you decide on the smallest cross -section 
to give to any part of the magnetic circuit ? Discuss the plan 
used in some of the early dynamos of making the electro- 
magnet very long compared with the diameter of the armature. 
If this be wrong, then why is a horse-shoe permanent magnet 
still made long compared with the dimensions of the armature ? 


6. What is meant by the strength of a magnetic field, the 
value of the magnetising force, and the magnitude of the 
induction in a piece of iron ? 

7. Explain exactly what you understand by the symbols 
B, H, and /x, and explain the relations between them. 

8. Show the analogy, and also the important differences, 
between the electric circuit aud the magnetic circuit. What 
is the electric equivalent of H ? 

9. Explain precisely what is meant by the magnetising 
force H. What is the analogous magnitude in the electric 

circuit ? 

10. The coil of a tangent galvanometer contains 10 turns 
and has a diameter of 20 cms. The current passing through 
it is 1 ampere. Find the strength of the magnetic field at a 
point on the axis of the coil, 10 cms. from the plane of the 

11. Deduce from first principles an expression for the 
strength of field at the centre of a long solenoid. 

12. A glass tube 1" external diameter and 1 yard long is 
wound uniformly from end to end with 900 turns of insulated 
copper wire, 0'9 mm. diameter bare and 1*0 mm. diameter 
over the insulation. Find the strength of the magnetic field 
inside the solenoid when a P.D. of two volts is applied to its 

13. A straight piece of wrought-iron wire 1 metre long 
and 1 mm. diameter is wound uniformly from end to end with 
1000 turns of wire. Find the strength of the poles when a 
current of 1 ampere is passed through the winding. (See Fig. 2.) 

1$. The following data apply to a lecture demonstration of 
the magnetometer method of testing the permeability of a 
specimen of iron wire. Length of solenoid and wire 1 metre, 
turns on solenoid 1400, diameter of iron wire 1-2 mm., distance 
from lower pole to needle 8 cms. (at right angles to meridian) 


the upper pole is vertically above the needle ; distance from 
mirror to scale, 17 feet ; deflection obtained with 2 amperes, 




10 20 30 40 50 60 70 80 90100110 120130140150 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 


80 inches ; horizontal component of the earth's field, 0'18. 
Find the permeability of the specimen. 

15. A glass tube 1" diameter is bent round to form a ring 
of 1 foot mean diameter. How many ampere-turns must be 
wound on the ring to produce a total flux of 1000 lines 
through the tube ? 

16. Find the ampere-turns re- 
quired to maintain a flux of 10,000 
lines round the wrought-iron ring 
(Fig. 3), the mean diameter of 
which is a^foot, and which is made 
up of three equal lengths of round 
bar of 1 cm., 2 cms. and 3 cms. dia- 
meter respectively. (See Fig. 2.) 

meter round iron. 

17. A ring with a mean diameter 
of 6 inches is made from \" dia- 
It is wound with 100 turns of insulated 


wire. Find the current necessary to produce a total flux in the 
ring of 5000 lines. The permeability p may be taken as 1000. 

18. An iron ring with a mean circumference of 100 cms. 
and a cross-section of 10 sq. cms. is wound with 400 turns of 
wire carrying a current of 2 amperes, and the flux is found to 
be 100,000 lines. Determine the permeability of the specimen 
of iron. 

19. How many ampere-turns are necessary to produce a 
flux density of 13,500 lines per sq. cm., in a soft iron ring 
15" mean diameter, made of round iron 1/5" diameter, if the 
permeability at this flux density be 900 ? 

20. An iron ring of 25 cms. mean diameter and 10 sq. 
cms. cross-sectional area has an air-gap of 1 mm. It is wound 
with 500 turns of wire carrying a current of 8 amperes. If 
the permeability be equal to 600, determine the magneto- 
motive force of the coil, the reluctance of the ring, and the 
flux density in the air gap. 

21. Given the following particulars of a direct current 
generator, find the ampere-turns which must be wound round 
the field to drive the required flux through the air-gap. 

Bipolar machine to give 200 volts at 2000 r.p.m. Length 
of armature, 32 cms. Length of single air-gap 1*8 cms. 
Portion of circumference of armature covered by pole- 
faces, 60 cms. Number of conductors round armature, 

22. An iron anchor ring of 6" mean diameter is made of 
round rod of 0*5" diameter,. and is wound with 250 turns of 
insulated wire. If it be sawn through across a diameter, find 
approximately the force required to pull the two semicircular 
halves apart when the coil is carrying a current of 1 ampere. 
The permeability of the iron for various values of the flux 
density per sq. cm. is as follows : 

B = 8000 ; 10,000 ; 12,000 
ft = 2580 ; 2270 ; 1540 

23. Calculate the ampere-turns required for the cast-steel 


magnet sketched in Fig. 4. The air-gap density is to be 
50,000 lines per sq. inch, and the coils are to be placed on the 
polar projections N. and S. The section of each polar 



















r 43: 

on A.B. 


FIG. 4. 


Lines pe 





jl ^^ 












10 15 20 

Ampere-turns per cm, 

FIG. 5. 


projection is 12 inches square. Leakage can be neglected. 
Show the direction of the current in the windings. (See Fig. 5.) 

2$. What materials are used in the various parts of the 



magnetic circuit of a good modern dynamo ? Give reasons for 
their adoption in each case. 

25. How would you find the permeability of a sample of 
steel for making dynamo or motor field castings ? Draw a curve 
showing approximately to scale the variation of permeability 
with induction which you would expect in a good sample. 

26. How would you determine the magnetic qualities of a 
specimen sheet of soft iron ? 

27. Explain how you would test a sample of sheet iron as 
to its suitability for armature construction. Indicate approxi- 
mately the results you would expect. 

28. An iron ring has a cross-section of 0*335 sq. cm. 
and a mean diameter of 10 cms. It is wound with a magnetis- 
ing winding of 320 turns and a secondary winding of 220 
turns. On reversing the current of 10 amperes the ballistic 
galvanometer gave a reading of 272 ; a Hibbert standard with 
10 turns and a flux of 25,200 lines gave a reading of 102. 
Find the permeability of the ring. 

29. Explain how you could 
determine the permeability of 
a bar of iron with the help of a 
spring balance. 

30. A horse-shoe permanent 
magnet is fixed in a stand, so 
that it can lift the keeper off 
the table. If the keeper is taken 
off and replaced on the table, 
the magnet will lift it again the 
moment it is released. This 
can be repeated indefinitely. 
Explain how it is that the 
magnet can do this work and 
yet remain unchanged. 

31. What is the approximate 
amount of energy stored in the 




> 6 






>v 1 J 


FIG. 6. 


magnetic field of a solenoid 1 foot long and 1" diameter, 
wound with 300 turns, and carrying a current of 5 amperes ? 

32. Prove the formula for the lifting power of an electro- 

33. Fig. 6 shows an electromagnet constructed throughout 
of wrought-iron bar of 2" diameter. If there are 50 turns 
on each limb, find the necessary current to support 2 cwts. 
(See Fig. 2 for B H curve.) 

35. A ring of G" mean diameter is made of y round 
wrought iron. If it be split across a diameter, find how many 
ampere-turns will be necessary to give it a lifting power of 
24 Ibs. 

Given B = 10,000 12,000 15,000 
p = 2500 1800 GOO 

35. (a) Calculate the ampere-turns necessary to produce 

a flux of a million lines 
through the magnetic circuit 
of the circular lifting magnet 
shown in section in Fig. 7. 
The cross-sectixm of iron 
throughout the magnetic 
path is 100 sq. cms., the 
mean length of the magnetic 
path is 40 cms. Assume an 

air gap of 2 mm. between the magnet and the armature. 

The quality of the iron is such that 

when B = 10,000 lines per sq. cm. /x = 2500 
B = 12,000 /* = 1800 
B = 15,000 A* = GOO 

(5) What weight will the above magnet support under 
these conditions ? 



1. A current of 400 amperes is carried by two bare copper 
wires in parallel. The wires have a diameter of ^", and are 
supported side by side, the distance between centres being J". 
Find the force on each wire per foot of length. 

2. If the connections between a dynamo and an electrolytic 
vat taking 1000 amperes consist of two parallel copper bars 
supported on insulators 6 inches apart, calculate the mechanical 
force between the conductors per foot. 

3. The moving coil of a galvanometer has 60 turns, a 
width of 2 cms. and a depth of 3 cms. It hangs in the plane 
of a magnetic field of 500 C.G.S. units. Find the turning 
moment acting upon the coil when it is carrying a current 
of 1 milliainpere. 

5. A 4-pole cylindrical armature 40 cms. diameter has 
944 wires on its periphery. The axial length is 24 cms. 
Two-thirds of all the wires are under the poles, and are so 
connected that they all exert torque in the same direction. 
If the strength of the field between the poles and armature is 
7000 units, find the torque exerted on the armature in inch-lbs. 
when each wire carries a current of 10 amperes. 

5. If the coil shown in Fig. 8 is free to move to the right 


. . . . . 

\\\\\\\\\\\ X \ 

FIG. 8. 


or to the left, consider whether it is in equilibrium or not. 
If it is, is the equilibrium stable or unstable ; if not, in which 
direction will it move ? 


6. A circle of wire is rotated in a uniform field about 
a diameter lying along a line of force. Describe exactly what 

7. A coil is moved past 
magnet poles in the direction 
indicated in Fig. 9. State the 
direction of the E.M.F. in- 
duced in the coil in various 

FlG> 9 - positions along its path. 

8. A coil is placed in a uniform magnetic field with its 
plane perpendicular to the lines of force. It is (#) moved 
vertically in its own plane, (#) moved in the direction of the 
field, (c) rotated about a vertical axis, (d) rotated about an 
axis parallel to the lines of force. 

In which case or cases is an E.M.F. induced, and why ? 

9. The north pole of a magnet is 
moved towards the open loop AB, as 
shown in Fig. 10. Which is at the higher 
potential, A or B ? 

The resistance of the loop AB is 1 
ohm, and the ends are joined to form a 
continuous ring. As the north pole is 
FIG. 10. moved towards it there is a momentary 

current of gV ampere. What is the P.D. at this moment 
between the joint AB and the opposite point C ? 

10. Two bar magnets and a rod of iron are placed as shown 
in the two Figs. 11 (a) and 11 (), and a short-circuited coil 


of wire is moved from right to left in each case. Indicate for 
each case the direction of the current induced in the coil when 

FIG. lla. 

FIG. 116.! 

it is at various points of its path, and mark the places, if any, 
where the current in the coil reverses. 

11. (a) A coil C is moved from a distance towards a magnet 
M, then onwards over the magnet the magnet 
being then inside the coil and finally is moved off 
to the left. At what point will the direction of the 
E.M.P. induced in the coil reverse ? (See Fig. 12a.) 


FIG. 12a. 



FIG. 126. 

Consider the same question when the coil is held 
horizontally and is moved under the magnet from 
right to left as shown in Fig. 12#. 


(c) If, in the first case, the coil be brought up nearly to 
the south pole, then turned through 180, i.e. reversed, 
and removed again to the right, trace out the various 
changes in the current observed on a galvanometer 
in series with the coil. 

12. What quantity of electricity will pass in a circuit of 
20 ohms resistance containing a horizontal coil of 100 turns 
with a mean area of 1000 sq. cms. if the coil be suddenly 
turned over in the earth's field ? Horizontal component of 
earth's magnetism = 0*18. Angle of dip = 67. 

13. A coil is in such a position that 1000 lines of force 
pass through it. It is then moved into such a position that 
no lines of force pass through it. If the coil has 100 turns 
and a resistance of 10 ohms, what quantity of electricity will 
flow round the coil if the time taken for the change of position 
is (a) 1 second, (&) 10 seconds, and (c) 100 seconds ? What 
conclusion can you draw from your answer ? 

15. C is a stationary coil of wire carrying a steady current, 
as shown by the arrow (Fig. 13), and D is a disc rotating about 
an axis which is also the axis of the coil. If there are sliding 

contacts at the axis and edge of 
the disc, will an induced current 
be sent through the galvanometer 
Gr, and, if so, in which direction ? 
If now the disc is kept at rest and 
the coil be rotated about its axis, 
sliding contacts being used to 
carry the current into and out of 
the rotating coil, consider care- 
FlG - 13 - fully whether there will be any 

difference in the induced current through the galvanometer 
Gr, from that obtained in the previous case. 

15. Find the change in magnetic density through a search 
coil with 10 turns, 5 sq. cms. area, 1 ohm resistance, which 
gives a deflection of 160 divisions on a ballistic galvanometer. 


Resistance of galvanometer and leads, 4 ohms. Sensibility 
of galvanometer, 1 division per microcoulomb. 

16. A circular coil of 100 turns of wire having a mean 
diameter of 30 cms. is rotated about a vertical diameter as an 
axis at a speed of 16 revolutions per second. Calculate the 
value of the instantaneous E.M.F. induced in the coil, (1) when 
it is at right-angles to, (2) when it is inclined at 30 to, 
(3) when it coincides with, the magnetic meridian. The 
horizontal component of the earth's magnetic field may be 
taken as 0*18. 

17. A coil of 20 turns with a mean area of 5 sq. cms. 
and 2 ohms resistance gives a throw of 100 divisions on a 
ballistic galvanometer on being turned through 180. The 
resistance of the galvanometer and leads is 4 ohms. The 
galvanometer gives a throw of 1 division per microcoulomb. 
What is the strength of the field in which the coil is placed ? 

18. A search coil 5 cms. in diameter is wound with No. 40 
wire, and is used with a field tester whose sensibility is 1 division 
per 10 microcoulombs and whose resistance is 20 ohms. Find 
the number of turns required on the search coil in order that 
the density per sq. cm. of the field in which the search coil 
is reversed may be ten times the reading. (2'25 feet of No. 40 
wire has a resistance of 1 ohm.) 

19. When a continuous P.D. of 150 volts was applied to 
the field circuit of the Bruce Peebles dynamo, the resistance 
of which is 30 ohms, the current rose to 60 per cent, of its 
maximum value in T25 seconds. If the bobbins had been 
wound with wire of half the diameter (in the same space) and 
a P.D. of 600 volts were applied, what time would be necessary 
for the current to rise to the same fraction of its ultimate 
value ? 

20. Indicate the general shape of the curve showing the 
growth of current following the application of a steady P.D. 
to an inductive circuit. What shape will the curve assume 



(1) If the resistance is very large compared with the 

inductance ? 

(2) If the inductance is very large compared with the 

resistance ? 

21. Explain exactly what happens when a copper disc is 
rotated between the poles of a magnet, as in the Thomson 
energy meter. 

22. Explain with the aid of sketches what happens when a 
large iron disc is rotated so as to cut though the narrow gap 
between the poles of a horseshoe magnet. 

23. Is there any objection to breaking the field circuit of 
a large shunt dynamo ? If so, why ? 

25. What precautions would you adopt when breaking a 
very inductive circuit ? Explain exactly why such precautions 
are necessary. 

25. Explain why the spark on breaking the circuit of an 
electromagnet is greater than that on breaking a non-inductive 
circuit carrying the same current. 

26. A circuit is made up of a battery, a solenoid, and a 
switch. On opening the switch, a flash is seen. Why is this ? 
Will there be any difference in the flash on breaking circuit 
if (a) a solid core of soft iron, (#) a core of soft iron wires, 
(c) a core of previously non-magnetised steel be placed in the 
solenoid ? 


1. Enumerate the various types of ammeters with which 
you are acquainted, and compare their relative advantages 
and disadvantages. Give a detailed description of any one 


2. Describe briefly, with sketches, the various types of 
instruments suitable for measuring alternating currents. 

3. A milli-ammeter reading up to 500 milli-amperes has 
a resistance of O'l ohm. How could this instrument be 
adapted to read (a) voltages up to 200, and (&) currents 
up to 20 amperes ? 

4. A moving coil instrument has a resistance of 100 ohms, 
and gives a full scale deflection with a P.D. of 3 volts. Explain 
how you could use the instrument for measuring (1) pressures 
up to 120 volts ; (2) currents up to 20 amperes. 

5. Describe the principle and construction of a moving 
coil ammeter and discuss its advantages and disadvantages as 
compared with an ammeter of the hot wire type. 

6. A wattmeter is employed to measure the power given to 
the apparatus A. Consider the errors that would be intro- 
duced by joining up the wattmeter as illustrated in Fig. 14 




s i 



FIG. 14. 

(1) and (2) respectively, and determine which way would give 
the least error. Think out a method of constructing a watt- 
meter so that it may be free from the errors introduced by 
either method (1) or (2). 

7. Describe the principle and construction of a wattmeter. 

8. Explain why a voltmeter should have as high a resist- 
ance as is practicable. A voltmeter reading from to 3 volts 
has a resistance of 300 ohms. How could this instrument be 
adapted to read from to 300 volts ? 


9. Show how to construct a C.O. voltmeter which, when 
connected to the mains in the generating station, will indicate 
the P.D. at the far end of a feeder. 

10. Describe with sketches the construction of an elec- 
trostatic voltmeter. An electrostatic voltmeter adapted for 
measuring the P.D. between two mains of about 2000 volts 
has one of its terminals connected with one main, while the 
other terminal is by accident left insulated. Consider whether 
the voltmeter will indicate any P.D. If so, of what value ? 

11. An electrostatic and an electromagnetic voltmeter are 
used to measure the P.D. between two direct current mains. 
Compare the effects on the readings of these two instruments 
of putting in a resistance between the instrument and the 

12. Illustrate with sketches some form of coulomb-meter 
and mention exactly under what conditions such an instrument 
can be used to measure the energy given to an electric circuit 
in a given time, and under what conditions it cannot. 

13. How does the construction of a quantity-meter differ 
from that of an energy-meter ? Under what circumstances 
can one be practically used instead of the other ? 

1$. What is a coulomb- or quantity-meter ? What are the 
principles used in the different types of coulomb-meters ? 

15. Explain how the Elihu Thomson energy-meter records 
B.O.T. units. 

16. If a supply-meter of the motor type has the armature 
and brake in the same magnetic field, consider how the rate 
will be altered by a weakening of the field. 

17. Define a coulomb, a kilowatt, and a Board of Trade 
unit. Describe with sketches three instruments such as are 
commercially employed for measuring electrical quantities in 
these three units respectively. 


18. Why is it desirable to know the maximum current 
taken during each quarter by each building that is supplied 
with electrical energy in order that the amount of the charge 
to be made may be estimated ? G-ive an example of this 
method of charging. 

19. Describe with sketches the construction of some form 
of maximum demand indicator, and consider whether a 
Thomson meter could be used both to measure the energy 
and the maximum demand if the permanent magnets instead 
of being fixed were arranged so as to be capable of motion. 

20. What will be the effect on the sensibility of a moving 
coil ballistic instrument if the permanent magnet grows weaker ? 
In some instruments a small piece of iron is fixed to the 
moving coil, and serves to counteract the first effect. How 
is this ? 

21. Prove that the swing of a moving-coil ballistic gal- 
vanometer is approximately proportional to the quantity of 
electricity passed through it. Is this true of the moving 
needle galvanometer ? If not, why not ? 


1. The iron ring of a bipolar Gramme armature has an 
external diameter of 12", internal diameter of 9", and an axial 
length of 12". It is wound with 1000 turns of 2 mm. 
copper wire. What is the approximate resistance between the 
brushes ? 

2. Compare the advantages and disadvantages of drum and 
ring windings for armatures. 

3. What happens if the armature of a dynamo is rotated in 
the wrong direction ? 


4. The armature of a certain series dynamo is normally 
rotated clockwise when looked at from the commutator end. 
What will happen if it be driven counter-clockwise without 
any other change being made ? 

5. Copy the accompanying diagram (Fig. 15). Can it 
represent a dynamo turning in a clockwise direction ? If so, 

FIG. 15. 

indicate the polarity and the directions of both armature and 
field currents. 

6. Make a sketch of a long-shunt compound-wound dynamo 
and show clearly the direction of the current in every part 
when the machine is running on load. 

7. Copy Fig. 16, which represents a compound- wound 
dynamo. Put in all the necessary connections and show the 
directions of the currents in the armature and field coils, 
the direction of rotation of the armature, the position of 


the brushes, the north and south poles of the field magnet, and 
the positive and negative terminals of the dynamo. 

8. "What is the exact function of a commutator ? Con- 
sider whether it is possible by using a commutator to generate 
a current always in the same direction in a coil of wire by 
moving it in a magnetic field. 

FIG. 16. 

9. Draw a diagram of a bipolar Gramme ring motor and 
show the polarity of the field magnets, the polarity of the 
brushes, the direction of the current in the armature and the 
direction of rotation. 

10. If we reverse the current through a series motor, do 
we thereby reverse the direction of rotation ? Give reasons. 

11. The current passing through a shunt motor is reversed. 
What effect will be produced on the direction of rotation of 
the motor, and why ? 

12. Show by means of sketches how to reverse the direction 


of rotation of a inagneto-motor, a series motor, and a shunt 
motor, respectively, from a distance. 

13. A machine has two windings on the armature, each 
winding being provided with a separate commutator and pair 
of brashes. One of the windings in combination with the 
field magnet is employed as a high P.D. motor to revolve the 
armature, while the other armature winding is used to generate 
a large current for lighting glow lamps. Make a sketch 
showing the direction of rotation of the armature, and the 
direction of the current in each armature winding, and con- 
sider what will be the demagnetizing action of the armature as 
compared with that in an ordinary dynamo or motor. 


1. One of the coils of a Gramme ring armature is dis- 
connected from the commutator but connected by flexible leads 
to a galvanometer. On reversing the field current the 
maximum galvanometer swing is obtained when the coil is 
halfway between two poles, whereas if the field is kept 
constant, and the armature turned suddenly through a small 
angle, the galvanometer swing is a minimum when the coil is 
in this position. Explain this. 

FIG. 17. 

2. A rectangle is rotated at uniform speed in a magnetic 
field as indicated in Fig. 17. How should a two-part com- 
mutator be attached to the ends of the rectangle, and how 
should the brushes be placed, to get the best direct E.M.F. 


produced at the brushes ? Give a curve connecting the value 
of the E.M.F. with the position of the rectangle. 

3. A Gramme ring armature contains 200 turns of wire 
and rotates at a speed of 1000 revolutions per minute. Its 
diameter is 2 feet and its axial length 1 foot. Each pole 
subtends an angle of 120 degrees. The flux density in the 
air-gap is 5000 lines per sq. cm. Find the P.D. between the 

4. A Gramme ring armature has a simple winding of Z 
turns, and rotates at n revolutions per minute. There are 2p 
poles, each carrying a flux of N lines. Find the P.D. between 
the brushes on open circuit. 

5. A bipolar drum armature has 1000 wires on its periphery 
and rotates at 500 revolutions per minute. Find the terminal 
P.D. if the flux entering the armature from the north pole is 
one million lines. 

6. The armature of a 2-pole 200 volt continuous current 
dynamo has 400 conductors on its periphery and makes 300 
revolutions per minute. Calculate the total flux entering the 
armature. If the number of turns of wire on each field bobbin 
is 1200, what is the average value of the E.M.F. induced in 
these coils if the magnetism dies away in ^ of a second ? 

7. A bipolar drum armature is built up of 400 core discs, 
each 0-025 inch thick, the discs being 7 inches external and 2 
inches internal diameter. There are 500 armature conductors 
and the machine is driven at 1000 revolutions per minute. 
What must be the flux density in the armature in order that 
the machine may generate 200 volts at no load ? 


1. Draw a diagram of a Gramme armature winding and 
describe the changes of E.M.F. and current in any one coil 
during a complete revolution. 


2. Discuss the reasons for shifting the brushes of a dynamo 
forward as the load increases. Why are carbon brushes 
employed ? 

3. Explain why sparking occurs at the brushes of a dynamo 
when they are not placed in the right position. 

$. What do you understand by armature reaction ? How 
does it affect the operation of dynamos and motors ? 

5. Explain with the aid of diagrams the effect of armature 
reaction in both dynamos and motors. 

6. When the load increases, will the armature of a dynamo 
with its brushes in the best position tend to strengthen or 
weaken the magnetic field ? Consider also the same question 
for a motor. 

7. Explain why the forward lead of the brushes of a 
dynamo is usually greater than that corresponding to the 
magnetic neutral axis. Should the backward lead of motor 
brushes be greater or less than that corresponding to the field 
distortion ? 

8. What kind of lead has to be given to the brushes of 
a O.C. motor ? What are the exact causes that necessitate 
this particular lead being given to the brushes ? 


1. Sketch and explain briefly the external characteristic 
curves of a separately excited, a series, a shunt, and a com- 
pound dynamo respectively. 

2. Given the curve connecting the P.D. and the external 
current for a shunt dynamo running at a particular speed, 
the E.M.F. of a battery of storage cells and their resistance, 
including that of the leads, show how to ascertain graphically 
the charging current which the dynamo, running at the given 
speed, will send through the cells. 


3. What is the characteristic curve of a dynamo ? Show 
how the characteristic curve of a series dynamo may be used 
to determine the current that the dynamo will send through 
a battery of accumulators having a given resistance and 

5. Compare the shunt and the series dynamo from the 
point of view of their suitability for charging accumulators. 

5. Can a compound-wound dynamo be safely used for 
charging cells ? Give full reasons for your answer. 

6. A series dynamo produces an E.M.F. of 5 volts on 
open circuit, but on reducing the external resistance the P.D. 
falls to zero. What is wrong, and how can the fault be 
rectified ? 

7. A series dynamo is run at a fixed speed, and the external 
resistance, which was originally very large, is gradually reduced. 
Draw a curve showing how the current varies with the external 
resistance. Consider also the same question with regard to a 
shunt dynamo. 

8. Having given the external characteristic of a series 
dynamo, draw a curve showing the variation of P.D. with 
external resistance. 

9. You are given the working drawings of a series dynamo 
and a description of the windings to be put on the armature 
and field magnets. Show exactly how to predetermine the 
E.M.F. for a given current and speed of rotation. 

10. If the curve connecting P.D. and current of a series 
dynamo is given for a certain speed, how would you construct 
the similar curve for another speed ? 

11. Distinguish between series, shunt, and compound 
dynamos. Show the general nature of the characteristic 
curves, and compare the relative advantages of each type. 

12. A shunt dynamo running at 1300 revolutions per 
minute is sending a current of 20 amperes through an outside 


circuit. The machine is stopped and then the speed is run 
up again to 1300 revs, per minute, when it is found that, 
even on opening the external circuit, the P.D. between the 
brushes remains quite small. Explain fully the cause of this. 

13. A dynamo is level-compounded at 1000 r.p.m. ; will 
it be level-compounded at 750 r.p.m., if the field rheostat 
remain unaltered? 

14. A series dynamo has a P.D. of 100 volts between its 
terminals when running at 400 r.p.m. and giving 2 kw. 
What will be the P.D. if the speed be raised to 700 r.p.m. 
and the output to 3 '8 kw. ? Total resistance of machine, 
1 ohm. 

15. Explain all the reasons for the decrease of the terminal 
P.D. of a shunt dynamo driven at constant speed as the 
current in the external circuit is increased. 

16. Draw curves with abscissae representing the external 
resistance, and ordinates representing the terminal P.D., in 
the case of (a) a series dynamo, (#) a shunt dynamo, (c) a 
compound dynamo. 

17. Two precisely similar series machines are coupled 
with leads having a known resistance. The current and P.D. 
curve of the machines at a certain speed is known. If one of 
the machines is driven as a generator at some other speed, 
show how to determine graphically the speed at which the 
other machine will be driven as a motor when a given current 
flows in the circuit. 

18. How is the E.M.F. and the P.D. of a series dynamo 
connected with the speed, if the current is kept constant ? 

19. A dynamo is required to give up to 20 k\v. at a 
constant P.D. of 200 volts, at a point J mile away. The 
cable used has a resistance of 0*24 ohm per 1000 yards single. 
Number of shunt field turns 2000. Find the number of 
compound coils required, neglecting their resistance. Fig. 18 



gives the results obtained from tests on the machine when 
separately excited. 

20. What is the exact function of the series coils in a 
compound-wound dynamo ? Criticise the statement that a 
compound-wound dynamo is a constant E.M.F. dynamo. 

21. Explain fully why a dynamo can be compounded to 


~ Q 

<3 2200 







= 190 

2 4 

Field Current 


25 50 75 

Main Current 

FIG. 18. 


produce a constant P.D., but cannot be compounded to 
produce a constant current. 

22. Prove that a series dynamo driven by a steam engine 
without a governor, but supplied with steam at a fixed pressure 
in the cylinder, must produce a constant current irrespective 
of the load. 

23. If the speed of an engine used to drive a dynamo 
charging accumulators slows down considerably, explain exactly 


what will happen, (a) if the dynamo be series wound, (b) if it 
be shunt wound. 

25. The belt driving a dynamo which is charging accumu- 
lators breaks. Explain exactly what happens (1) if the dynamo 
is shunt wound, (2) if it is series wound. 


1. The resistance of the armature and of the field winding 
of a shunt dynamo are respectively 0*15 and 30 ohms, while 
that of each of a set of 50 accumulators in series is 0*001 
ohm. If the E.M.F. developed by the dynamo be 130 volts 
and that of each cell 2*2 volts, calculate what current will be 
produced and what proportion of the energy developed by 
the dynamo will be used, (1) in charging the cells, (2) in 
heating the cells, (3) in heating the armature of the dynamo, 
(4) in heating the field winding. 

2. Trace the magnetic changes undergone by each particle 
of iron in a Gramme ring armature during one complete 
revolution of the armature. 

3. How will the iron losses in the armature of a dynamo 
vary with the speed and with the magnetic flux ? Give 

5. What methods are employed to reduce the losses in 
dynamos and motors due to (a) eddy currents, (&) hysteresis, 
(c) armature reaction, (d) armature copper loss, (e) windage ? 

5. What do you understand by the term "leakage 
coefficient of a dynamo " ? How would you determine it 
experimentally for any given machine ? 

6. The power given out by a shunt motor is always less 
than the mechanical power supplied to it. Enumerate the 


various losses and discuss the variation of each loss with 
variation of load on the motor. 

7. What tests would you make on a new dynamo or motor 
before putting it finally into operation ? Describe the con- 
struction of the instruments and the methods you would 
employ to carry out these tests. 

8. A 2000 volt E.M.F. 6'7 ampere constant current dynamo 
has a total resistance of 25 ohms. If the line consists of 8 
miles of No. 16 copper wire (resistance 7*7 ohms per 1000 
yards), calculate the combined efficiency of the dynamo and 
line, (a) at full load, (1) at 1000 volts E.M.F. 

9. How, and why, do the steady outputs of open, semi- 
enclosed, and enclosed motors of the same size vary ? How 
does intermittent running affect the rated output of a motor ? 

10. Show how to obtain the efficiency of a shunt motor 
quickly and approximately without a dynamometer. Point 
out the defects of the method and the errors likely to be 


1. Current is supplied to a motor of resistance m ohms 
through line wires of resistance I by a generator of resistance 
g with fixed E.M.F. of E volts. Determine at what speed 
the motor should run, (a) so that the total power given to 
the motor shall be a maximum, (#) so that the mechanical 
power developed by the motor shall be a maximum. 

2. Discuss the effect on a shunt motor supplied at constant 
P.D. of (a) increasing the load without altering the field 
current and (&) weakening the field current without altering 
the load. 

3. If the speed of the armature of a shunt motor be 
increased until the E.M.F. it generates exceeds the P.D. 


maintained between the terminals of the machine by the 
outside mains to which it is connected, explain how the 
current in the armature and in the field coils will be altered 

5. If constant P.D. be maintained between the terminals 
of a shunt motor, the speed varies to a small extent with the 
load. Show how this speed variation is affected by 

(a) the resistance of the armature, 
(&) the reaction of the armature. 

5. In order to keep the speed of a shunt motor exactly 
constant, it is necessary to weaken the field as the load is 
increased. Explain fully the reason for this. 

6. Why does the speed of a shunt motor usually decrease 
when resistance is cut out of its field circuit ? Under what 
conditions will it not do so ? 

7. A bipolar shunt motor has a flux of 5 millions lines 
per pole. It has 60 conductors on its armature. The 
armature resistance from brush to brush is 1 ohm. The 
applied P.D. is 100 volts. Calculate the current taken by 
the motor and the speed when loaded with a torque of 85 

8. A 200 volt shunt motor takes 3*6 amperes when running 
light. To pass 20 amperes through the armature at rest 
requires a P.D. of 6'6 volts. The field current is one ampere. 
Find the output and efficiency when the motor current is (a) 
20 amperes, (#) 40 amperes. 

9. When a shunt machine having its brushes connected 
with 100 volt mains is driven by an engine at 1000 r.p.m., 
its armature current falls to zero. If uncoupled from the 
engine, at what speed will the machine run as a motor when 
developing 10 H.P. if its armature resistance is 0'05 ohm ? 

10. A shunt dynamo has a capacity of 150 kw. at 500 


volts, and is driven at a speed of 200 r.p.m. The resistance 
of the armature is 0'05 ohm, and the resistance of the field 
windings is 200 ohms. If the same machine be run as a 
motor, calculate its speed when supplied with 150 kw. at 
500 volts. The armature reaction may be neglected. 

11. Explain what happens when the field circuit of a 
loaded shunt motor is broken. 

12. A shunt motor, the resistance of the armature of 
which is 0*23 ohm, is connected across supply mains having 
a P.D. of 106 volts. On turning the armature at 1200 revs, 
per minute it is found that no current passes through it. 
Calculate the speed at which it will run when developing 
1, 2, and 3 horse-power if armature reaction be neglected. 

13. A shunt dynamo has an output of 40 kilowatts at 
200 volts and 200 r.p.m. The armature resistance is 0'025 
ohm, and field resistance 50 ohms. Calculate its speed as a 
shunt motor, taking 40 kilowatts at 200 volts. 

15. A 10 H.P. shunt motor is run off the 100 volts supply 
mains. It has an armature resistance of 0-05 ohm and a 
full-load efficiency of 90 per cent. Find the approximate 
change of speed from no-load to full-load. 

15. A constant P.D. is maintained at the terminals of a 
series motor. The armature is first held at rest and then 
allowed to rotate faster and faster. Describe the way in 
which the current will vary, and the reason for such a 
variation. What determines the steady value of the current 
through the motor in such a case ? 

16. The torque of a standard tramway motor is given by 
the formula 

T = 21-4 x 10- 6 x NC inch-lbs., 

where N is the flux per pole and C the current supplied to 
the motor. How many conductors are there on the motor 
armature ? 



17. If a 4-pole motor has a series-wound armature with 
944 conductors on its periphery, prove that the torque is given 
by the formula 

Torque = 0'307 X 10~ 6 x NO metre-kilogrammes, 

where N is the flux per pole and is the current taken by 
the motor. 

18. What are the peculiar characteristics of a series motor 
which make it suitable for traction purposes ? Compare the 
relative merits of a shunt and a series motor for driving a 
circular saw through a belt drive. 

19. A series motor, employed to raise a definite weight, is 
joined up to constant pressure mains with a resistance inserted 
between the motor and one of the mains. Describe exactly 
what change will be produced in the current, the P.D. between 
the motor terminals, and the speed when this resistance is 

20. A ventilating fan is driven at 200 revolutions per 
minute by a series motor taking 10 amperes at 400 volts. If 
the resistance of the motor is 2 ohms, and the resistance to 
motion of the air varies as the square of the speed, calculate 
approximately the P.D. and current required to run the fan 
at 250 revolutions per minute. 

21. Why does a series motor race if the load is thrown 
off ? A small series fan-motor was found not to race to any 
great extent when the blades were removed. What is the 
probable cause ? 

22. A series motor runs on a constant-torque load, and the 
terminal P.D. is kept constant. What determines the speed 
at which the motor will run ? 

23. A series dynamo is run at a given speed, and observa- 
tions made of the current and P.D. for a number of external 
resistances. From the curve drawn to represent these results, 
show how to construct (1) a curve connecting the E.M.F. 


and current for that speed, (2) a curve connecting the P.D. 
and current when the machine is run as a motor at the same 

2$. If it is desired that the energy of a tramcar when 
stopping or coasting downhill may not be wasted at the 
brakes, but be supplied to other cars on the line, consider 
what type of motor must be used, and also what the driver 
would have to do when stopping a car. 

25. Explain the effect on current and speed of shunting 
the field coils of a series motor with a resistance equal to that 
of the field coils, if the torque on the motor is unchanged. 

26. Explain fully, with sketches, the use of a tramcar 
motor as a brake. 

27. Describe the methods used for keeping the speeds of 
electric motors constant under varying loads. Also explain 
how the speeds of motors working under constant torque are 
varied in practice. 

28. How do the speed and current of (a) a shunt motor, 
and (#) a series motor, vary with the torque, if the applied 
P.D. is constant ? What advantages has a compound motor 
over either of the above types ? 

29. Account fully for the behaviour of a shunt motor at 
varying loads. How can a motor supplied at constant P.D. be 
compounded to run at very nearly constant speed at varying 
loads ? Discuss whether armature reaction tends to increase 
or diminish this constancy of speed. 

30. If a compound dynamo be used as a motor without 
altering the connections, in what way will its speed vary when 
the load on the motor is varied ? Give reasons. 

31. If a motor is differentially compounded so as to run 
at exactly the same speed at all loads, how will its starting 
torque be affected by trying to start very rapidly ? 



1. Sketch and describe a motor starter with no voltage 
and overload releases, suitable for a 5 H.P. motor. What 
resistance should such a starter have ? 

2. Calculate the resistances of the various steps and the 
number of steps for a 5 H.P. 200 volt shunt motor starter, 
capable of starting under full load. Current not to exceed 
twice the normal current, and allowed to fall to 1-15 times the 
normal current. Efficiency 90 per cent., half the losses being 
armature copper losses. 

3. Calculate the resistance of the various steps and the 
number of steps of a starting resistance for a 20 H.P. series 
motor for 500 volts. Assume that the motor starts on full 
load with a current variation between 1^ times and twice the 
normal full load current. Efficiency of motor, 80 per cent. 
Resistance of armature and field, 1 ohm. Assume that the 
flux increases 10 per cent, as the current increases from 1| to 
twice its normal value. 

5. If you were required to design a starting switch and 
resistance for a 20 H.P. 400 volt motor as efficiently and yet 
as cheaply as possible, what further information would you 
require, and how would it affect the design ? 

5. Explain how the risk of breaking the field of a shunt 
machine is avoided in the ordinary motor starting switch. 


1. Explain what is meant by the root-mean-square value of 
a variable electromotive force. Find the R.M.S. value of a 
current which has the following steady values for equal 



intervals of time, suddenly jumping from one value to the 
next; 0, 1, 2, 3, 2, 1, 0, -1, -2, -3, -2, -1, 0, 1, etc. 

2. A rectified sine-wave has a maximum value of 10 
amperes. Find the quantity of electricity passing round the 
circuit per hour. 

3. A rectified sine-wave P.D. having a maximum value 
of 100 volts is applied to a non-inductive resistance of 10 
ohms. What will be the readings on a moving coil and a 
hot wire ammeter respectively, connected in series with the 
resistance ? Why will they differ ? Could such a current 
be used for charging accumulators? If so, which type of 
ammeter should be used ? 

4. An alternating P.D. having a maximum value of 570 
volts is applied to a non-inductive resistance of 120 ohms. 
Find the average value of the current that flows and the 
reading of an electrostatic voltmeter connected across the 

5. A direct current 
changes in strength every 
second from 10 to 5 or 
from 5 to 10 amperes as 
shown in Fig. 19. Find 
the steady current which 
has (a) the same electro- 
lytic effect, (b) the same 
heating effect. 

6. Explain exactly what is meant by a root-mean-square 
current of 10 amperes. What is the ratio of the R.M.S. to 
the mean value of the current, for an alternating current of 
sine form ? 

7. A hot wire ammeter and a moving coil ammeter were 
found to give different readings on a rectified current circuit. 
What does each instrument measure, and what would be the 
ratio of their readings, assuming the current to be sinusoidal ? 





a e 



3 1 2 


3 4 5 

FIG. 19. 


8. What is meant by the E.M.S. value of an alternating 
current or voltage ? An alternating sine-wave P.D. with a 
maximum value of 100 volts is applied to a non-inductive 
resistance of 5 ohms. A hot wire ammeter and a moving 
coil ammeter are connected in series in the circuit. Find the 
reading on each. 

9. Find the relative heating effect of the two currents 
shown in Fig. 20. 

/' \ 

/ \ 

/ "* \ 





N V J 


FIG. 20. 

10. Find the form factor of the pulsating P.D. obtained 
between one brush on the commutator and one slip ring of a 
rotary converter. 

11. An alternating current has a maximum value of 10 
amperes and follows a sine law. What is the greatest rate of 
change ? Frequency 50 cycles per second. 


1. What do you understand by the term " coefficient of 
self-induction of a coil " ? How would you determine it 
experimentally ? 

2. Define the coefficient of self-induction of a circuit. 
The coefficient of self-induction of the armature of the 
Ferranti alternator is practically constant at all loads, while 
that of the Pyke and Harris inductor alternator varies con- 
siderably ? Why is this ? 

3. How do the following resistances to an alternating 
current differ : (a) a straight wire ; (b) a solenoid ; (c) a glow 


lamp ; (d) a water resistance ? Why are concentric mains 
employed for alternating current ? 

4. A choking coil has a resistance of 10 ohms, but when 
connected across 100 volt 50 cycle mains, the current taken 
is only 1 ampere. If the coil has 1000 turns of wire, what flux 
is produced by a continuous current of 1 ampere ? 

5. (a) Calculate the approximate self-induction of a solenoid 
1 cm. diameter, 1 metre long with 1000 turns of wire. 

(b) Find also its resistance if the wire with which it is 
wound has a diameter of J mm. 

(c) What P.D. must be applied at any moment if the 
current is 1 ampere, but is increasing at the rate of 10,000 
amperes per second ? 

6. A wooden toroid or anchor ring has a mean diameter 
of 6 inches and a circular section of 1 inch diameter. It is 
uniformly wound with 400 turns of 1 mm. copper wire. 
Calculate its resistance and inductance. Neglect insulation, 
and assume p = 0'7 X 10~ 6 ohms per inch cube. 

7. How many foot-lbs. of energy are stored in the magnetic 
field of a coil of 1 henry self-induction when carrying a con- 
tinuous current of 1 ampere ? 

8. Explain in your own words why the alternating current 
passing through a choking coil lags behind the terminal 

9. Explain the effect of self-induction in A.C. circuits, 
and prove the formula E = C V R 2 + o> 2 L 2 f or a circuit con- 
taining inductance and resistance in series. 

10. If a sine-wave P.D. is applied to the terminals of a 
choking coil with an iron core, plot out approximately the 
shape of the current wave, assuming that the saturation of the 
iron is carried very high. 

11. Explain exactly what is meant by saying that the alter- 
nating current flowing in a circuit lags behind the E.M.F. 


producing it. Find the lag and the maximum value of the 
current in a circuit of 2 ohms resistance and O'OOG henry self- 
induction, when a sine-wave P.D. of 100 volts R.M.S. value 
and 50 cycles per second is applied. 

12. An alternating P.D. of 200 volts with a frequency of 
50 cycles per second is applied to a coil having a resistance 
of T25 ohms and an inductance of 0*07 henry. Find the 
value of the current and the cosine of the angle of lag. 

13. An alternating current at a frequency of 100 is passed 
though a non-inductive resistance of 10 ohms and a choker 
whose resistance and inductance are 1*3 ohms and 0*018 
henry respectively. When the P.D. across the whole is at 
its maximum value of 100 volts, what will be the instantaneous 
P.D. across the non-inductive resistance ? 

1$. An alternating E.M.F. of 110 volts is applied to an 
inductive resistance. When the frequency is 80 the current 
is 15'6 amperes, when the frequency is 40 the current is 19*7 
amperes, and when the frequency is 120 the current is 121 
amperes. Find the value of the resistance, the self-induction 
and the time constant of the circuit. 

15. What must be the self-induction of a choking coil 
placed in series with a 50 volt 10 ampere lamp, so that the 
latter may be used on 100 volt 50 cycle mains ? 

16. A 30 candle-power 80 volt osram lamp takes f ampere : 
what must be the inductance of a choking coil of negligible 
resistance which will enable the lamp to be used on a 200 volt 
50 cycle circuit ? Find the angle of lag between the P.D. 
of the mains and the current. What fraction of a second does 
this lag represent ? 

17. An alternating current of 10 amperes is passed through 
a choking coil with an inductance of O'Ol henry and a negli- 
gible resistance, and a non-inductive resistance of 6*28 ohms in 


series with the choking coil. The frequency is 100 cycles per 

Find (a) the reading of a voltmeter across the choking coil, 
(&) resistance 

(c) whole 

(d) the angle by which the current lags behind the 

P.D. across the whole. 

18. A wooden cylinder rotates in a uniform field about an 
axis perpendicular to the field. This wooden armature carries 
two coils, one of 100 turns, the other of 50 turns ; the two 
coils are displaced 60 from each other. The strength of field 
H = 10, the area of each coil is 2000 sq. cms., the drum rotates 
at 1000 r.p.m. Find the reading on a hot wire voltmeter 
connected across the two coils in series. 

19. A circular coil of 1000 turns of wire is rotated with 
a uniform velocity of 20 revolutions per second about one of 
its diameters, 50 cms. long, in a uniform magnetic field of 
strength 1000 G.G.S. units. If the diameter about which the 
coil rotates is perpendicular to the lines of force, calculate the 
value in volts and direction of the induced E.M.F. for six 
positions of the coil 60 apart and also the R.M.S. value of 
the induced E.M.F. 


1. Explain what is meant by a condenser and its capacity. 
Although the capacity of a condenser made of paraffined paper 
may be ten times the capacity of a well insulated Leyden jar, 
show how it may be possible to put a much larger charge on 
the coatings of the latter than on those of the former. 

2. What is an electric condenser, how is it constructed in 
practice, and what are its uses ? 

3. Explain why a condenser cannot correctly be said to 
store electricity. 


4. How many foot-pounds of energy are stored in a 
condenser of 20 microfarads charged to a P.D. of 50 volts ? 

5. Calculate the energy stored in a condenser of 100 
microfarads capacity when the P.D. between its terminals is 
1000 volts. 

6. The insulated spherical conductors A and B (Fig. 21) 

^^^^ are connected with the ter- 

/^"^\ (III f i m ^ na ^ s f a well-insulated 

[*) l|l| I B J battery. State what you 

v */ know about the potentials 
of A and B in the two dis- 
tinct cases (1) and (2). 

7. Three similar con- 
densers connected in series 
FlG> 21 - have a capacity of 1 micro- 

farad. Find the combined capacity when connected in 

8. Prove the formula giving the relation between the 
applied alternating P.D. and the current through a resistance 
in series with a condenser. 

9. A sine-wave P.D. of 100 volts with a frequency of 
50 cycles per second is applied to the terminals of a condenser 
of 30 microfarads capacity. What will be the reading on an 
A.C. ammeter connected in series with the condenser ? What 
quantity of electricity will pass into the condenser during the 
time the current is flowing in one direction ? 

10. Explain in your own words why a condenser takes 
a leading current. 

11. Explain how a condenser shunted by a non-inductive 
resistance acts like a negative self-induction. Calculate the 
equivalent inductance of a given capacity and resistance. 

12. A 500-volt motor takes 20 amperes at a power-factor 


of 0-75. 

What capacity would have to be employed to 
the power-factor to unity ? Frequency 50 cycles per 

13. What capacity must be placed in parallel with a 
choking coil of 1 ohm resistance and 0'05 henry self-induction 
in order to bring the current taken from the mains into phase 
with the pressure ? Frequency = 50. 

1$. A circuit is made up of an inductive resistance of 
7 ohms with a self-induction of 0'04 henry, joined in series 
with a condenser of 20 microfarads capacity. Find the current 
in the circuit and the P.D. across the inductive resistance 
when an alternating P.D. of 200 volts and 50 cycles per 
second is applied to the circuit. 

15. (a) A 15-ampere arc lamp requires a P.D. of 50 volts 
across its terminals, and has to be connected to 100 volt 
50 ~ mains. Calculate the value of the inductance to be 
placed in series with the lamp and the power-factor of the 
arrangement, assuming the power-factor of the lamp itself to 
be unity. 

(#) In the above question, how could a condenser be used 
to bring the current taken from the mains into phase with the 
P.D. ? Calculate the requisite capacity of the condenser. 

16. An arc lamp taking 10 amperes at 40 volts is run off 
200 volt 50 cycle mains by means of a suitable choking coil. 
Find the inductance of the choking coil and the P.D. between 
its terminals. How could you make the load non-inductive, 
i.e. bring the current taken from the mains into phase with 
the P.D. ? 

17. A coil having a self-induction of 0'54 henry and a 
resistance of 6 '7 ohms is connected in series with a con- 
denser of 6 microfarads capacity and a P.D. of 70 volts is 

(a) Calculate the frequency to give resonance. 


(#) Calculate the current under these conditions. 
(c) What will be the percentage variation in current for 
an increase of 1 per cent, in speed ? 

18. Why is Ohm's law apparently not true under certain 
conditions in an alternating current circuit ? Show how to 
determine the value of the resulting current when a P.D. of 
given frequency is applied to a circuit containing resistance, 
self-induction, and capacity connected in series. 

19. Explain the following phenomena observed with the 
oscillograph : 

(a) Using the Wenstrorn machine, which gives a pure sine 
wave of P.D. , the current passing through a choking coil with 
a saturated iron core was very distorted. 

(b) Using the Pyke and Harris alternator, which gives a 
peaked wave of E.M.F., the current passing through a choking 
coil without iron core was much less peaky, i.e. the irregulari- 
ties were smoothed out. 

(c) On replacing the choking coil in (])) by a condenser, the 
irregularities in the P.D. wave were highly magnified in the 
current obtained. 


1. A coil has a resistance of 10 ohms and an inductance 
of O'Ol henry. If an alternating P.D. of 100 volts with a 
frequency of 50 cycles per second is applied to its terminals, 
find (a) the current, (#) the power taken by the coil, (c) the 

2. What is meant by the power-factor of an alternating 
current circuit ? Calculate the power-factor of a circuit of 
50 ohms resistance and 0*025 henry inductance, if the fre- 
quency is 50 cycles per second. 


3. What is meant by the power-factor of a circuit ? Calcu- 
late the power-factor of a circuit of 20 ohms resistance, and 
0'02 henry self-induction. Frequency 50. 

5. Explain how the power-factor of an inductive load is 
improved by connecting a condenser in parallel with the load. 
What are the advantages of an improved power-factor ? 

5. If a non-inductive resistance of one ohm be connected 
to an A.C. supply with a frequency of 100 cycles per second, 
calculate what amount of self-induction added to the circuit 
will reduce the current to J, J, |, , respectively, of what it 
would be with no self-induction. What will be the relative 
amounts of power given to the circuit in the five cases ? 

6. How could the power-factor of a circuit be measured, a 
suitable ammeter, voltmeter, and wattmeter being provided ? 
Give a diagram of the connections. 

7. Find the power taken by a coil without iron core, having 
a resistance of 5 ohms and a self-induction of ^ henry, when 
an alternating P.D. of 100 volts and 50 ~ is applied to the 

8. Why is it more economical to use a choking coil in 
series with an arc lamp instead of an ordinary resistance on 
alternating current circuits ? 

9. Calculate the mean value of the product of two sine 
functions of the time having the same frequency but differing 
in phase ; and apply your result to show how a dynamometer 
may be used to measure the lag between two alternating 

10. Prove that, although the alternating current and P.D. 
may be in phase, the power-factor is not unity unless they 
have the same wave form. (If you can, prove it generally ; if 
not, take some specific case.) 

11. A 10-ampere A.C. arc lamp requires a terminal P.D. of 
35 volts at 50 cycles per second. What must be the self- 


induction of a choking coil to enable the lamp to be run on 
100 volt mains ? 

Could the choking coil be replaced by a condenser ? If so, 
what should its capacity be ? 

What is the amount of energy continually being stored 
and given out in the above choking coil arid also in the 
condenser ? 


1. Describe with sketches the main features of construction 
of a large modern alternator for 25 cycles per second at a 
speed of 300 r.p.m. 

2. Explain with sketches the construction of an alternator 
of (a) copper type, (b) iron type, (c) inductor type. Which 
type would you advise for use in (a) a railway generating 
station ; (b) for use with a high-speed engine on an electric 
lighting circuit with a fairly constant load ; (c) for use in a 
district where noiselessness is of first consideration ? 

3. What is the principle of the inductor alternator ? Give 
a sketch of a good type of inductor alternator, showing clearly 
the armature and field coils and the path of the flux. 

5. What advantages are possessed by three-phase as com- 
pared with single-phase alternators ? 

5. Explain how it is that the E.M.F. curve of an alter- 
nator with a distributed winding is more nearly a sine wave 
than the E.M.F. induced in any one of the coils in the 

6. The armature of a single-phase alternator is completely 
covered with a uniformly distributed winding of S tarns in 
series. The R.M.S., E.M.F. induced in one turn is 1 volt. 
What is the E.M.F. of the whole armature winding ? 

7. A B.C. motor armature is tapped at three equidistant 


points on the winding and connected to three insulated slip- 
rings on the shaft. If the P.D. between the brushes on the 
commutator is 100 volts, what will be the R.M.S. value of the 
P.D. between two of the slip-rings ? 

8. Two rectangular coils are arranged so that one can turn 
within the other, somewhat like the coils of an electro-dynamo- 
meter. How will the fixed coil be affected if the moving coil 
is supplied with alternating current at a frequency of 50, and 
is simultaneously revolved at a speed of 3000 revolutions per 
minute ? 


1. Explain briefly with the aid of a simple vector diagram 
the action of a transformer. 

2. Give a vector diagram showing the primary and 
secondary voltages and currents in a transformer (1) when 
unloaded, (2) with a non-inductive load, (3) with an inductive 

3. A 500 kilowatt step-up transformer has 100 turns in the 
primary winding and 10,000 in the secondary winding. The 
primary terminal P.D. is 500 volts at 25 cycles per second. 
The resistances of the two windings are ohm and 20 
ohms respectively. 

(a) If the maximum flux density is 5000 lines per sq. cm., 
find the cross-sectional area of the core. 

(#) Find secondary terminal P.D. on full load, assuming 
that all the pressure drop is due to resistance and that the 
load is non-inductive. 

$. Upon what does the ratio of the primary to the secondary 
P.D. of a transformer depend ? 

Explain carefully how the relation is affected when the 
transformer is loaded. 


5. Upon what does the P.D. between the secondary 
terminals of a transformer depend ? How is this P.D. affected 
by changes of load if the primary voltage is kept constant ? 

6. Enumerate the various losses of energy in a transformer 
and state how each loss is dependent upon (a) the load on the 
transformer, (#) the frequency of supply. 

7. Enumerate the various causes leading to 
(a) Losses of power in transformers ; 

(&) Pressure drop in transformers ; 

and indicate the means by which these may be reduced to 
a minimum. 

8. Describe the various losses which occur in a transformer. 
How does each loss affect the working of the transformer ? 

9. Give a complete account of the method of measuring 
the power and efficiency of a transformer. 

10. Alcohol, instead of mercury, thermometers are some- 
times used in testing transformers. Why is this ? 

11. What tests would you carry out on a transformer 
before accepting it ? 

12. What would be the effect of introducing an air-gap 
of say J" in any part of the magnetic circuit of a transformer ? 


1. Describe the principle and construction of a three-phase 
induction motor. What are the disadvantages of this type of 
motor ? 

2. How many poles has a 3-phase generator running at 
250 r.p.m. and giving 50 cycles per second ? 

What would be the speed of an induction motor having the 
same number of poles but having 5 per cent, slip at full load ? 


3. A 6-pole 3-phase induction motor is operated from 
a supply having a frequency of 25 cycles per second. The 
slip at full load is 5 per cent., what is the speed of the motor ? 

$. Explain with the aid of diagrams how a uniform 
rotating field is produced in a polyphase induction motor, 
and show why the motor revolves. 

Find the speed of a 3-phase 6-pole induction motor when 
supplied with current at a frequency of 50 cycles per second, 
if the slip be 4 per cent. 

5. An alternator is coupled to an engine running at 
250 r.p.m. The frequency of the alternator P.D. is 50 cycles 
per second. How many poles has the machine ? At what 
speed would an 8-pole synchronous motor run when connected 
to these 50 cycle supply mains ? 

6. Show how the rotating field is produced in a polyphase 
induction motor, and explain why a starting resistance is 
necessary for large motors of this type. 

7. Explain with the help of diagrams the production of 
a rotating field by means of 3-phase current. 

8. Explain how a rotating uniform magnetic field is pro- 
duced in a 2-phase induction motor. Why are squirrel-cage 
motors rarely used in large sizes ? 

9. Enumerate the various sources of loss of energy in an 
induction motor. 

10. Enumerate the various methods of starting both 
synchronous and induction motors. What is the relation 
between speed and torque in the two types ? 

11. Enumerate the properties, and state the most suit- 
able applications of synchronous and asynchronous motors 

12. How is it that putting a load on a squirrel-cage 



induction motor causes the current taken by the motor to 
increase ? 

13. Explain exactly how you could reverse the direction 
of rotation of (1) a 2-phase induction motor ; (2) a 3-phase 
induction motor. 

1$. Sketch the speed load curve for a synchronous and an 
induction motor respectively. 

What are the principal characteristics and uses of these 
two types of A.O. motors ? 


1. Explain the working of the Duddell oscillograph, show- 
ing how a stationary wave is produced and what the wave 
means. Would the current wave be the same if taken in any 
part of the same circuit at the same time and under the same 
conditions ? 

2. How would you measure the power given to a trans- 
former by means of an oscillograph ? 

3. What are the advantages and disadvantages of alternating 
currents for practical work as compared with continuous 
current ? 

4. What are the relative advantages and disadvantages of 
single and 3-phase systems with regard to (a) generation, 
() transmission, (c) distribution ? 

5. Explain what is meant by star and delta connection in 
3-phase work ? If three 100-ohrn resistances are star-connected 
to a 3-phase supply with 500 volts between the lines, find the 
current taken. 

6. Define "power-factor" and "load-factor," and explain 
their importance from the point of view of the engineer of 
an electric generating station. 


7. Define the terms " form-factor," " power-factor," and 
" load-factor." What influences have the latter two factors 
on the efficient working of a central station ? 

8. Under what conditions would you use a choking coil, 
in preference to a resistance, to steady an arc lamp ? 

9. A rotary converter is connected both to D.C. and A.C. 
mains. What determines to which circuit the converter will 
deliver energy ? 

10. Would you rather use a motor generator or a rotary 
converter to transform from high pressure A.C. to low 
pressure D.C. ? Give reasons for your choice. 


1. (a) Calculate the distance to which 10,000 K.W., at 
60,000 volts, can be transmitted over cables O'l square inch 
cross-section, with a line resistance loss of 20 per cent, of the 
power delivered. 

1 mile of 0'2 square inch cable has a resistance of 0'2 

(&) Calculate the cross-section of the cable to transmit the 
same power at 2000 volts over the same distance, with the 
same percentage loss as above. 

2. Calculate the diameter of the cable necessary to deliver 
1000 K.W. at 30,000 volts P.D., 50 miles away, if 100 K.W. 
be wasted in line resistance losses. 

Resistance of 1 mile of 0*08 square inch cable is 0'55 

3. It is required to deliver 1000 H.P. at 30,000 volts at 
a point 60 miles away with an efficiency of 75 per cent. What 
must be the resistance and cross-section of the line ? 

5. What size of copper wire should be employed to 


transmit 10,000 H.P. a distance of 100 miles, (a) at 10,000 
volts, (J) at 100,000 volts ? 

Assume single-phase transmission with 90 per cent, 

5. A 50 H.P. 500 volt motor is to be supplied with con- 
tinuous current from a distributing centre 250 yards away. 
The efficiency of the motor is 80 per cent. What must be the 
cross-section of the cable, if the loss in transmission be 3 per 
cent, of the motor output ? Specific resistance of copper may 
be taken as 0*66 x 10" 6 ohms per inch cube. 

6. Find the cost of copper to transmit 15,000 K.W. a 
distance of 100 miles, allowing 15 per cent, loss in line with 
voltages of (a) 10,000, () 140,000 at the receiving end. 

Specific resistance of copper, 0'66 microhm per inch cube. 
Weight of a cubic inch, 0'32 Ib. Cost of copper, 80 per ton. 

7. Calculate the distance to which 10,000 K.W. at 60,000 
volts can be transmitted and delivered over a cable O'l square 
inch cross-section, having a resistance of 0'44 ohm per mile, 
with a line resistance loss of 20 per cent, of the power 

8. 400 H.P. has to be transmitted a certain distance. 
Calculate the relative cost of copper in the following two cases, 
allowing a loss of 20 per cent, of the original power : (a) Con- 
tinuous current, 500 volts at receiving end ; (&) alternating 
current, 2000 volts at receiving end. Efficiency of step-down 
transformers at receiving end, 90 per cent. 

9. Assuming the price of copper to be 80 per ton and the 
cost of poles, etc., and erection to equal the cost of the copper, 
consider the advisability of building a generating station 100 
miles away from London with coal at 5s. per ton, instead of in 
London with coal at 15s. per ton. 

Maximum output of station = 40,000 K.W. 
Pressure of transmission = 60,000 volts. 


Annual load factor = J. 
Assume 2J Ibs. of coal per B.O.T. unit. 
Allow 10 per cent, for interest and depreciation on line. 
Assume 80 per cent, efficiency of transmission. 
Specific gravity of copper, 8'9. Specific resistance, 0'66 
microhm per inch cube. 

10. Tabulate the advantages and disadvantages of using 
large P.D.s for the transmission of power. 

11. If it be decided to treble the power received by glow 
lamps at the end of a given pair of mains without wasting a 
greater percentage of the power en route, calculate what change 
must be made in the P.D. between the mains at the trans- 
mitting end and in the pressure at which the lamps are 
intended to run at the receiving end. 

12. Compare the relative advantages and disadvantages of 
continuous and alternating current systems for a large coal 

13. What are the advantages and disadvantages of alter- 
nate current as compared with continuous current electric 
distribution ? How low may be the frequency supplied to a 
glow lamp without the eye noticing the periodic changes of 
current ? 

1$. Explain clearly the advantages of transmitting power 
at a high voltage. What is the advantage of using alternating 
current for a high voltage transmission, and what con- 
siderations will limit the voltage used ? 

15. Consider the conditions likely to determine the most 
economical voltage for a transmission scheme in the colonies. 

16. What are the special advantages and disadvantages of 
large P.D. continuous current systems ? 

17. Give a brief account of the Thury system of the 
electric transmission of energy by means of high voltage 
continuous current, 


What are the practical considerations which limit the 
distance to which electrical energy can be transmitted ? 

18. What would you consider the best type of cable for 
connecting an electric coal-cutter with the supply mains ? 
Give reasons. 

19. Describe briefly the principle of the 3-wire system of 
distribution, and discuss its advantages and disadvantages 
compared with the 2-wire system. 

20. What are the advantages of the 3-wire system of 
distribution ? Describe the several methods employed. Why 
must a fuse or any other description of cut-out never be 
placed in the neutral wire ? 

21. A dynamo is supplying current for lighting a building 
half a mile away on the 3-wire system. The cross-section of 
the two outer wires is 0*3 square inch each, and that of the 
neutral 0'15 square inch. There are 500 lamps on one side 
and 300 lamps on the other, each lamp taking 0'3 ampere. 
What voltage must be maintained at the generator end of the 
feeder, (a) between positive lead and neutral wire, (Z>) between 
negative lead and neutral wire, in order that the pressure 
across each lamp may be 200 volts ? (Resistance of an inch 
cube of copper may be taken to be f microhm.) 

22. Explain the action of a motor balancer set in a 3-wire 

23. Is an A.C. 3-wire system possible ? If so, what sort of 
balancer could be employed ? How could it be regulated ? 


1. Why is a secondary battery called an accumulator ? 
What does it accumulate ? Give approximately the connection 
between the weight of a secondary battery, the horse-power 


which it can steadily develop without injury, and the number 
of foot-pounds which it can give out. 

2. Why are some cells called primary and others secondary ? 
What are their relative advantages and what are the faults to 
be especially guarded against in secondary cells ? 

3. Describe briefly the improvements that have been 
introduced into accumulators during the past eighteen years. 

5. What are the industrial uses of accumulators, and which 
are the properties of an accumulator that are particularly 
valuable in each case ? 

5. Show how the resistance of a storage cell may be 
ascertained at frequent times while it is being charged, and 
how the energy wasted in charging the cell (apart from that 
wasted in discharging it) can be measured. 

6. Give approximately the numerical results that you 
would expect to find on testing a good accumulator intended 
for road traction. 

7. A set of accumulators is being charged by means of a 
series dynamo. Explain fully why the lowering of the speed, 
even for a very short time, may produce serious damage both 
to the cells and the dynamo. What sort of result do you 
think would be obtained if cells were charged with a Thomson- 
Houston constant current dynamo ? 

8. State approximately the current that may be taken from 
a square foot of the positive plate of an accumulator without 
damage and the energy in foot-pounds that can be safely taken 
out of one pound weight of positive plate. 

9. Describe all the precautions that should be taken in 
using accumulators in order that they may have a long life. 

10. Find the capacity of a battery of 100 cells connected 
in series, if the capacity of each cell be 300 ampere-hours. 


11. Taking the mean P.D. that has to be maintained 
between the terminals of an accumulator in charging as 2*1 
volts, and the mean P.D. maintained between the terminals in 
discharging as 1*9 volts, and assuming that the total quantity 
of electricity that passes through in discharging is 90 per cent. 
of the quantity that passes through in charging, what is the 
energy efficiency of the accumulator ? 

12. If the E.M.F. of a storage cell on charge and 
discharge be 2'1 and 1'95 volts respectively, find the difference 
in foot-pounds in the energy stored and restored when 100 
ampere-hours are passed through the cell. 

13. Enumerate the various causes of the excessive weight 
of secondary cells, and discuss the possibility of reducing it. 

1$. After fully charging a secondary cell to 2*5 volts and 
letting it stand, the P.D. is found to fall gradually, whereas on 
standing after discharge to 1*8 volts the P.D gradually rises. 
Explain these phenomena. 

15. A storage cell contains 15 plates, each plate is 10" 
square and ^" from its neighbour. Find the resistance 
of the electrolyte if 1 inch cube of the solution has 3 ohms 

16. If it is only the spongy lead on the surface of the 
accumulator plate that takes part in the chemical action, why 
are accumulator plates always rendered heavy by being made of 
thick lead ? Why is it that a depth of 3 inches is always left 
between the bottom of the plates and the bottom of the 
cells ? 

17. Explain why the discharge of an accumulator should 
be stopped when the P.D. drops to a certain value. 

18. Draw the normal curves of charge and discharge of an 
accumulator with constant current, and explain iti detail the 
reason for their particular shapes. 


19. A cell which cannot be detached from a battery of 
accumulators wants charging for a longer time than the other 
cells. Describe with sketches how you would do this. 

20. A battery of accumulators is being charged. What 
indications would serve to show when the cells are fully 
charged, and what signs would lead you to suspect that any 
individual cell was out of order ? What steps would you take 
to discover the fault and remedy it ? 

21. A battery consists of 55 storage cells in series, each cell 
has a resistance of O'OOl ohm, an E.M.F. of 2'05 volts, and 
contains 10 + and 11 - plates 12" X 12". If 0'04 ampere be 
taken from the cells per square inch of positive plate surface, 
what will be the P.I), at the distributing board at full load 
current, if the leads to the board have a resistance of 0'017 

22. Give a simple explanation of the chemical actions 
involved in charging and discharging an accumulator. 

Explain the changes which occur in the specific gravity of 
the electrolyte. 

23. Explain the chemical action of the secondary cell 
during charging and discharging. Why should the cell never 
be discharged below 1/8 volts ? 

24. Explain why the density of the acid serves as an 
indication of the state of charge of an accumulator. 

25. A storage cell is being charged with a current of 36 
amperes. Find the weight of sulphuric acid liberated per hour 
due to the chemical action taking place, having given that 1 
coulomb of electricity deposits 0-00107 gramme of lead. Find 
also the weight of lead peroxide formed in the same time. 

26. If the capacity of a cell for central station use is about 
2J ampare-hours per pound of cell, what percentage of the 
total weight of the cell enters into the chemical reactions ? 


27. Why has accumulator traction not proved satisfactory 
up to the present ? 

28. How far will a battery weighing 10 cwt. propel a cab 
weighing 1^ tons (including battery and motor) ? The output 
of the battery is 10 watt-hours per pound weight. Resistance 
to traction is 30 pounds per ton. Efficiency of motor and 
gearing 75 per cent. 

29. A tramcar weighing 6 tons without battery is to be 
propelled at 10 m.p.h. If the power given by the cells is 7 
watts per pound and the necessary tractive force 15 pounds 
per ton, find the weight of cells required. Efficiency of motor 
85 per cent. 

30. What are the advantages and disadvantages of accu- 
mulators for electric traction ? 

A car is fitted with accumulators and a motor which has to 
develop 1J H.P. for 4 hours. What must be about the least 
weight of the motor and of the accumulators so that they will 
stand this discharge without damage ? Also about how much 
energy must be used in replacing the energy taken out in the 
discharge ? 

31. When accumulators are charged by a dynamo driven 
by a gas engine, the engine can be started by means of the 
accumulators, the dynamo automatically changing from a 
motor into a dynamo when the gas engine gets up speed. Give 
sketches showing this arrangement in detail. 

32. What are the advantages of accumulators in an electric 
generating station ? Sketch the arrangement of a good 
battery switch to enable the battery to be charged from a 
dynamo and at the same time be connected to the supply 

33. Explain how a storage battery is utilised in a central 
station to keep the load on the generators constant. What is 
the function of a booster in such a station ? 


3$. What advantages and disadvantages are introduced by 
having a battery in a tramway generating station ? 

35. Compare the advantages and disadvantages of an 
accumulator battery as compared with spare generators, (a) in 
a lighting station, (b) in a traction station. 

36. Describe the action of a battery as commonly used in 
a traction station. Explain the effect of adding an automatic 
reversible booster. 

37. What is the function of a booster in a central station ? 
A reversible booster is used in conjunction with a 200 volt 

battery having a discharge capacity of 200 amperes. The 
charging current until the P.D. of each cell rises to 2*3 volts 
is 100 amperes and from 2'3 volts to the end of charge is 50 
amperes. Find the K.W. capacities of the booster and booster- 
motor respectively. 


1. If the tractive resistance of a car on the level be 30 
pounds per ton, find the gradient down which the car will 
coast at a uniform speed. 

2. Find the relation between the tractive resistance in 
pounds per ton and the energy consumption in watt-hours per 
ton mile. 

How many watt-hours per ton-mile must be added for a 
1 per cent, gradient ? 

3. What are the factors which determine the mechanical 
pull required to draw a car along a line ? A trarncar is 
equipped with 2 motors and is running on a line up an incline 
of 1 in 30. The weight of the car is 12 tons and the resistance 
to traction 25 pounds per ton. If the motors are exerting 10 
H.P. each, find the speed of the car in miles per hour. 


$. Weight of locomotive = 40 tons. 

"Weight of train (without locomotive) = 250 tons. 

Tractive resistance = 12 pounds per ton. 

What is the maximum acceleration possible on the level, 
and what time is required to reach a speed of 60 miles per 
hour, if the rails are clean but wet and give an adhesive force 
on the wheel of 15 per cent, of the dead weight ? Assume 
total weight of locomotive on driving wheels. 

5. A tramcar weighing, when loaded, 12 tons has motors 
which give a torque of 5000 pound-feet on the wheels while 
starting. The tractive effort required to overcome friction is 
20 pounds per ton. Diameter of wheel 30 inches. Find the 
time taken to bring the car from rest up to a speed of 15 miles 
per hour. 

6. A train of 50 coal trucks each weighing 15 cwt. is being 
hauled up an incline of 1 in 20 at the rate of 2 miles per hour. 
The tractive force required on the level is 50 pounds per ton. 
What current will be taken by the 200 volt haulage motor, 
the efficiency of which, inclusive of gearing, may be taken as 
60 per cent. ? 

7. The resistance to traction of a tramcar on the level is 
15 pounds per ton. The highest speed attainable by a 10-ton 
car up an incline of 1 in 40 is 8 miles per hour. Find the 
current taken in this case from the 500 volt trolley wire, if the 
combined efficiency of motor and gearing be 75 per cent. 

8. An electric train, weighing 100 tons, is standing on an 
incline of 1 in 40. The tractive force is 15 pounds per ton on 
the level. The train starts up the slope with a uniformly 
increasing speed, attaining the full speed of 25 miles per hour 
in 15 seconds. The gear ratio is 4*8, the wheels are 33" 
diameter, the efficiency of the gearing is 80 per cent., and there 
are four motors. What torque must be exerted by each motor 
during the start ? 

9. What weight of cells would be necessary to make a 50 


mile run with a driver and 4 passengers in a carriage weighing 
1 ton without passengers or cells ? Assume a level road, 
tractive force 20 pounds per ton : 1 pound of cells gives 8 to 
12 watt-hours. 

10. An electric automobile weighs 2 tons gross, 15 cwt. of 
which is due to the cells. If the cells have a capacity of 10 
watt-hours per pound weight, and the efficiency of the motor 
and gearing be 70 per cent., what distance would it be possible 
to run on a single charge, if the tractive force on the level be 
50 pounds per ton and the average gradient a rise of 1 in 

11. Tabulate the advantages and disadvantages of the 
trolley system, conduit system, and surface-contact system of 
electric traction for street tramways. 

12. How can the series motors of a tramcar be used as 
brakes ? Give a diagram showing the alteration of connections 
from running to braking position. 

13. What is the principle and object of series-parallel 
control of traction motors ? Explain the various steps by 
which a tramcar with two motors is gradually started and 
brought up to full speed. 

1$. What are the advantages of series parallel control in 
traction work ? Give a sketch showing the connections of the 
reversing barrel of a tramcar controller. 

15. In what proportion is the energy wasted in starting 
resistance reduced by the use of two motors and series-parallel 
control ? What further reduction could be effected by the 
employment of 4 motors ? 

16. What is the principle and action of the magnetic blow- 
out in a tramcar controller ? Give a sketch showing the 
arrangement of the magnet coil and the path of the flux in a 
modern controller. 



1. State the principles upon which the measurement of the 
intensity of a source of light depends. Describe a reliable 
form of photometer and the method of using it to obtain the 
candle-power of a glow lamp. 

2. If the barometer varies over a range of 3 inches and the 
humidity of the air varies from 2 to 20 litres per cubic metre, 
find the greatest possible difference in the candle-power of a 
16 c.p. glow lamp as determined by means of a Pentane lamp 
on two different occasions. Tests made at the National 
Physical Laboratory showed that the candle-power of a 10 c.p. 
Pentane lamp was given by the formula 

C.P. = 10 - 0-008(760 - I) + 0-066(10 - A) 

where # = height of barometer in mm. and h = humidity in 
litres of water vapour per cubic metre of dry air. 

3. Give a brief account of the method of manufacture of 
modern carbon filament glow lamps. How are the dimensions 
of the filament for a given candle-power influenced by the 
voltage for which the lamp is designed ? 

4. Why do incandescent lamps use a greater number of 
watts per candle than arc lamps ? What are the considerations 
that enable you to settle the proper P.D. to maintain at the 
terminals of an incandescent lamp ? Consider whether in- 
candescent lamps when supplied with alternate current should 
have a greater or less pressure maintained between the 
terminals than when supplied with continuous current. 

5. Glow lamps are purchased for running at 100 volts. 
Consider what will be the advantages and disadvantages of 
running them at a steady pressure of, (a) 97 volts instead of 
100, (fe) 103 volts instead of 100. Give examples when it 
would be profitable to adopt (a) and when to adopt (6). 


6. Why are metallic filament lamps of small candle-power 
only made for low voltages ? How is this disadvantage over- 
come in the use of the lamps on high voltage systems ? 

7. Why is a ballast resistance necessary in the Nernst 
lamp ? Explain the peculiar type of resistance employed. 

8. The ballast resistances of Nernst lamps are contained 
in bulbs filled with hydrogen because the hydrogen cools the 
filament much better than would a vacuum. Explain the 
meaning of this statement in face of the fact that the iron 
wire has to be raised to a red heat to make it effective. 

9. What are the points to be considered in ascertaining the 
best P.D. to be maintained between the terminals of a 
particular type of glow lamp ? What are the advantages and 
disadvantages of changing over the supply of electric energy 
in a district from 100 volts to 200 volts ? 

10. A tantalum lamp for 110 volts has a filament 650 
mm. long and ~Q mm. diameter. The specific resistance of 
tantalum when running is 83 microhms per cm. cube. The 
efficiency is If watts per candle. What is the candle-power 
of the lamp ? 

11. The B.O.T. limits the variation of P.D. on a consumer's 
terminals to 4 per cent, above or below the declared pressure. 
To what variation of candle-power does this correspond : (a) 
for a carbon lamp, and (5) a metal filament lamp, the index for 
the relation between O.P. and P.D. being 6*5 and 4 re- 
spectively ? 

12. If the C.P. of a glow lamp varies as the cube of the 
watts and also as the seventh power of the voltage, find the 
efficiency of a lamp at 90 volts which at 100 volts gave 16 c.p. 
for | ampere. 

13. Write down in symbols or figures the approximate 
equations connecting 


(a) Candle-power and potential difference ; 

(6) and current 

for electric glow lamps under normal conditions of use. Com- 
pare the ratios of the corresponding constants in (a) and (6) 
for carbon filament and metallic filament lamps respectively, 
of equal candle-power and voltage. Explain the differences, if 
any, in these ratios for the two kinds of lamps. 

14. If the candle power of a carbon filament glow lamp 
varies as V 7 and also as C 3 , find the relation between current 
and resistance. 

15. Draw curves showing approximately the relation 
between (a) C.P. and P.D., (6) C.P. and current, (c) C.P. and 
watts per C.P. in a 16 C.P. 200 volt carbon filament glow 

16. If carbon glow lamps costing Is. each produce 1C 
candles when run at 3 watts per candle and last 500 hours, 
while they produce 13 candles and last 1000 hours, when run 
at 4 watts per candle, calculate which is the more economical 
number of watts per candle to employ when a B.O.T. unit 
costs 5d. 

17. If the wholesale price of a good modern glow lamp be 
taken at 2s., calculate at about what price it would be 
necessary to be able to obtain a B.O.T. unit so that light for 
light electricity could compete with gas. 

Take gas at 2s. IQd. per 1000 cubic feet, and inverted burners 
giving 10 candle-hours per cubic foot. Assume consumption 
of 1*3 watts per candle for electric lamp. Cost of mantle, 4d. ; 
life of mantle, 300 hours. Life of electric lamp, 1200 
hours. Assume 50 c.p. lamps. 

18. If a new 16 c.p. carbon lamp cost Is. and take 60 
watts, find when it must be replaced in order to get the 
minimum total cost per candle-hour under the following con- 
ditions : 

Cost of energy, 4=d. per unit. Watts taken by lamp 


constant during whole life, but C.P. decreases uniformly, 
reaching 8 c.p. after 1000 hours. 

19. What life must a 16 c.p. metallic filament lamp have 
to make it as efficient as regards total cost per candle-hour as 
the ordinary carbon filament lamp, assuming the former takes 
1J watts per candle-power and costs 2s. 9d, while the latter 
takes 4 watts per candle-power, costs 9^., and is renewed every 
1000 hours ? Neglect decrease of C.P. during life. Energy 
4d. per unit. 

20. If a Welsbach burner gives an average of 6 candle- 
hours per cubic foot of gas, if a mantle lasts 300 hours and 
costs 5^., and the price of gas is 2s. Wd. per 1000 cubic feet, 
calculate at what price a B.O.T. unit must be sold so that 
using 20 watt 16 c.p. lamps lasting 600 hours and costing 
2s. Qd. each may be as economical as employing Welsbach 
burners. Assume 40 c.p. for the gas burner. 

21. The following are the results obtained on testing 
carbon glow lamps ruu^at 100 volts 

Time in Hours. C.P. per Lamp. Current in Amperes. 

16 ... 0-62 

100 18 ... 0-65 

250 16 ... 0-64 

500 *^.?" 15 ... 0-68 

750 ... 14 ... 070 

1000 ... 12 ... 0-70 

The price of a B.O.T. unit is 3J<#., price of a new lamp is 
9d., and the lamps are renewed every 800 hours. Calculate 
the average cost of 100 candle-hours. In this case which will 
diminish the cost of lighting the more, a 20 per cent, reduction 
in the price of a lamp or in the cost of a B.O.T. unit ? 


1. What do you understand by the candle-power of (a) a 
glow lamp, (Z>) an arc lamp ? How would you determine the 
candle-power in each case ? 



2. Why is it necessary to place a resistance in series with 
an arc lamp ? Under what circumstances could the resistance 
be replaced by a choking coil ? 

3. An arc lamp using solid carbons 5 mm. apart and taking 
10 amperes is to be run off a 100 volt circuit. What resistance 
will it be necessary to insert in series with the arc and how 
many watts will be spent in the resistance ? What proportion 
of the whole power is used in the arc ? (See Fig. 22.*) 

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 
Current in Amperes 

FIG. 22. P.D. and current for different lengths of arc. Solid carbon 
+ 11 mm., 9 mm. diameter. 

$. An arc is maintained between solid carbons of 11 and 9 
mm. diameter. The supply P.D. is 70 volts and the resistance 
in series with the arc is 1J ohms. What are the limits between 

* Fig. 22 is reproduced from Mrs. Ayrton's book " The Electric Arc," 
by the kind permission of the authoress and publishers. 


which the length of the arc can be varied and what are the 
greatest and smallest currents ? (See Fig. 22.) 

5. How does the P.D. between the carbons of a direct 
current open arc change when the carbons are slowly separated 
and the outside resistance slowly varied so as to keep the 
current constant ? How does the current vary when the 
carbons are slowly separated and the outside resistance slowly 
varied so as to keep the P.D. constant ? Explain the cause of 
the results obtained. 

6. Mrs. Ayrton found that for solid carbons the power ex- 
pended in the arc was a linear function of the current when the 
length was kept constant, and also a linear function of the 
length when the current was kept constant. 

Prove from these facts that the P.D. across the arc is 
represented by the following formula 


. . 

where a, ,/, and g are constants. 

7. Draw a polar curve showing approximately the dis- 
tribution in a vertical plane of the light given out by an arc 
lamp of the open type. Show also a construction by which the 
mean spherical candle-power of such a source can be de- 
termined. Give proof. 

8. If the polar curve of an arc be rotated about a vertical 
axis, it will describe a solid of revolution. It has been 
suggested that the radius of a sphere of equal volume would 
be the mean spherical candle-power. Investigate this. 

9. Tests on a flame arc with downward feeding carbons, 
gave the following C.P. in different directions 

Angles to the"! 
horizontal / 

0, 10, 









C.P. (Hefner) 

900, 1300, 










Draw the polar curve. 

A hall 100 feet long, 60 feet wide, and 40 feet high, is 
illuminated by the above lamp suspended at the centre 5 feet 
below the ceiling. Compare the illumination of the floor at the 
centre with that of the floor in a corner of the room. Neglect 
reflection from walls and ceiling, etc. 

10. Find the approximate mean spherical candle-power and 
the mean hemispherical candle-power of the lamp in the fore- 
going question. 

11. How is the distribution of the light from an arc lamp 
affected by an opaline globe put round it ? How would you 
proceed to determine the absorption of the globe ? Would you 
obtain the same results from tests made on a piece of the same 
glass 3" square ? 

12. Under what circumstances can simple shunt or simple 
series arc lamps be used ? Why are differential lamps essential 
in other cases ? Describe with sketches the mechanism of any 
arc lamp with which you are acquainted. 

13. In alternating current arcs themselves, not including 
the mechanism, the watts are less than the product of amperes 
and volts. How do you account for this ? 


1. 1120 grammes. 2. 18,000 coulombs. 5. 1 B.O.T. = 3415 
B.Th.U. 6. 0-3<7. 7. U. 8.11-6%. 9.22-7%. 10. (a) 1 H.P.- 
hour = 640,000 cal ; (6) 6 to 12 Ibs. 12. 1 unit = 1'34 H.P.- 
hours = 2,650,000 ft.-lbs. 13. 53. 14. lid. 15. 85 H.P., 4'7d. 
16. 33-6%. 17. (a) 9-7 H.P ; (6) 0'07d. 18. 18-1 H.P., Id. 

19. 0-47cZ. 21. 1-72 microhms. 22. 94 microhms per cm. cube. 
23. 0-485. 24. 10. 25. 3^. 26. 103-6, 102-6, 102-1. 28. 10. 
29. Power 3 : 4. Energy 3 : 2. 30. (a) R c = R, + B* ; (6) 
R c = 3(R^ -f B,). 31. 50 C. 33. 40'6 ft., 0-123 inch. 


1. 0. 2. 187-5. 10. 0-222. 12. 12-35. 13. 8'3. 14. 69. 

15. 15,100. 16. 304. 17. 6 amps. 18. 1000. 19. 1430. 

20. 5025, 0-023, 21,800. 21. 8950. 22. 30'3 Ibs. 23. 34,030. 
28. 35-7. 31. 23,450 ergs. 33. 1-7 amps. 34. 164-5. 35. (a) 3320 ; 
(6) 1790 Ibs. 


1. 0-0432 Ib. 2. 0-09 Ib. 3. 18 dyne-cms. 4. 1870 inch-lbs. 
12. 42-5 microcoulombs. 13. 10~ 4 coulombs. 15. 1600. 16. 0, 
0-0111, 0-0128. 17. 300. 18. 122. 19. 1'25. 

1. 0'929. 

3. 325 volts. 5. 83^ volts. 6. 10 7 ; 1200 volts, each. 7. 7450. 

14. 190 volts. 19. 40. 



1. 97-1 amps., 81-5%, 8-6%, 11-6%, 8-3%. 8. (a) 55 % ; 


7. 20 amps., 1600 r.p.m. 8. (a} 4'2 H.P., 79 % ; (6) 9 H.P., 
84-7%. 9. 960 r.p.m. 10. 188-5 r.p.m. 12. 1180, 1160, 1140 
r.p.m. 13. 190 r.p.m. 14. 4 %. 16. 760. 


2. 5 steps, 1-8 + 1-15 + 0-7 + 0-45 + 0'3 = 4-4 ohms. 

3. 4 steps, 1-95 + 1-5 + 1'25 + I'O = 5'7 ohms. 


1. 1-78. 2. 22,900 coulombs. 3. 6-36, 7'07. 4. 3-02 amps, 
403 volts. 5. (a} 7-5; (6) 7'9. 6. I'll. 8. 14-15, 12-73. 9. 2 : 1. 

10. 1-225. 11. 3142 amps, per sec. 


4. 31,450. 5. (a-) 10~ 4 henry; (6) 2-72 ohms; (c) 3-72 volts. 
6. 0-73 ohm, 0-21 millihenry. 7. 0-37. 11. 43-5, 51-2 amps. 
12. 9-01 amps., 0-0566. 13. 44-2 volts. 14. 4-95 ohms, 0-01 
henry, 0-002. 15. 0-0276 henry. 16. 1-165, 66, 0-00367. 17. 
(a) 62-8; (6)62-8; (c) 89; (d) 45. 18. 1-96 volts. 19. 1230 volts. 


4. 0-0185. 5. 50 joules. 7. 9 mfds. 9. 0-944, 0-0085 coulomb. 
12. 84-2 mfds. 13. 199 mfds. 14. 1-37 amps., 19-8 volts. 
15. (a) 0-0184 henry, 0'5 ; (6) 414 mfds. 16. 0-0624 henry, 196 
volts. 17. (a) 88-6 ; (1) 10'45 amps. ; (c) 26'5 %. 


1. (a) 9-54; (6) 910; (c) 0-954. 2. 0-987. 3. 0-955. 5. 2-76, 
4-5, 16-17, 7-8 millihenries, 1, 1, , ^, ^5. 7. 1429 watts. 

11. (a) 29-8 millihenries ; (6) 340 mfds. ; (c) 2-98 joules. 



6. 7. 61-25. 



3. (a) 900 sq. cms. ; (6) 49,600 volts. 

* These questions admit of a certain amount of latitude. 


2. 24, 237-5. 3. 475. 4. 960. 5. 24, 750. 

5. 2-89. 


1. (a) 90 miles ; (6) 90 sq. inches. 2. \" . 3. 402 ohms, 
0-0126 sq. inch. 4. (a) 5'9 ; (6) 0-059 sq. inch. 5. 0-108 sq. inch. 
6. (a) jei,040,000 ; (6) 5,300. 7. 82 miles. 8. 1 : 14-4. 
11. V 3 times. 21. (a) 219 ; (6) 197'9. 


10. 300 amp. -hours. 11.81-4%. 12. 39,800 ft.-lbs. 15.0-000536. 
21. 104-45. 25. 132, 160-5 grammes. 26. 6 %. 28. 94 miles. 
29. 308 Ibs. 37. 12 K.W., 4-5 K.W. 


1. 1 in 75. 2. (a) Ibs. per ton = watt-hours per ton-mile 
x 0-503; (&) 44-8. 3. 6-25 rzj.p.h. 4. 0'5 ft. per sec. per sec., 
3 minutes. 5. 4-88 sees. 6. 200 amps. 7. 30-1 amps. 8.2160 
Ib.-feet. 9. 374 Ibs. 10. 48 miles. 15. 50%, a further 12-5 %. 


2. 14-4 to 17-3. 10. 25 c.p. 11. Carbon, +29%, -23%. 
Metal, + 17 %, - 15 %. 12. 6-8 watts per c.p. 17. 2^. 18. 400 
hours. 19. 200 hours. 20. 2-36 pence. 21. 1-57 pence. 


3. 4-49 ohms, 449 watts, 55-1%. 4. 2-2 to 5-4 mm., 7'5 to 
16-5 amperes. 9. 14-1 : 1. 10. 1060, 2050. 

* Unless otherwise stated, the voltages and powers in the exercises 
in Section XX. are those at the consumers' end of the line. 


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4 Mr. Edward Arnold's List of 

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Mr. Edward Arnold's List of 


General Editor : DR. J. E. MARK, F.R.S. 

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