ALTERNATING-CURRENT TRANSFORMER 67

Substituting successive numerical values for ii gives the values
recorded in the following table and plotted in. Fig. 33.

ii
€0

0
2120

20
2114

40
2116

60
2126

80
2148

100
2176

120
2213

140
2256

160
2308

180
2365

200
2430

13. ALTERNATING-CURRENT TRANSFORMER

60. The alternating-current transformer consists of one mag-
netic circuit interlinked with two electric circuits, the primary
circuit which receives energy, and the secondary circuit which
delivers energy.

Let n . = resistance, #1 = 2 7r/S2 = self -inductive or leakage

reactance of secondary circuit}

ro = resistance, x& = 2T/>Si = self-inductive or leakage
reactance of primary circuit,

where $2 and Si refer to that magnetic flux which is interlinked
with the one but not with the other circuit.

Let

a = ratio of —:-------- turns (ratio of transformation).

primary

An alternating e.rn.f. EQ impressed upon the primary electric
circuit causes a current, which produces a magnetic flux $ inter-
linked with primary and secondary circuits. This flux $ gener-
ates e.m.fs. jBi and JS» in secondary and in primary circuit,which

E-i
are to each other as the ratio of turns, thus J?»- = —

Let E = secondary terminal voltage, /i = secondary current,
0i = lag of current Ji behind terminal voltage E (where 6\ < 0
denotes leading current).

Denoting then in Fig. 34 by a vector OE = J? the secondary