304 ELECTRICAL APPARATUS

that is, the frequency of rotation—while the e.m.f. of alternation
is 90° ahead of the flux alternating through the coil—that is, the
flux parallel to the axis of the coil—and proportional to the fre-
quency. If, therefore, Zf is the impedance corresponding to the
former flux, the e.m.f. of rotation is —jSZ'I, where S is the
ratio of frequency of rotation to frequency of alternation, or the
speed expressed in fractions of synchronous speed. The total
e.m.f. consumed in the circuit is thus:

E = Z«I + ZI - JSZ'L (2)

Applying now these considerations to the alternating-current
motor, we assume all circuits reduced to the same number of
turns—that is, selecting one circuit, of n effective turns, as start-
ing point, if Hi = number of effective turns of any other circuit,
all the e.m.fs. of the latter circuit are divided, the currents multi-

71'

plied with the ratio, --> the impedances divided, the admittances

11

multiplied with (—J2. This reduction of the constants of all

circuits to the same number of effective turns is convenient by
eliminating constant factors from the equations, and so permit-
ting a direct comparison. When speaking, therefore, in the fol-
lowing of the impedance, etc., of the
different circuits, we always refer to
their reduced values, as it is cus-
tomary in induction-motor designing
practice, and has been done in pre-
ceding theoretical investigations.
173. Let, then, in Fig. 147:
EQ, foj ZQ = impressed voltage,
current and self-inductive impedance
respectively of a stationary circuit,
FIG. 147. $i> /i? Zi = impressed voltage,

current and self-inductive impedance
respectively of a rotating circuit,
r ==. space angle between the axes of the two circuits,
Z = mutual inductive, or exciting impedance in the direction
of the axis of the stationary coil,

Z' = mutual inductive, or exciting impedance in the direction
of the axis of the rotating coil,

Z" = mutual inductive or exciting impedance in the direction
at right angles to the axis of the rotating coil,