62

ELECTRICAL APPARATUS

hence by (14) :

Pi = ii (eo - rii - aj£
expanded, this gives :

Pi = eoii - r

+ i* (itii — n«),

+• i2

(16)

(17)

where: i = total current. That is, the power out-

put at the armature conductors is the power input minus the
i2r loss.

The curfent in the field is :

hence, the fir loss in the field; of resistance, r\.

(18)

— /=27)2r, HQ^

— e o 7*1. (,iy;

The hysteresis loss in the induction motor of mutual induced
voltage, e, is: ezg, or approximately:

Pf = eQ*g, (20)

in the synchronous motor, the nominal induced voltage, ef does
not correspond to any flux, but may be very much higher, than
corresponds to the magnetic flux, which gives the hysteresis
loss, as it includes the effect of armature reaction, and the hys-
teresis loss thus is more nearly represented by e^g (20). The
difference, however, is that in the synchronous motor the hys-
teresis loss is supplied by the mechanical power, and not the
electric power, as in the induction motor.

The net mechanical output of the motor thus is:

= e0ii - iV - 626Vi - e\ (21)
and herefrom follow efficiency, power-factor and apparent
efficiency.
44, Considering, as instance, a typical good induction motor,
of the constants:
eQ = 500 volts;
70 = o.Ol - 0.1 j;
Z0 = 0.1 + 0.3J; '
Zi = 0.1 + 0.3 j.