ALTERNATING-CURRENT MOTORS 321

that is, the polyphase induction-motor equations, <r = cos 8 +

L
j sin 6 = I* representing the displacement of position between

stator and rotor currents.

This shows the polyphase induction motor as a special case of
the polyphase shunt motor, for c = o.

The e.m.fs. of rotation are :

E\ = -JSZ (- j/i + /o sin 6 + ;/7o cos 6)

= SZ(<r/0-/i);
hence :

The power output of the motor is:

p = [tfi, id

cZo) z> (as + c) z + ^

which, suppressing terms of secondary order, gives :
P — Sea2z2{s(ri+c(x0 sin 0 — r0 cos 0)) +c (fi cos 0+:ci sin 0 — cr0) }

[sZZo + ZZi + Zo^,]2 ~ ...... " ....... " ..... " '

(82)

for Sc = o, this gives:

the same value as for the polyphase induction motor.
In general, the power output, as given by equation (82), be-
comes zero:
F = o,
for the slip
— _ ri cos 6 + xi sin 6 — crp ,fi .
0 "~ ri + c (#o sin 0 — r0 cos 0)
183. It follows herefrom, that the speed of the polyphase
shunt motor is limited to a definite value, just as that of a direct-
current shunt motor, or alternating-current induction motor.
In other words, the polyphase shunt motor is a constant-speed
motor, approaching with decreasing load, and reaching at no-
load a definite speed:
So « 1 - so. (84)
The no-load speed, /So, of the polyphase shunt motor is, how-
ever, in general not synchronous speed, as that of the induction