102

ELECTRICAL APPARATUS

M

a

reaction of the motor is eliminated by the comparison with the
polyphase motor.

In calculating the effective impedance of the motor at stand-
still, we consider the same as an alternating-current transformer,
and use the equivalent circuit of the transformer, as discussed
in Chapter XVII of "Theory and Calculation of Alternating-
current Phenomena." That is, the induction motor is con-
sidered as two impedances, Z0 and Zi, connected in series to the

t

z

FIG. 35. — The equivalent circuit of the induction motor.

impressed voltage, with a shunt of the admittance, YQ, between
the two impedances, as shown in Fig. 35.
The effective impedance then is:

Z =

1

-7+ i

- /„ + -

(30)

approximately, this is:

Za =

(31)

This approximation (31), is very close, if Zi is highly inductive,
as a short-circuited low-resistance squirrel cage, but ceases to be
a satisfactory approximation if the secondary is of high resistance,
for instance, contains a starting rheostat.
As instances are given in the following the correct values of the
effective impedance, Z, from equation (30), the approximate
value (31), and their difference, for a three-phase motor without
starting resistance, with a small resistance, with the resistance
giving maximum torque at standstill, and a high resistance: