4 ELECTRICAL APPARATUS

This gives curve A of Fig. 1. At any value of torque, T, corre-
sponding to slip, s, the secondary current is:

herefrom follows by (2) the value of r'i, and from this the new
value of slip :
*' -s- s = r\ - n. (3)
The torque, T, then is plotted against the value of slip, s', and
gives curve B of Fig. 1. As seen, B gives practically constant
torque over the entire range from near full speed, to standstill.
Curve B has twice the slip at load, as A, as its resistance has
been doubled.
3. Assuming, now, that the internal resistance, r*i, were made
as low as possible, r: = 0.05, and the rest added as external
resistance of high temperature coefficient: r° = 0.05, giving the
total resistance :
r't = 0.1 (1 -h 0.5 z'i2 10-4). (4)
This gives the same resistance as curve A: r\ = 0.1, at light-
load, where i\ is small and the external part of the resistance cold.
But with increasing load the resistance, r'i, increases, and the
motor gives the curve shown as C in Fig. 1.
As seen, curve C is the same near synchronism as A, but in
starting gives twice as much torque as A, due to the increased
resistance.
C and A thus are directly comparable: both have the same
constants and same speed regulation and other performance at
speed, but C gives much higher torque at standstill and during
acceleration.
For comparison, curve A' has been plotted with constant
resistance TI = 0.2, so as to compare with B.
Instead of inserting an external resistance, it would be pref-
erable to use the internal resistance of the squirrel cage, t6 in-
crease in value by temperature rise, and thereby improve the
starting torque.
Considering in this respect the motor shown as curve C. At
standstill, it is: ii = 153; thus r\ = 0.217; while cold, the re-
sistance is: r'i = 0.1. This represents a resistance rise of 117
per cent. At a temperature coefficient of the resistance of 0.35,
this represents a maximum temperature rise of 335°C, As seen,