2 . ELECTRICAL APPARATUS
a given torque when starting by autotransformer. However,
high rotor resistance means lower efficiency and poorer speed
regulation, and this limits the economically permissible resistance
in the rotor or secondary.
Discussion of the starting of the induction motor by arma-
ture rheostat, and of the various speed-torque curves produced
by various values of starting resistance in the induction-motor
secondary, are given in *' Theory and Calculation of Alternating-
current Phenomena" and in " Theoretical Elements of Electrical
Engineering."
As seen, in the induction motor, the (effective) secondary re-
sistance should be as low as possible at full speed, but should
be high at standstill—very high compared to the full-speed
value—and gradually decrease during acceleration, to maintain
constant high torque from standstill to speed. To avoid the
inconvenience and complication of operating a starting rheostat,
various devices have been proposed and to some extent used, to
produce a resistance, which automatically increases with in-
creasing slip, and thus is low at full speed, and higher at standstill.
A. Temperature Starting Device
2. A resistance material of high positive temperature coeffi-
cient of resistance, such as iron and other pure metals, operated
at high temperature, gives this effect to a considerable extent:
with increasing slip, that is, decreasing speed of the motor, the
secondary current increases. If the dimensions of the secondary
resistance are chosen so that it rises considerably in tempera-
ture, by the increase of secondary current, the temperature and
therewith the resistance increases.'
Approximately, the ^temperature rise, and thus the resistance
rise of the secondary resistance, may be considered as propor-
tional to the square of the secondary-current, iit that is, repre-
sented by:
r = r° (1 + aii2). . (1)
As illustration, consider a typical induction motor, of the
constants:
eo = 110;
Yo = g- jb = 0.01 -0.1;;
ZQ = r0 +jxQ = 0.1 + 0.3;;
Zi = ri+jxi = 0.1 + 0.3;';
the speed-torque curve of this motor is shown as A in Fig. 1,