THEORY OF SINGLE-PHASE MOTOR 



233 



which shows the variation of the torque with speed on the supposition 

 that B a is constant* The exact shape of this curve will depend on 



FIG. 145. To illustrate Theory of Single-phase Induction Motor. 



-X leakage reactance at synchronism 

 the value of^ = 13555^ 



In Fi" 146 are 



plotted the curves connecting sin 20 2 sin 20i with the speed, ex- 

 pressed as a fraction of the synchronous speed, for four different 



values of. The curves marked A, B, C, and D correspond to 



#A 

 values of-* equal to 20, 5, 2, and 1 respectively. Curves A and B 



may be regarded as fairly typical of ordinary single-phase induction 

 motors. Curves C and D correspond to effects which might be pro- 

 duced by introducing additional resistances into the rotor windings. 

 It will be seen that the introduction of resistance has an effect 

 markedly different from that obtained with a polyphase motor. Not 

 only is the maximum value of the torque rapidly reduced, but when 



v\ 



is made equal to unity, the motor becomes quite incapable of 



exerting a driving torque at any speed whatsoever (curve D). Hence 

 the introduction of resistances into the rotor for purposes of speed 

 regulation is attended with the serious disadvantage of reducing the 

 overload capacity of the motor, and cannot be used as freely and 

 advantageously as with polyphase motors.f 



It may be shown that for a single-phase induction motor as for 

 a polyphase one there exists a circle which represents the locus of 



* This condition Is, of course, not strictly fulfilled, on account of the existence of 

 the primary or stntor leakage flux; as the latter increases, B decreases, 

 t Resistances are introduced at starting to limit the starting current. 



