MONOPHASE INDUCTION MOTORS. 159 



Therefore the input of the motor, being the scalar product of 

 i\ and E\ t is given by 



r( ?* , pl , Knr 2 KSis 2 . 



W= { -37-0-7 2 2\ + H 1 + 27 2~T~2 2^ 4- 



L\ar + c 2 s 2 *> I cr^ + rV 



4- 



,_, n 2 ^ 1 ^ 

 *e ^ 



Therefore the efficiency of the motor is given by 

 P_ 



r a (l-*) 



Cl 



(p 4~ ?*IP 4" ^1" )(^*a 4~ K* 



K 



(22) 



It is to be noticed from equation (14) that the torque is pro- 

 portional to the square of e. Now e is the E.M.F. induced per 

 turn in the stator winding by the rotating magnetic field ; there- 

 fore, for a given angular velocity of the rotary field, e is propor- 

 tional to the field strength. To produce a large torque, it is 

 necessary, therefore, to work at a high induction density in the 

 stator. It follows that a high efficiency and large torque are 

 antagonistic, since with a high induction density the hysteresis 

 loss is large. 



MONOPHASE INDUCTION MOTORS. 



1O9. In the induction motors already described, the torque at 

 any instant is due to a difference between the angular velocity of 

 the magnetic field and that of the rotor. 



Suppose that in an induction motor the stator coils form a 

 single circuit fed by a single alternating current, while the rotor 

 is exactly the same as in a rotary field motor. In this the 

 resultant magnetic field preserves a constant direction, and 

 simply alternates in sense as in a stationary transformer; so 

 that if the rotor is at rest, the alternating currents induced in the 

 rotor coils produce no torque, since the impulses are alternately 

 in opposite directions. If, however, the rotor has, by some means, 



