THE INDUCTION MOTOR. 



359 



Hence the voltage induced in the rotor conductors 

 by the rotating field will partly be spent in overcoming 

 the self-induction of the rotor winding (i.e., producing 

 the rotor stray field), and part only will be spent in pro- 

 ducing the currents which furnish the torque. The 

 conditions may therefore be represented by a triangle 

 of electromotive forces as in Fig. 179, in which the ratio 

 of the sides 



AB E.M.F. due to self-induction or leakage lines 

 B C E M.F. due to lines which cross the air gap 



= tan <h, where is the angle of lag of the 

 useful field 



current in the rotor circuit. 



In this triangle CB represents the phase of the current 

 so that it will be seen that the current lags behind the 

 total E.M.F. of the rotor. This is an important matter, 



FIG. 179. VOLTAGES IN ROTOR CIRCUIT. 



Stationary. Slip. Synchronous. 



FIG. 180. RELATION BETWEEN SLIP AND TORQUE OF MOTOR. 



since the line AC represents the phase of the inducing 

 field acting upon the conductor for which CB represents 

 the phase of the current induced. The pull exerted 

 upon the conductor is proportional to the product of 

 strength of field and current in conductor. These 

 quantities are, however, never at their maximum values 

 at the same time, the average value of their product being 

 c.z. cos <j), where c and z are the virtual values of the 

 current and flux respectively. This may be proved in 



