THE IXDUCTION MOTOR 2-17 



proportional to the current times the flux, other factors remain- 

 ing constant. In general, it may be said that the torque for a 

 given slip is proportional to the square of the line voltage. For 

 this reason a 10 per cent, drop in voltage may cause a 19 per 

 cent, reduction in the break-down and starting torques. The 

 etTect of line voltage upon torque is shown in Fig. 234, the torque 

 at one-half line voltage being one-quarter the torque at full-line 

 voltage for each value of slip. 



The stator impedance also reduces the break-down torque. 

 A high stator impedance means a comparatively large impedance 

 drop in the stator for a given current. This decreases the back 

 en if., E, hence the air-gap flux becomes less, and therefore the 

 value of the rotor current at any given slip is reduced. This 

 results in a reduction of torque for each value of slip. 



The effect of each of these various factors upon the break-down 

 torque is shown in the following equation: 

 The break-down torque 



KV* 



where K is constant, V is the terminal voltage, r\ is the stator 

 a nee, x\ is the stator reactance, and z 2 is the rotor reactance 



at standstill. 



The above equation shows that: 



The break-down torque is proportional to the square of the line 

 voltage. 



The break-down torque is reduced by an increase in the stator 

 resistance, and by an increase in the stator and rotor reactances. 



The break-down torque is independent of the rotor resistance. 



The stator and rotor reactances are proportional to the fre- 

 quency and to their respective inductance-. Therefore, it is 

 desirable that the stator and the rotor inductances be kept low 

 and that the frequency lie not too high. 



As the squirrel-rage motor is ordinarily started at low voltage, 

 it develops in it little starting torque. 1 MM -a use the tlu\ is >mall and 

 the rotor currents are ennnderably out of space-phase with the 

 flux. 



It is doiraMe that the stator and rotor inductances be as low 

 as possible This is accomplished by having the slots partially 



