196 ALTERNATING CURRENTS 



of the rotor windings ; so that a given stator current will produce 

 a definite torque, no matter what the resistance of the rotor may 

 be. Increasing the rotor resistance does not, therefore, affect the 

 value of the torque corresponding to a given value of the stator 

 current. 



Again, on referring to equation (12) for the slip, we notice that, 

 corresponding to a given value of OS, and hence also OP (i.e. a given 

 value of the stator current), the slip is directly proportional to the 

 rotor resistance. For a given value of the stator current, therefore, 

 an increase in the rotor resistance has the effect of increasing the slip. 



The introduction of resistance into the motor windings has thus 

 a totally different effect, according as the resistance is introduced 

 into the stator or the rotor windings. For a given value of the 

 stator current, the introduction of resistance into the stator windings 

 reduces the torque and lowers the efficiency ; whereas its introduction 

 into the rotor windings leaves the torque unaltered, but increases the 

 slip and lowers the efficiency.* 



113. Use of Starting Resistances 



Let us next consider the effect of introducing resistance into the 

 rotor windings at the moment of starting, when the slip is unity. 

 By equation (12), 110, we have, putting s = 1 



r 2 x OS = constant 



Hence OS will vary inversely as r 2 . Now, in order to secure high 

 efficiency, it is desirable to make the rotor windings of very low 

 resistance. If, therefore, we simply short-circuit the rotor at starting, 

 ?- 2 being very small, OS will be very large, and hence the point P 

 in our circle diagram (Fig. 129) will lie in the neighbourhood of 

 K. As a result, the length of the perpendicular let fall from Z 

 on OK will be small, i.e. the starting torque will be small, in spite 

 of the fact that the current OP taken by the motor is very large. 

 Let us now suppose that r 2 is momentarily increased by the intro- 

 duction of starting resistances ( 63) into the rotor windings. In- 

 creasing r 2 will cause OS to shorten, the point P travelling downwards 

 from its original position in the neighbourhood of K. This will 

 obviously increase the torque, while at the same time the current 

 is reduced. If necessary, the maximum torque, corresponding to 

 XY, may be obtained at starting by giving to r 2 a value such that 

 the point Z falls on Y. 



We thus see that large starting torque can only be obtained by 



* Since there is a decrease of speed without any change of torque. 



