ROTOR SLIP 183 



rotor windings are supposed to be identical, it is evident that LI = La, 

 TI = r 2 , i>i = ro, and v\ = i/a> so that 



L- - M 2 _ 9 a _ 2 _ _ 1 



Since in a well-designed motor the difference between L and M 

 would always be small, we may write, approximately, .L -f M = -JM, 

 so that 



105. Behaviour of Motor Independent of Number 

 of Turns in Rotor Winding. Rotor Slip 



We shall next show that, so long as the number and shape of the 

 slots in the rotor core, and the total cross-section of copper in each 

 slot, remain unaltered, no difference whatever is produced as regards 

 the behaviour of the motor by altering the number of turns in the 

 rotor winding. 



For, let us suppose that the turns have been increased w-fold. 

 This will have the effect of an w-fold increase in the e.m.f. induced 

 in the secondary winding. But the resistance and self-inductance of 

 this winding having both been increased w 2 times, the impedance 

 will be increased in the same ratio, while the angle of lag, whose 



tangent is given by - , will remain unaltered. Thus the 



resistance 



current will be reduced in the ratio , but its phase will remain 



m 



unaltered. The ampere-turns on the rotor, and the rotating field due 

 to them, will obviously be the same as before, for while the current 



has been reduced to th of its original value, the turns have been 

 m 



increased w-fold ; the phase of the current having undergone no 

 change. 



On account of the rotation of the rotor, the frequency of the rotor 

 currents is much less, under normal running conditions, than that of 

 the stator currents. Let n\ be the primary frequency, and 712 the 

 secondary. The slip s ( 61) is defined by the equation 



and is frequently expressed as a percentage, in the form 100 . 



