366 THE INDUCTION MOTOR. 



In order to get over the necessity for special calcula- 

 tions for each case, the method often adopted is the 

 following : 



The resistance from terminal to terminal between each 

 pair of terminals is measured, the three resistances being 

 then added together; the result when divided by two 

 is called the " equivalent " resistance of the winding. 

 It is evident that for a star-connected stator the 

 equivalent resistance 



_ 3 x 2r _ 



2 



where r = resistance of each phase winding. 

 In the case of a mesh-connected winding 



- 



R = 



The special convenience of the equivalent resistance 

 is that when multiplied by the square of the current 

 supplied to the motor it gives the copper losses in watts 

 directly. 



Thus in the case of the star winding losses = 3 c 2 r, 

 and since line current = current per phase and 3r =B 

 losses - C*R. 



Similarly with mesh-connection phase current = 



,-q- line current, and losses = 3 ( ,-- V r = (TV. 



And since in this case r --= E 



We have watts lost in resistance = C 2 E. 



Speed Regulation of Induction Motors. The speed of an induc- 

 tion motor depends primarily on the speed of the rotating 

 field, i.e., on the frequency of the supply. The revolutions 

 per minute of the motor when running synchronously 



= v = , where n = periodicity of supply circuit 



and p = number of pairs of poles in the motor. 



The actual speed under working conditions will be 

 slightly less than this on account of the slip, but will 

 generally be between the speed as given above and a 

 speed about 5 per cent, lower. 



It is not generally possible to vary the periodicity of 

 the supply current in order to regulate the speed of the 

 motor. 



