THE INDUCTION MOTOR. 365 



number of deflections in either direction in one minute, 

 divided by number of pairs of poles, gives the value of 

 the slip in revolutions per minute. 



The slip at any load can be approximately pre- 

 determined without actual measurement from a knowledge 

 of the rotor current and resistance, as given in the 

 following formula for a 3-phase rotor : 

 S _ 3 c.f r, 

 v W + 3 c 2 2 r 2 

 the symbols having the following significations : 



S Slip in revolutions per minute. 



v = Speed of rotating field in revolutions per minute. 



c, = Current in rotor winding per phase. 



r 2 : = Resistance of rotor winding per phase. 



W = Output of motor in watts. 



The above formula may be arrived at from the follow- 

 ing considerations : 



watts output 

 Thetorqueonageneratorarmature = speed relative to field" 



The watts generated in the rotor armature are 3 c, 2 r 2 , and 



3 Co 2 r 

 hence torque on motor shaft = n ' - 2 . 



Also torque exerted by the rotor is equal to 



output of motor W 



speed of rotation of shait = 2 2 where " 2 = s P eed of rota- 



tion, hence torque = 



Adding the two ratios together we obtain 

 W + 3 c 2 2 r, _ 3c 2 2 r 



27T ( 2 + ti) ' %TT S 



or since v* + S = v we obtain 



S _ 3 c 2 2 r 2 



_ 



v W + 3 c,- r, 

 as in the equation above. 



Measurement of Resistance of Windings. The measurement 

 of the resistance is usually carried out by sending a 

 measured direct current through the windings, and noting 

 the drop in voltage. In 3-phase motors the resistance 

 per phase will not be obtained by this method, since in a 

 star-connected stator there will be two windings 

 between each pair of terminals, and in the case of a 

 mesh-connected winding there will be two paths in 

 parallel between the terminals. 



