THEOKY OF THE INDUCTION MOTOR. 155 



1O8. We will, however, for simplicity, consider the induction 

 motor alone. 



Suppose that each circuit in the stator consists of NI turns of 

 wire, and each rotor circuit of N% turns ; and let the resistance 

 and reactance of each stator circuit be r\ and s\ respectively, and 

 of each rotor circuit, when at rest, r 2 and s 2 respectively ; and let 

 the E.M.F. induced per turn in the stator coils be e. 



If wi and W2 are the angular velocities of the rotating field and 

 rotor respectively, and the frequency of the current i\ in a stator 

 coil be n, then the frequency of the current 2 in the rotor coils 

 will be 



or, putting K for the slip 



0)1 



the frequency of the rotor currents is MI. 



We will suppose that the E.M.F. s and currents have their 

 E.M.S. values. 



It follows that the E.M.F. E% induced per turn in the rotor 

 coils is K. The E.M.F. induced in each circuit of the rotor 

 coils is therefore given by 



2 = K N*e ....... (6) 



and the vector equation of E.M.F.s is 



7*2*2 + kK&2fa = KNtf ...... (7) 



the reactance, when in motion, being KS%. Thus 



/ox 



' ' ' ' ' ' \ / 

 KS 2 



The power spent per circuit in heating the rotor is then the scalar 

 product of i 2 and J 2 , that is 



a 

 Power wasted == - 2 -^-^ 



Transactions of the American Institute of Electrical Engineering, vol. xii. pp. 851-365 

 (1895); also "Alternating-current Motors," by W. G. Rhode?, Electrical Beview, 

 vol. xxxvii. pp. 599, GOO (1895); and vol. xxxviii. pp. 139-142 (1890). 



