134 THE MAGNETIC CIRCUIT [An. 11 



actual secondary current (one to one ratio of transformation), and 

 the primary and the secondary voltages induced by the useful flux 

 are also equal. Each electric circuit of the stator then can be 

 combined with the corresponding rotor circuit. In this manner 

 the so-called " equivalent diagram " of the induction motor is 

 obtained, 1 a way of representation which greatly simplifies the 

 theory of the machine. 



Let 12 be the secondary current in the coils or bars of the actual 

 rotor, and i f 2 that in the equivalent rotor. The counter-m.m.f. 

 of both rotors must be the same, this being the condition of their 

 equivalence, so that 



from which 



12/^2= ( / m2/m 1 )(k b2 n2/k b in 1 ) ..... (65) 



This is the ratio of current transformation in an induction motor. 

 The ratio of transformation of the voltages is different, namely, 



(66) 



In an ordinary transformer 2 '/ 62 = 12/12 =ni/n 2 , because there 

 k b i = k b 2=l, and m2 = m\ = \. For this reason, the induction 

 motor is sometimes regarded as a generalized transformer. 



Taking the product mie for the actual and the equivalent rotor 

 it will be found that the total electric power input is the same in 

 both, provided that the same phase displacement is preserved in 

 the equivalent rotor as in the original one. The latter condition is 

 essential in order that the operating characteristics of the two 

 machines be the same. This means (a) that the total i 2 r loss of 

 the equivalent rotor must be equal to that of the original rotor, in 

 order to preserve the same slip, and (b) that the leakage react- 

 ances of the two rotors must affect the power factor of the 

 primary current in the same way. 



Let r 2 and r 2 ' be the resistances of the actual and of the equiva- 

 lent rotor, per pole per phase. We have the condition that 



(67) 



1 Chas. P. Steinmetz, Alternating Current Phenomena (1908), p. 249; 

 Elements of Electrical Engineering (1905), p. 263. 



