1 86 



ALTERNATING CURRENTS 



and investigate the law according to which the primary and secondary 

 currents, the power factor, etc., vary with increasing load when the 

 primary p.d. across the terminals of the transformer is kept constant. 



FIG. 126. Transformer Equivalent of Induction Motor. 



The method which we shall follow is one originally given by F. Bedell,* 

 and recently applied to the induction motor by J. Bethenod.f 



Let Ii be the (r.m.s.) primary current, and TI the primary resist- 

 ance (per phase). The primary phase p.d., J which we shall denote 

 by V, may be regarded as made up of the following components : 



(1) The resistance component, rili, in phase with Ij. 



(2) The primary self-inductance component, ^?LiIi, 90 ahead of Ii. 



(3) The component corresponding to the mutual inductance of 

 the two circuits. In order to find the value of this, let us assume 

 the instantaneous value of the secondary current to be i 2 = I m sin pt. 

 The hypothetical liux through the primary, due to this secondary 

 current, is Mi 2 , and the e.m.f. induced by it in the primary is 

 given by 



- -^(M-i 2 ) = - M-7T = - pMI m cos pt 



In order to balance this, the primary phase p.d. must provide a com- 

 ponent + ^>MI m cos pt, i.e. a component whose r.m.s. value is, say, 

 z, and which is 90 ahead of I 2 . 



Considering next the secondary circuit, we have in it 

 (1) The e.m.f. induced by the hypothetical field through the 



* Proceedings of the Physical Society of London, vol. xiv. p. 327 (189G). 

 t L'ticlairage Electrique, vol. xl. p. 253 (1904). 



J I.e. the p.d. per phase, or - x line p.d. 



