THE TRANSFORMER 275 



where 



BiH=the resistance reaction; 



7ViX(the rate of change of flux) = the back e.m.f. of self- 

 induction. 



In ordinary transformers the term R\ii is very small 

 compared with JViX(the ra t e of change of flux), so that we 

 may neglect it without introducing an appreciable error. 

 We may therefore write 



ei=NiX(rateof change of flux), . . (65) 

 or, in virtual values, 



. ...... (66) 



Effective Flux in the Core Constant. From this equation 

 we see that there must always be a certain flux (effective) 

 through the core in order to balance the e.m.f. impressed 

 on the primary; this flux must exist in spite of any demag- 

 natizing action the secondary current may produce. 



Increase in Primary Current to Balance the Demagnetizing 

 Effect of a Secondary Current. For a secondary current 

 equal to zero there exists a small magnetizing current in 

 the primary; if some load is put on the secondary so that 

 its current is some value 1-2, the secondary coil will 

 produce a demagnetizing action on the core equal to 

 .4x^2/2- But the primary current must always be sufficient 

 to produce in the core the flux <|> e j, hence when the secondary 

 current increases, the primary coil automatically draws from 

 the line an increased current. This increase in primary 

 current will be just sufficient to overcome the demagnetizing 

 action the secondary current has produced. 



Ratio of Currents. We may, therefore, put 



..... (67) 



where I\ is the increase in I\ to overcome the demagnetizing 

 effect of 1 2. But as the magnetizing current of a trans- 



