THEORY OF TRANSFORMER. 99 



If the external circuit is non-reactive, this becomes 



I 



tan A = - 

 Y a 



If, further, there is no leakage, so that 



Sl s 2 = 



it reduces to 



tan d> = - (24.i 



82 i 



r 2 ri 



which is always a small quantity, but never zero, so that the 

 secondary P.D. lags behind the primary P.D. by nearly 180 degrees 

 in phase. 



Now in the eneral case 



' /, ' ~~ ' ' Jv ' 



&T 2 0s' 2 a a ftT 2 Ds 2 

 is greater than, equal to, or less than 



b 



a 

 according as 



(ft 2 -f & 2 )s 2 ' 



is greater than, equal to, or less than 0. That is, the angle of lag 

 $ increases as the self-induction of the external secondary circuit 

 increases and becomes negative when the reactance becomes 

 negative, due to capacity. 



The secondary terminal P.D. is in exact opposition to the 

 primary terminal P.D. when 



brz -f- as% = 



The output, W\ of the transformer is the scalar product of F' and i z . 

 From equations (12) and (22) and 37, Chap. VII., this can be 

 determined. 



Writing (12) in the form 



p Me 



+ kb)e 



