98 TREATISE ON ALTERNATING CURRENTS. 



-Again, from equations (13) 



12 pM 



If, now, the secondary resistance is negligible compared with its 

 reactance, and if its reactance is due simply to its self-induction 

 2, this equation becomes 



ii __ L% 



iz~~ M 



If, further, there is no leakage, and the external circuit is non- 

 reactive, so that (see Ex. 5, p. 9) 



LI being the primary self-induction, we have (see Ex. 9, p. 9) . 



where N\ and N z are the number of turns on the primary and 

 secondary coils respectively. 



Let F f be the P.D. between the secondary terminals. 



If 5 2 ', TZ are the reactance and resistance respectively of the 

 external secondary circuit, we have 



V = rA + fcfc'ia ...... (21) 



and the secondary terminal P.D. is in phase with the secondary 

 current if the external circuit is non-reactive. Combining equa- 

 tions (12) and (21), and putting for shortness 



we get 



a kb 



That is, F' lags behind e by an angle TT ^>, where 



tan ^ = W-^', (23) 



