Study of Transformers. 



181 



E'. 



C if there is no 

 magnetic leakage. 



C if there is a leakage 

 of one-tenth of 

 one per cent. 



1 



•5 

 •2 

 •1 



9-0909 sin kt. 

 16-6667 sin M. 

 33-333 sin M. 

 50 sin let. 



8-79 sin (7tf- 15°). 

 14-907 sin {Jet -27°). 

 23-57 sin {Jet -45°). 

 27-74 sin(to-56°). 



So that even wnen the leakage is so insignificant as this, its 

 effect is very marked when there is a heavy load on the 

 transformer. Of course, the secondary current and secondary 

 voltage would exhibit the same kind of discrepance. 



I do not know how much magnetic leakage there may be 

 in an ordinary transformer ; and indeed my present purpose 

 is only to show students that as there is always some leakage, 

 it ought to be taken into consideration. 



I think it impossible that the leakage should be less than one 

 one-thousandth of the whole induction. That is, that *001 of 

 the whole induction produced by the primary escapes the 

 secondary coil, and '001 of the whole induction produced by 

 the secondary escapes the primary. The result is practically 

 the same as if I said that '0005 of the primary escapes the 

 secondary, and "0015 of the secondary escapes the primary. 

 Now, taking a current of frequency 159 with the above- 

 mentioned transformer, let the primary voltage be 



Y=a 1 $m(1000t + u 1 ) + a 2 sin (2000* + a 2 ) + a 3 sin (3000* + a 3 ) 

 + a 4 sin (4000 t + a 4 ) + &c. 



If there were no leakage, the primary current would be 

 with great exactness, if B/ = 1 ohm, 



C= 



«3 



^L sin (1000 1 + «i) + ^ sin (2000 t + « 2 ) 



+ jf sin (3000 * + « 3 ) + j^ sin (4000 t + « 4 ) + &c. 



Whereas with only one-tenth of one per cent, of leakage, the 

 primary current is 



= I ^sin (1000 * + ai -15°)+ fH^sin (2000 t + « 2 -28°-6) 

 + j^sin (3000 t + « 3 _39°) + ^sin (4000 * + * 4 -48°) + Ac. 



