[mcnaughton] electric SERIES TRANSFORMERS 



Substituting in Equation (13) 



195 



(14) 



M N, f r -(x-Jy) ^ (x+J y) 



=l,L^ N^ AI 1 -(x-Jy)R2 -(x+Jy) + R, 

 IL L, L 



R^t 



e L, — 



■X t 



-(x-Jy) /y* (x+Jy) 

 (x-Jy) + R2 -(xJy) + R, 



■Jyt 



Rationalizing the denominator and abbreviating by 

 writing X for /r^ '^ 



— X 



Then 



^2 J 



(15) 



:MNjA L 



r- 



L^N, (.V + y^) 



(x-Jy) (X-Jy) + (x + Jy) (X + Jy) 



-Rat 



f L, 



-xT 



+ Jyt -Jyt 



- (x-Jy) (X-Jy) s + (x + Jy) (X+Jy) e 



Expanding :- 



(16) 

 i,=M N, A 



L,N, (X^ +y^) 



R^t - xt 

 2 Jy(X + x) U J-^e 



■1 



(xX-y=^)Jy+(X + x: 



-Jyt 



1+Jyt 



xX-y2-Jy (X + x) e 



Collecting terms:- 



(17) 



• _^^, A 



"«"L.N, (X^+y2) 



-R;t - xt 



2 Jy (X + x) £ L^ - e 



] - J y t + J y^ 

 xX — y^jf — £ 



Jy 



x + 



3 



r 



-Jyt +Jyt 



€ + e 



