Alternate Current Transformer. 15 



and the above equation in P2 can be put into the form 

 _ 6Cos0 



•^"l+2;)^Cos<^+^^CosV (/ + ?') 

 or 



j>/ = ^Cos<^[l-2/eCos.^ + (3/-^^)^^OosV] 

 Inverting this series we get 



^Cos0 =y[\+2py + (5/ + ^^)/] 



[where Do = 1 +/j + i(4/ + ^^)/l 

 a very important relation, as it will enable us to transform all 

 our fornmlae from the independent variable to what is the 

 practically important independent variable, namely, the output of the 

 transfortner. 



19. Thus if we let 



a= 



riTi( 1 + .TiCosS + j 



= Primary current on open secondary, 

 the formulae in § 13 become 



Ci = Co V /I^o'( 1 + 2x,CosS + 2-^ ) + 2_>'Sin(8 + <^ ) + jj-^ 



71 



C,--iDoCoy 



n. 



F r^ */ 1 ^ i „. Cos</)\ / , 1\ 



O" -L'o ^ ~2 '2 



^ ;/, -x^ / , . ^ CN . SinS 



Do(l+.riCos8 + ^) 



also 



r 1 / Cos<?i\ „ / „ 1 \ ^ 



Iron loss = PoSin8-^ jp + 2_y(xjSin<^ + -^^ j +/(^"2 +^2) \ 



( /I 1 X'l^ o ^Sin8^ ^ Sin(8 + 0) 

 Copper losses = Poi/Do'(- + - + 2-C0S8 + 2 ) + 2y ^ -^ 



^^ r Vn T2 Ti T1T2 / -^ Ti 



^D„ 



_ Cos8 + jt^Sin (^ + ( X + 2/Sin (/. )y ' 

 tan a - gj^^g ^^^^^ </. + (T + 2/Cos )/ ^^'P'^ 



Cot^ = tan(8+^) + ^^^^^(q.p.) 



