Alternate Current T^^ans former. 73 



D A Cosa= SinS + - + e-{cos<P + '^ ^"^ ^ ' + {x,.,->rX.JCos{h + <P) 

 + 2(x.^Sin(t>+-^ )Sin8 + 2— Sin0 + (jCi.,x-,,i + ~ )Cos0| 



\ T2 '''1 ^ ''"l''"2 / 



r^i^22 ■ ■^21 ~l" ■^12 ~| p Sil'E^'^ t ^ ■ '^12^21 ^ 



L Tj r2 J Tl TiTa^ T.^ 3 



Q=^„ + ^,^ + ^#(say). (VII.) 



The power Pj taken in by tlie transformer on the primary side 

 being 



= lEiCiCosa 

 we find 



P=l?J % (VIII.) 



63. From equations (V.) and (VI.) we get 

 ex,., r,r, D 



R 



;72C,_«iEi 1 ^jj^> 



and as E2Cos<^=RC2 and 0= j^ Cos^, 



we find that 



E2='1^^^E,. (X.) 



As the output P2 = ^E2C„Cos<^ we find that, substituting for 

 E2 and C2, that 



P,=^3' ^'^Oos.^. (XI.) 



64. Equation (IV.) of i^ 61 can be written in the form, 



(1 +*•!./) {n,C, + n,C,) = - {(x^-x,^e'^+^e " '(l~V + 



^ T2 



but niC^ + n.jG^i—F/a; 



and, by § 59, fi, we find that 



F/o- «A (XII.) 



