Tl = 



Alternate Current Transformier. 

 E, E, 



rA(l+^r:Cos8 + ^^) ''^^^ 



[The same is obvious otherwise, for 



where Lj is the inductance of the primary on open secondary]. 

 Also on open secondary as ^' = 0, ic. 



tana= y=Cot8 (q.p.) 



Sin8+ — 



or Cosa=:SinS 

 that is, //le poiver Jaclor of a closed circuit transformer on open 

 secondary is equal to the sine of the angle of magnetic retardation 

 of its iron for the period audflux density used. 



8. In the diagram Fig. 2, we see that 0,2 is behind Cj in phase 

 by an angle tt-/? where ;8=:0NM. 



Projecting ON on NM and on a line perpendicular to NM, 

 we find that 



A'Cos;8=:Sin(8 + <^') + ^'Cos<^' 



A 'Sin^=Cos(S + </)'). 



Also if Cj be behind Ej in phase by an angle tt + X we see that 



A = a-/3. 



9. The amplitudes of the different quantities can now be 

 written down in terms of Ej as follows : — 



E, A' 



Ci t-i 

 1 ~ ~ T\' 



...F^. 



F_«iCi_ «A _ E, n. 



Amp («,c, + «A) ----^- o^c;^' = v;r, D' 



and if E'o be the total e.m.f. generated in the secondary, 

 «o El 



E'.,= 7f«„F = - :f^, 



The total power P'.^ developed in the secondary 

 = iE,C.Xos,^ =i^^Cr- ^.^ -^,^-^^- 



10. If E.J be the terminal e.m.f. of the secondary and Cos</> 

 the power factor of the load, the relations connecting these 



