168 THE TRANSFORMER. 



Now, c.,R 2 = e 2 = instantaneous value of secondary vol- 

 tage if R,, = total resistance of secondary circuit 

 (including the secondary winding of the transformer). 



Al ^1 



Also e, -- - -^ e a 



where e 1 = instantaneous value of primary back voltage 



N 

 and -^=i = ratio of transformation. 



Hence e, = _=L 

 a 



or 



Consequently the reading of the dynamometer 



COS (h 



Where K = the constant of the dynamometer, so that when 

 used in the usual way c = K ./] 



But Cj e l cos (f> is the power given to the primary winding 

 of the transformer exclusive of the copper losses in 

 the coil. Let this *= W l 



N 



.-. The deflection of the dynamometer = 8= ,_., * . - W 



K- N l R, 



or W l = IT- S -S^S. 



^2 



Tli3 total power supplied to the transformer 



= Wi + watts lost in resistance of winding 



= W, + c\ r lt 



where c, = virtual amperes as read on an ammeter. 

 Also t e useful output 



= c\ (R, - r 2 ). 



Where JR. 2 = total resistance of secondary circuit. 

 r 2 = resistance of secondary winding. 



Hence efficiency of transformer = - 



input 



c./ (R., - r 2 ) 

 K S ~f- R, + c/ n 

 This result forms the basis of the next experiment. 



