292 ELECTRICAL ENGINEERING 



This e.m.f. induced in the primary is almost equal in value and 

 opposite in phase to the impressed e.m.f., the vector sum of the 

 two being the small component of impressed e.m.f. required to 

 drive the exciting current through the impedance of the primary 

 winding. Thus 



EI + Eb = / 2i. 



This component has been neglected in Fig. 266. The induced 

 e.m.fs. Eb and E 2 are directly in phase since they are produced 

 by the same flux, and their intensities are in the ratio of the turns 

 on the two windings; therefore, 



E b 4.44/n^ 10- 8 m 



^r = j j4 -i = = ratio of turns. . . (275) 



E 2 4.44/n 2 $ 10~ 8 n^ 



If the secondary is connected to a receiver circuit of impedance 

 Z = R + JX, a current 7 2 flows in it. The primary current is at 

 the same time increased by a component /', the primary load 

 current, which exerts a m,m.f. equal and opposite to that of the 

 secondary current. 



Thus 



nil' = 712/2 

 and 



7? = = ratio of transformation. . (276) 



/ 7l2 



The resultant m.m.f. acting on the magnetic circuit of the trans- 

 former is still that of the primary exciting current and the flux 

 threading the two windings remains almost constant. 



The primary current under load is 7i and has two components I Q 

 the exciting current, which is proportional to the flux, and /' the 

 load current which is proportional to the secondary current. 



The exciting current / can be expressed as the product of the 

 primary induced e.m.f. Eb and the primary exciting admittance 

 yo = go fio', thus 



/ = E b (0 - j&o) = W (g - j&o), .... (277) 



where E' is the component of impressed e.m.f. required to over- 

 come the induced e.m.f. E b . 



The primary load current is I' = / 2 , and is opposite in phase 



to/2. 



As the load on the transformer is increased, the primary in- 

 duced e.m.f. decreases (except when the power factor of the load 



