CHAP. IV] 



INDUCED E.M.F. 



(51 



Core 



primary electric circuit, that is, the one connected to the source of 



!, were perfect, that is, if it possessed no resistance and no 



reactance, the alternating magnetic flux in the core would be the 



same at all loads. It would have such a magnitude that at any 



instant the counter-e.m.f. induced l>y it in the primary wind- 



ould be practically equal and opposite to the impressed 



voltage. In reality the resistance and the leakage reactance of 



ordinary commercial transformers are so low that for the purposes 



of calculating the magnetic circuit the primary impedance drop may 



l>e disregarded, and the mag- 



ilux considered constant 



and independent of the load. 



If the primary applied volt- 

 age varies according to the sine 

 la\v, which condition is nearly 

 fulfilled in ordinary cases, the 

 counter-e.m.f., which is practi- 

 cally equal and opposite to it, 

 also follows the same law. 

 Hence, according to eq. (25), 

 the magnetic flux must vary 

 according to the cosine law, 

 because the derivative of the 



ic is minus the sine. In 

 other words, both the flux and 

 the induced e.m.f. vary accord- FIG. 12. A core-type transformer, 

 ing to the sine law, but the t wo 



sine waves are in time quadrature with each other. When the 

 flux reaches its maximum its rate of change is zero, and tin 

 the counter-e.m.f. is zero. When the flux passes through /en. its 

 rate of change wit h the time is a maximum, and therefore the 

 induced voltage at this instant is a maximum. 



I t m be the maximum value of the flux in the core, in webers, 

 and l<-t / be the frequency of the supply in cycles per second. 

 Then the flux at any instant t is = wl ro8 2/T//, and the e.m.f. 

 induced at this moment, per (urn of the primary or secondary 

 winding is 



e- -d*/dt-2nft m niii '2* ft. 

 Thus, the maximum value of the induced voltage per turn is 



