8 ALTERNATING CURRENTS 



instant, the magnetic flux to which it gives rise will similarly change, 

 and will thus give rise to an induced e.m.f., which becomes superposed 

 on the impressed e.m.f. The resultant e.m.f., which is instrumental in 

 maintaining the current through the resistance of the circuit, is at any 

 instant equal to the algebraical sum of the impressed and induced 

 e.in.f.'s. 



It is therefore obvious that, for given values of the resistance and 

 the impressed e.m.f., the magnitude of the current will be determined 

 by the magnetic ftux to which the current gives rise. In other words, 

 resistance is, in the case of an alternating current circuit, not the only 

 factor determining the value of the current, which also depends on 

 the total flux linked with the circuit when conveying a unit current. 



This latter quantity the flux linked with the circuit when con- 

 veying unit current is defined to be the self -inductance* or in- 

 ductance simply, of the circuit. 



5. Fundamental Equation for a Circuit in 

 which the Current is Variable 



Let us suppose, in the first instance, that all the quantities are 

 expressed in C.G.S. units. If L = self-inductance of circuit, and 

 i = value of current at time t, then the total flux linked with the 

 circuit at time t is Li. The induced e.m.f. is numerically equal to 

 the rate of change of the magnetic flux, but since it always opposes 

 the changes which give rise to it, it must be taken with a negative 

 sign. Thus the induced e.m.f. at time t is given by 



Now, although L = - - is constant for coreless coils, it 

 current 



is no longer so in the case of coils provided with iron cores. It may, 

 however, be assumed to be approximately constant even in this latter 

 case, so long as the magnetization is well below the knee of the 

 B H curve. Assuming, then, L to be constant, we have for the 

 induced e.m.f. the value 



T di 

 " L dt 



If e = impressed e.m.f. at time t, then the resultant e.m.f. at the 

 same instant is given by 



The older term is self-induction, or coefficient of self-induction. 



