92 ELECTRICAL ENGINEERING 



= Xi = inductance of A, 

 >A/! = ^ft = mutual inductance of A upon #, 

 tti0 Sl = X Sl = self-inductance of A, 

 but 0i = 0ji/i + Sl , and therefore 



^ = ^ + ^, (129) 



and, similarly, 



^ = ^ + ^- ' - . . . (130) 



When there is no mutual inductance the inductance of a cir- 

 cuit is the same as its self-inductance. 



68. Self-Inductance of Continuous Current Circuits. The 

 self-inductance of continuous current circuits is only apparent 

 when the current is increasing or decreasing. The two most im- 

 portant cases are when the current is starting and when it is 

 stopping. 



Starting of Current. When a constant electromotive force E 

 is impressed on a circuit of resistance R and inductance L the 

 current does not immediately reach a steady value on account of 

 the opposing e.m.f. due to inductance. If at time t after E is 

 impressed the current is changing at the rate 



di. 



the e.m.f. of inductance is 



e = -L-- 



By Lenz's law it opposes the impressed e.m.f. and is therefore 

 negative. 



The e.m.f. acting on the circuit is 



and the current is 



._ E-Ldi. 

 R dt' 



, . E L di 



therefore t __=___, 



di Rdt 

 or, transposing, = - ; 



