ELECTRIC CIRCUITS 93 



the integral of this is 



log* (i - j = - jr + log, C, 

 where loge C is the constant of integration. This reduces to 



R- 



or i = - 



it 



when t = 0, i = 0, and C = -5- 

 Substituting this value the current is 

 i = -^f 1 e 



E 

 When t = oc and i = = 



and the current has reached its steady value, which is independ- 

 ent of the inductance of the circuit; calling this value I and sub- 

 stituting 



(132) 



73 



The expression =- is called the time constant of the circuit. 

 Li 



Stopping of Current. If the impressed electromotive force E is 

 removed from a circuit of resistance R and inductance L, when 



IP 



it is carrying a current I = -^ , and the circuit is closed through a 



resistance Ri, the current will not at once fall to zero. 

 The e.m.f. of inductance at time t after the circuit is closed is 



di 



and it opposes the decrease of current. 



The current in the circuit at this instant is 



u/o (R T RTJ 7, 

 or, transposing, = j at, 



