450 Induction of Currents in Linear Circuits [CH. xiv 



Let us consider first the continuous discharge of which the graphs are 

 shewn in fig. 132. The first part of the discharge is similar to the flow 

 already considered in 513. At first we can imagine that the condenser is 



exactly equivalent to a battery of electromotive force E = ^ , and the act of 



discharging is equivalent to completing a circuit containing this battery. 

 After a time the difference between the two cases comes into effect. The 

 battery would maintain a constant electromotive force, so that the current 



would reach a constant final value -^ , whereas the condenser does not supply 



a constant electromotive force. As the discharge occurs, the potential differ- 

 ence between the plates of the condenser diminishes, and so the electromotive 

 force, and consequently the current, also diminish. Thus the graph for i in 

 fig. 132, can be regarded as shewing a gradual increase towards the value 



Tji i r\\ 



^ ( where E ^ j in the earlier stages, combined with a gradual falling off of 

 the current, consequent on the diminution of E, in the latter stages. 



For the oscillatory discharge to occur, the value of L must be greater than 

 for the continuous discharge. The energy of a current of given amount is 

 accordingly greater, while the rate at which this is dissipated by the genera- 

 tion of heat, namely Ri*, remains unaltered by the greater value of L. Thus 

 for sufficiently great values of L the current may persist even after the con- 

 denser is fully discharged, a continuation of the current meaning that the 

 condenser again becomes charged, but with electricity of different signs from 

 the original* charges. In this way we get the oscillatory discharge. 



INDUCTION IN A PAIR OF CIRCUITS. 



518. If L, M, N are the coefficients of induction (L u , L 1Z , L&) of a pair of 

 circuits of resistances R, 8, in which batteries of electromotive-forces E 1} E 2 

 are placed, the general equations become 



(440), 

 (441). 



Sudden Completing of Circuit. 



519. Let us consider the conditions which must hold when one of the 

 circuits is suddenly completed, the process occupying the infinitesimal inter- 

 val from t to t = r. Let the changes which occur in ^ and i. 2 during this 

 interval be denoted by Ai x and At' 2 . Equations (440) and (441) shew that 



