CURRENT ON OPENING. 519 



542. CURRENT ON OPENING. Let us first consider the case 

 in which, having closed the current in the principal circuit C, con- 

 nection with the battery is broken by leaving the circuit open; 

 an induced current is formed in the secondary circuit C', but the 

 principal current is entirely broken. The first of the equations (27) 

 no longer holds, and the second reduces to 



L' 



dt 



it is identical with equation (9), and therefore the law of the extra 

 current will be the same in both cases. 



In like manner, on the hypothesis that the opening of the 

 circuit C was instantaneous, and that the current is not prolonged 

 with a variable resistance, as in the case in which a spark is 

 produced, we may determine the initial value of the current pro- 

 duced in C'. 



Let us integrate the second of these equations (27), taking E' = 0, 

 from /=0, to a time T which is infinitely small in comparison with 

 the duration of the induction current in C' ; denoting by l\ the 

 intensity of the current induced at the time r, we shall have the 

 equation 



_M-+L'I;+R' f T r<#=o. 



R Jo 



If we make T diminish towards zero, the last term tends itself to 

 zero, seeing that T has an infinitely small value, and that the intensity 

 I' of the current retains a finate value ; we have then, in the limit, 



ME M 

 (33) ' 1 " 



Thus the initial intensity of the induced current is to the 

 intensity of the inducing current I in the ratio of the coefficients 

 M and L'. 



Hence, at any given instant, we shall have, by equation (10), 



ME _RL< 

 (34) 1' = --'. 



