514 PARTICULAR CASES OF INDUCTION. 



We get from these equations, in the two cases, 

 L//=Q , 



f 

 J 



These results were evident a priori, for the discharge is com- 

 plete, and the work it produces is reduced to a disengagement of 



/e 



heat ; the calorific work RIV/ should be equal to the electrical 



energy (89) which the conductor had before the discharge, that 



iQ 

 is to say, - . 



537. The nature of the discharge is very different according 

 as the solution is given by equations (22) or equations (23). 



In the first case the discharge is continuous. The strength 

 of the current begins by being zero, passes through a maximum, 

 and then decreases to zero. The maximum is at the time deter- 



dl 

 mined by the condition -r = ^t r 



R \ 2a* R 



a ) e = 1-a, 



2 L J 2 L 



which gives 



538. In the second case, the values of Q and of I are given 

 by the periodic functions; the conductor takes alternately charges 

 in contrary directions, and the wire is the seat of alternating 

 currents. 



The times of maxima and minima of charge correspond to 

 1 = 0, that is to say, to 



sin a'/=0, or a!t = nir. 



