508 PARTICULAR CASES OF INDUCTION. 



532. VARIABLE STATE OF A CURRENT. The establishment of 

 a current in a circuit represents a certain amount of work which 

 is the potential energy of the current; this energy is absorbed at 

 the starting of the current, and is restored when the electromotive 

 forces disappear. In all cases, the effects of self-induction, which 

 are the consequence, determine the law of intensity during the 

 variable period, whether at the closing or opening of the circuit. 



Consider a single circuit. Let R be the total resistance, L its 

 coefficient of self-induction, and E the electromotive force which 

 it contains. We have the equation 



dt 



If we suppose L constant as well as E, the strength at each 

 moment is given by the formula 



(2) l-^ + ^-l^-r, 



I being the initial value and I x that which corresponds to the 

 permanent state. 



The total quantity of electricity which passes in time /, is 



f' -d g-) 



J' l ^ 



If the time / is sufficiently great, we have simply 



C \ L 



\o) i \ JR. 



Jo 



We have also, for a sufficiently long time, 



this expression is proportional to the calorific energy expended in 

 the circuit. 



