VARIABLE STATE OF A CURRENT. 509 



It may be observed that these values of the two integrals are 

 the same as if there had been a current of strength - during 



T 



the time - , which had been succeeded by a current of the 

 R 



normal intensity I v during the rest of the time. 



Suppose that the electromotive force is constant, and that we 

 measure the time from the closing of the circuit ; we have then 



i.-o, 



and therefore 



'- 



533. The expression ^T represents the strength of the extra 

 R 



current obtained after the moment /. It will be seen that the current 



only attains its normal strength after an infinitely long time ; but if 

 -p 



the ratio - is very great, which it is in most cases, the exponential 

 J_/ 



tends rapidly towards zero, and after a very short time, the real 

 strength only differs from the final strength, by a quantity which 

 may be neglected. In order to calculate after what time this 



difference would be below a given quantity, - for instance, we 

 may put 



from which we deduce 



The total quantity of electricity which corresponds to the extra 

 current is 



(6) 



R 2 



it is the same as if the current had had half the intensity of the 



11 lE - 2L 



normal value - -- m the time . 

 2 R R 



