510 PARTICULAR CASES OF INDUCTION. 



534. EXTRA CURRENT ON OPENING. Suppose that the per- 

 manent regime being established, we suddenly introduce a resistance 

 r in the circuit ; we shall have at the two limits 



IO ~R' 



E 

 E 



and the strength at any instant is given by the equation 

 (7) I " 



The value of the total quantity of electricity which corresponds 

 to the extra current is 



(8) ' EL 



This case has some analogy with that in which the circuit 

 is broken in air, the resistance r being that of the layer of gas 

 traversed by the spark on breaking; but in reality this resistance 

 is far from being constant 'while the phenomenon lasts. 



Suppose that instead of breaking the circuit we had separated 

 it from the battery, by replacing the latter by a wire of the same 

 resistance, so that the total resistance of the circuit is still repre- 

 sented by R, which simply amounts to suppressing the electromotive 

 force. Equation (i) reduces to 



(9) L 



Determining the constant by the conditions that for /=0 we 

 p 



have I = , it follows that 

 R 



E _R 



(10) ! = -* L. 



In this case the law of the extra current of opening is the 

 same as that of the current of closing (533), and the quantities 

 of electricity put in motion are the same. 



