528 PARTICULAR CASES OF INDUCTION. 



There is evidently a difference of phase between the principal 

 current and the sinusoidal electromotive force which produces it. 



549, Let us further consider as an application the experiment 

 by which Faraday proved the existence of the direct extra current 

 which is produced when the circuit is broken. A battery is closed 

 by a circuit with two branches, like that which we have been con- 

 sidering; one of the wires, of the resistance r', is rectilinear, the 

 other, of the resistance r, consists of a coil formed of a great 

 number of turns. 



If E is the electromotive force of the battery, R the resistance, 

 and I the principal current, after closing the circuit we shall have 

 the equations 



(48) E-RI 



L 



dt 



Putting 



and observing that the currents are zero for /=0, we deduce for 

 the current which traverses the coil at the period /", 



r'E / _PlL_\ 



1 = ( I-e L(K+rO ) 9 



P* \ ) 



and for that which traverses the rectilinear wire, 



If, when once the steady condition is established, we break 

 the principal circuit, so that the spark on breaking has no ap- 

 preciable duration, making R = oo, equations (47) give 



and therefore 



L- 



