520-522] Pair of Circuits 453 



and therefore immediately after the break, the initial current in circuit 2 is 



. MEi 

 l *~NR' 



This current simply decays under the influence of the resistance of the 



circuit. Putting E 2 = and i, = in equation (441) we obtain 



* 



Ji = ~~ffi 1 *' 

 and the solution which gives i 2 = ^r~ initially is 



- 



2 ~ NR 



The changes in the current i, during the infinitesimal interval r are of 

 interest. These are governed by equation (440), the value of R not being 

 constant. 



The value of E, is finite, and may accordingly be neglected in comparison 

 with the other terms of equation (440), which are very great during, the 

 interval of transition. Thus the equation becomes, approximately, 



(449). 



The value of -^- (Mi, -f Ni 2 ) is, as we have already seen, finite, so that we 



M 



may subtract -^ times this quantity from the left-hand member of equation 



(449) and the equation remains true. By doing this we eliminate i 2 , and 

 obtain 



M z \di, 



The solution which gives to i, the initial value (^) is 



giving the way in which the current falls to zero. We notice that if 

 LN if 2 is very small, the current falls off at once, while if LN M 2 is large, 

 the current will persist for a longer time. In the former case the breaking 

 of the circuit is accompanied only by a very slight spark, in the latter case 

 by a stronger spark. 



One Circuit containing a Periodic Electromotive Force. 



522. Let us suppose next that the circuits contain no batteries, but that 

 circuit 1 is acted upon by a periodic electromotive force, say E cospt, such as 

 might arise if this circuit contained a dynamo. 



