Examples 461 



20. Two conductors ABD, ACD are arranged in multiple arc. Their resistances are 

 /?, S and their coefficients of self- and mutual-induction are L, N, and M. Prove that 

 when placed in series with leads conveying a current of frequency p, the two circuits 

 produce the same effect as a single circuit whose coefficient of self-induction is 



(L + N- 

 and whose resistance is 



21. A condenser of capacity C containing a charge Q is discharged round a circuit in 

 the neighbourhood of a second circuit. The resistances of the circuits are R, S, and their 

 coefficients of induction are L, J/, ^Y. 



Obtain equations to determine the currents at any moment. 



If x is the current in the primary, and the disturbance be over in a time less than r, 

 .shew that 



and that 



T I x' l dt vari< 

 Jo 



Examine how x' 2 dt varies with S. 



