Question

If the current in the ineer loop changes according to `i=2t^(2)` then, find the current in the capacitor as a function of time.

Answer 1

`M=mu_(0)/(2b)pia^(2)`
`|"emf induced in larger coil"|=M[((di)/(dt))"in smaller coil"]`
`e=mu_(0)/(2b)pa^(2)(4t)=(2mu_(0)pia^(2)t)/b`
Applying `KVL`:-
`+e-q/c-iR=0`
`(2mu_(0)pia^(2)t)/b-q/c=iR=0`
differentiate `wrt` time :-
`(2mu_(0)pia^(2)t)/b-i/c-(di)/(dt)R=0`
on solving it
`i=(2mu_(0)pia^(2)t)/b[1-e^(-t//RC)]`