Two colis have a mutual inductance 0.005 H. The current changes in the first coil according to the equation where A and The maximum value of the emf induced in the second coil is

Options

A. `5pi`
B. `4pi`
C. `2pi`
D. `pi`

Answer

A

Explanation

The emf induced in the second coil is
`epsilon = M (di)/(dt)`
where M is the mutual inductance of two coils , `(di)/(dt)` is the rate of change of currnet in the first coil .
But `(di)/(dt)= d/(dt) (i_(m) sin omega t) = i_(m) omega cos omegat `
` :. " " epsilon Mi_(m) omegacos omega t `
For maximum value of emf induced , `cos omega t = 1 `
` :. ` The minimum value of the emf induced is
`epsilon _(max) = Mi_(m)omega `
Here ,
`M = 0.005 H , i_(m) = 1 A , omega = 100 pi " rad s"^(-1)`
`:. epsilon _(max) = (0.005 H ) (10 A ) (100 pi ) = 5pi V `