Two coils have mutual inductance 0.005 H. The current changes in the first coil according to equation `I = I_(0)` sin `omega t`, where `I_(0) = 10 A` and `omega = 100 pi` rad `s^(-1)`. The maximum value of induced emf in the second coil is

Options

A. 5
B. `5 pi`
C. `0.5 pi`
D. `pi`

Answer

b

Explanation

Mutual inductance, M = 0.005 H
`I = I_(0) sin omega t`
`I_(0) = 10 A`
`omega = 100 pi` rad/s
The emf induced in second coil.
`e = M (dI)/(dt) = M (dI)/(dt) = 0.005 xx (dI_(0) sin omega t)/(dt)`
`= 0.005 xx I_(0) omega cos omega t = 0.005 xx I_(0) omega cos (2 pi)/(t) t`
`implies e_("max") = 0.005 xx 10 xx 100 pi xx 1 = 5 pi` volt