Two coils A and B have mutual inductance `2xx10^(-2)` Henry if the current in he primary coil is i=5 sin `(10pit)` then the maximum value of emf induced in coil B is

Options

A. `pi` volt
B. `pi//2` volt
C. `pi//3`volt
D. `pi//4` volt

Answer

A

Explanation

`I = 5 sin (10 pi t)`
`e_(B) = M(dI)/(dt) = Md/(dt) (I_(0)sin omega t) = MI_(0)omega cos omega t`
this is maximum when `cos omega t =1`
`:.` Maximum e.m.f. = `MI_(0)omega`
In this problem `M = 2 xx 10^(-2) H, I_(0)=5A and omega = 10 pi`
`:. e_(max) = 2 xx 10^(-2) xx 5 xx 10 pi = pi "volt"`.