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. `5pi`
C. `0.5 pi`
D. `pi`

Answer

B

Explanation

Mutual inductance , `M=0.005 H`
`l=I_(0)sin omega t`
`I_(0)=10 A, omega =100 pi rads^(-1)`
e.m.f, `e=M(dI)/(dt)`
`=0.005 (d)/(dt)[I_0 sin omega t]`
`=0.005 I_(0) omega cos omega t`
`0.005 I_(0) omega cos (2pi)/(t) .t`
`0.005 I_(0)omegacos 2pi `
`=0.005 I_(0) omega xx 1`
`e_("max")=0.005 xx10 xx 2pi = 5pi ` volt .