A current `I = 10 sin (100pi t)` amp. Is passed in first coil, which induces a maximum e.m.f of `5pi` volt in second coil. The mutual inductance between the coils is-

Options

A. 10 mH
B. 15 mH
C. 25 mH
D. 5 mH

Answer

D

Explanation

From Faraday's law of electromagnetic induction, ltBrgt `e=-(Mdi)/(dt)implies M=-(e)/(di//dt)`
Given, `e=5piV and i=10sin(100pit)` ,
`therefore ((di)/(dt))_(max)=10xx100pi`
`therefore M=-(5pi)/(10xx100pi)=-5xx10^(-3)H=5mH`