A current `I=20sin(100pit)A` is passed in the first coil, which induces a maximum emf of `10piV` in the second coil. The mutual inductance for the pair of coils is

Options

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

Answer

D

Explanation

Let `I = I_(0) sin omega t`
Where `I_(0) = 20 A, omega = 100 pi "rad s"^(-1)`
Then, `epsilon = M(dI)/(dt) = M(d(I_(0)sin omegat))/(dt) = MI_(0)omega cos omega t`
`rArr epsilon_("max") =MI_(0)omega = 10 pi`
`M = (10 pi)/(20 xx 100pi)`
`M = 0.005 H = 5 mH`