Question

A $50\, Hz \,AC$ current of peak value $2\, A$ flows through one of the pair of coils. If the mutual inductance between the pair of coils is $150\, mH$, then the peak value of voltage induced in the second coil is

• A. $ 30\,\pi V $
• B. $ 60\,\pi V $
• C. $ 15\,\pi V $
• D. $ 300\,\pi V $

Answer 1

The Correct Option is A

$ M=150\times {{10}^{-3}}H $ $ i=2A $ $ f=50\,Hz $
Induced voltage, $ e=\frac{d\phi }{dt} $
$ =\frac{d}{dt}(Mi)=\frac{d}{dt}(M{{i}_{0}}\sin \omega t)\omega \cos \omega t $ e is maximum when $ \cos \omega t=1 $
$ \therefore $ $ e=M{{i}_{0}}\omega $
$ =150\times {{10}^{-3}}\times i\times 2\pi f $
$ =150\times {{10}^{-3}}\times 2\times 2\pi \times 50 $
$ =30\text{ }\pi V $