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

Answer: (A)

$30\,\pi V$

Answer 2

$M=150\times {{10}^{-3}}H$ $i=2A$ $f=50\,Hz$
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 $\cos \omega t=1$
$\therefore$ $e=M{{i}_{0}}\omega$
$=150\times {{10}^{-3}}\times i\times 2\pi f$
$=150\times {{10}^{-3}}\times 2\times 2\pi \times 50$
$=30\text{ }\pi V$