Question

Two coils have a mutual inductance $0.005 \, H.$ The current changes in the first coil according to equation $I=I_{0}sin \left(\omega t\right),$ where $I_{0}=10A$ and $\omega =100\pi \, rad \, s^{- 1}.$ The maximum value of emf in the second coil is

• A. $2\pi $
• B. $5\pi $
• C. $\pi $
• D. $4\pi $

Answer 1

Answer: (B)

emf, induced in second coil $e=M \frac{d I}{d t}$
$\Rightarrow e=M \frac{d}{d t} I_0 \sin \omega t=M I_0 \omega \cos \omega t$
$\Rightarrow e=0.005 \times 10 \times 100 \pi \cos \omega t$
$\Rightarrow e=5 \pi \cos \omega t, e_{\max }=5 \pi$
(emf is maximum for $\cos \omega t=1$ )