Q152 / 160 · TS EAMCET 2016 · Physics

Two coils have mutual inductance $0.005 \mathrm{H}$. The current changes in the first coil according to equation $I=I_0 \sin \omega t$, where $I_0=10 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} \mathrm{s}$. The maximum value of induced emf in the second coil is

  • A
    5
  • Correct answer
    B
    $5 \pi$
  • C
    $0.5 \pi$
  • D
    $\pi$

Solution

Mutual inductance, $M=0.005 \mathrm{H}$ $$ \begin{aligned} & l=I_0 \sin \omega t \\ & I_0=10 \mathrm{~A} \\ & \omega=100 \pi \mathrm{rad} / \mathrm{s} \end{aligned} $$ The emf induced in second coil, $$ e=M \frac{d l}{d t}=M \frac{d l}{d t}=0.005 \times \frac{d l_0 \sin \omega t}{d t} $$ $\begin{aligned} & =0.005 \times l_0 \omega \cos \omega t=0.005 \times l_0 \omega \cos \frac{2 \pi}{t} t \\ \Rightarrow e_{\max } & =0.005 \times 10 \times 100 \pi \times 1=5 \pi \mathrm{volt}\end{aligned}$

Hence, the correct answer is option: 'B'.

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