Two coils have a mutual inductance of $0.004 \mathrm{H}$. The current changes in the first coil according to…

Two coils have a mutual inductance of $0.004 \mathrm{H}$. The current changes in the first coil according to equation $\mathrm{I}=\mathrm{I}_0 \sin \omega \mathrm{t}$, where $\mathrm{I}_0=10 \mathrm{~A}$ and $\omega=50 \pi \mathrm{rad} \mathrm{s}^{-1}$. The maximum value of e.m.f. in the second coil in volt is
  1. $5 \pi$
  2. $4 \pi$
  3. $2.5 \pi$
  4. $2 \pi$

Solution

$\begin{aligned} & \left|e_s\right|=M \frac{d_p}{d t} \\ & \left|e_s\right|=M \frac{d}{d t} I_0 \sin \omega t \\ & \left|e_s\right|=M I_0 \omega \cos \omega t \\ \therefore \quad & \left|e_s\right|_{\max }=M I_0 \omega=0.004 \times 10 \times 50 \pi \\ \therefore \quad & \left|e_s\right|_{\max }=(2 \pi) \text { volt }\end{aligned}$

Asked in: MHT CET 2023 (12 May Shift 1)

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