Two coils have a mutual inductance $0. 003 \mathrm{H}$. The current changes in the first coil according to…

Two coils have a mutual inductance $0. 003 \mathrm{H}$. The current changes in the first coil according to equation $\mathrm{I}=\mathrm{I}_0 \quad \sin \omega \mathrm{t}$, where $\mathrm{I}_0=8 \mathrm{~A}$ and $\omega=100 \pi \mathrm{rad} \mathrm{s}^{-1}$. The maximum value of e.m.f. in the second coil is
  1. $\quad 2 \pi \mathrm{~V}$
  2. $2.4 \pi \mathrm{~V}$
  3. $5 \pi \mathrm{~V}$
  4. $7.2 \pi \mathrm{~V}$

Solution

$\begin{array}{ll} & \left|e_s\right|=M \frac{d I_p}{d t} \\ & \left|e_s\right|=M \frac{d}{d t} I_0 \sin \omega t \\ & \left|e_s\right|=M I_0 \omega \cos \omega t \\ \therefore \quad & \left|e_s\right|_{\max }=M I_0 \omega=0.003 \times 8 \times 100 \pi \times 1 \\ \therefore \quad & \left|e_s\right|_{\max }=(2.4 \pi) \text { volt }\end{array}$

Asked in: MHT CET 2024 (10 May Shift 1)

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