Q122 / 150 · MHT CET 2022 (05 Aug Shift 1) · Physics

Two coils $\mathrm{P}$ and S have a mutual inductance of $3 \times 10^{-3} \mathrm{H}$. If the current in the coil, P is $I=20 \sin (50 \pi t) \mathrm{A}$, then the maximum value of the e.m.f. induced in coil $\mathrm{S}$ is

  • A
    $15.70 \mathrm{~V}$
  • Correct answer
    B
    $9.42 \mathrm{~V}$
  • C
    $3.14 \mathrm{~V}$
  • D
    $6.25 \mathrm{~V}$

Solution

The correct option is (B). Concept: Flux associated among the coils is $\phi=\mathrm{MI}$ and the induced emf is given by $\mathrm{E}=-\frac{\mathrm{d} \phi}{\mathrm{dt}}$. Therefore, $\mathrm{E}=-\mathrm{M} \frac{\mathrm{di}}{\mathrm{dt}}$. Given, $\mathrm{I}=20 \sin (50 \pi \mathrm{t})$ and $\mathrm{M}=3 \times 10^{-3} \mathrm{H}$, Therefore, $\mathrm{E}=-\mathrm{M} \frac{\mathrm{di}}{\mathrm{dt}}$. Given, $\mathrm{I}=20 \sin (50 \pi \mathrm{t})$ and $\mathrm{M}=3 \times 10^{-3} \mathrm{H}$, therefore $\mathrm{E}=-\mathrm{M} \frac{\mathrm{di}}{\mathrm{dt}}$. Given, $\mathrm{I}=20 \sin (50 \pi \mathrm{t})$ and $\mathrm{M}=3 \times 10^{-3} \mathrm{H}$, therefore $E=\left(-3 \times 10^{-3} \mathrm{H} \times 50 \pi \times 20\right) \cos (50 \pi \mathrm{t}) \mathrm{A}$ The maximum emf is given by $\left|E_0\right|=3 \times 10^{-3} \times 50 \pi \times 20 \mathrm{~V}=9.42 \mathrm{~V}$

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

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