Q113 / 150 · MHT CET 2021 (23 Sep Shift 1) · Physics

In the part of an a.c. circuit as shown, the resistance $\mathrm{R}=0.2$ $\Omega$. At a certain instant $\left(\mathrm{V}_{\mathrm{A}}-\mathrm{V}_{\mathrm{B}}\right)=0.5 \mathrm{~V}, \mathrm{I}=0.5 \mathrm{~A}$ and $\frac{\Delta \mathrm{I}}{\Delta \mathrm{t}}=8 \mathrm{~A} / \mathrm{s}$. The inductance of the coil is Figure

  • A
    $0.04 \mathrm{H}$
  • B
    $0.02 \mathrm{H}$
  • C
    $0.08 \mathrm{H}$
  • Correct answer
    D
    $0.05 \mathrm{H}$

Solution

In the part of an a.c. circuit $$ \begin{aligned} & V_A-V_B=L \frac{d I}{d t}+I R \\ & 0.5=8 L+0.5 \times 0.2 \\ & \therefore 8 L=0.4 \\ & \therefore L=\frac{0.4}{8}=0.05 \mathrm{H} \end{aligned} $$

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

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