The current following through an inductance coil of self-inductance $6 \mathrm{mH}$ at different time instants is as shown. The emf induced between $t=20 \mathrm{~s}$ and $t=40 \mathrm{~s}$ is nearly

• A

  $2 \times 10^{-2} \mathrm{~V}$
• B

  $3 \times 10^{-2} \mathrm{~V}$
• C

  $4 \times 10^{-3} \mathrm{~V}$
• Correct answer
  D

  $30 \times 10^{-4} \mathrm{~V}$

Solution

As we know, Induced emf, $|e|=L \frac{d I}{d t}$ Here, $L=6 \mathrm{mH}=6 \times 10^{-3} \mathrm{H}$ From the given graph,

$\begin{aligned} |e| &=L \frac{\left(I_{2}-I_{1}\right)}{\left(t_{2}-t_{1}\right)} \\ &=\frac{L}{20}=\frac{6 \times 10^{-3}}{20}=3 \times 10^{-4} \mathrm{~V} \end{aligned}$

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