In a coil, the current changes from $-2 \mathrm{~A}$ to $+2 \mathrm{~A}$ in $0.2 \mathrm{~s}$ and induces an…

In a coil, the current changes from $-2 \mathrm{~A}$ to $+2 \mathrm{~A}$ in $0.2 \mathrm{~s}$ and induces an emf of $0.1 \mathrm{~V}$. The self inductance of the coil is :
  1. $4 \mathrm{mH}$
  2. $1 \mathrm{mH}$
  3. $5 \mathrm{mH}$
  4. $2.5 \mathrm{mH}$

Solution

$(E m f)_{\text {induced }}=-L \frac{d i}{d t}$
In magnitude form, $\begin{aligned} & \left|\operatorname{Emf}_{\text {ind }}\right|=\left|(-) L \frac{\mathrm{di}}{\mathrm{dt}}\right| \\ & \Rightarrow 0.1=\frac{(\mathrm{L})[+2-(-2)]}{0.2} \\ & \Rightarrow \mathrm{L}=\frac{0.1 \times 0.2}{4}=5 \mathrm{mH} \end{aligned}$

Asked in: JEE Main 2024 (06 Apr Shift 2)

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