A circuit has self-inductance ' $L$ ' and carries a current ' $\mathrm{I}$ '. To prevent sparking when the…

A circuit has self-inductance ' $L$ ' and carries a current ' $\mathrm{I}$ '. To prevent sparking when the circuit is switched off, a capacitor which can withstand potential difference ' $\mathrm{V}$ ' is used. The least capacitance is
  1. $\frac{\mathrm{IV}}{\mathrm{L}}$
  2. $\mathrm{L}\left(\frac{\mathrm{V}}{\mathrm{L}}\right)^2$
  3. $\mathrm{L}\left(\frac{\mathrm{I}}{\mathrm{V}}\right)^2$
  4. $\frac{\mathrm{LI}}{\mathrm{V}}$

Solution

The energy stored in the inductance is given by $\mathrm{U}=\frac{1}{2} \mathrm{LI}^2$ Energy stored by the capacitor is given by $\mathrm{W}=\frac{1}{2} \mathrm{CV}^2$ This energy must be transferred to the capacitor. $\begin{aligned} & \therefore \frac{1}{2} \mathrm{CV}^2=\frac{1}{2} \mathrm{LI}^2 \\ & \mathrm{C}=\mathrm{L}\left(\frac{\mathrm{I}}{\mathrm{V}}\right)^2 \end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 1)

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