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A circuit has an inductance of 100 mH and carries a current of 3 A. To prevent sparking when the circuit is switched off, a capacitor is connected across the switch. If the capacitor can withstand a maximum voltage of 300 V, the minimum capacitance $(in μF)$ it must be equal to _____.

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answer is 10.

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Detailed Solution

To Prevent sparking, the energy stored in the induction must at least be equal to that can be stored in the capacitor, i.e.

$\frac{1}{2} {LI}^{2} = \frac{1}{2} {CV}^{2} C = \frac{{LI}^{2}}{V^{2}} = \frac{0 .1 \times (3)^{2}}{(300)^{2}} = 10 \times 10^{- 6} F = 10 μF$

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