An inductor of inductance $2 μH$ is connected in series with a resistance , a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x} F$ , where the value of $x$ is ________(Take $π = \frac{22}{7})$

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answer is 3872.

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Detailed Solution

For maximum current, $X_{C} = X_{L}$
$\Rightarrow ω = \frac{1}{\sqrt{LC}} \Rightarrow C = \frac{1}{ω^{2} L}$

$\Rightarrow C = \frac{1}{{(2 \times \frac{22}{7} \times 7 \times 10^{3})}^{2} \times 2 \times 10^{- 6}} = \frac{1}{4 \times 22^{2} \times 2} = \frac{1}{3872}$

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