An inductor of inductance is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. [2023]

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Solution

Q.
An inductor of inductance $2 μ H$ 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 $π = \frac{22}{7}$ ) [2023]

Ans.
(3872)

$\frac{1}{2 π f C} = 2 π f L$

$C = \frac{1}{4 π^{2} f^{2} L} = \frac{1}{4 \times π^{2} \times 49 \times 10^{6} \times 2 \times 10^{- 6}}$

$C = \frac{1}{3872} F$

$\Rightarrow x = 3872$

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