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

Question

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 x 1 ​ F , where the value of x is ______. (Take π = 7 22 ​ )

TestHub · Accepted Answer

For maximum current in series LCR circuit,

$X_{C} = X_{L} \Rightarrow \frac{1}{2 π f C} = 2 π f L$

$\Rightarrow C = \frac{1}{4 π ^{2} f ^{2} L} = \frac{1}{4 \times π ^{2} \times 49 \times 1 0 ^{6} \times 2 \times 1 0 ^{- 6}}$

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

Therefore, $x = 3872$ .

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