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  4. 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 (1/ x ) F, where the value of x is (. Take .π=(22/7))

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Q. An inductor of inductance $2\, \mu H$ 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__
$\left(\right.$ Take $\left.\pi=\frac{22}{7}\right)$

JEE MainJEE Main 2023Alternating Current

Solution:

$\frac{1}{2 \pi fC }=2 \pi fL$
$ C =\frac{1}{4 \pi^2 f ^2 L }=\frac{1}{4 \times \pi^2 \times 49 \times 10^6 \times 2 \times 10^{-6}} $
$ C =\frac{1}{3872} F $
$ x =3872$