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QJEEM23Ph166c: JEE Main 2023 Physics - Class 12 JEEM23Ph166c Solution: An inductor of inductance 2 is connected in series with a…

An inductor of inductance 2 μH\mathrm{\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 1xF\frac{1}{x}\mathrm{F} , where the value of xx is ___________.

(Take π=227\pi=\frac{22}{7} )

Step-by-Step Verified Solution

Current drawn is maximum when circuit is in resonance.

ω=1LC\omega = {1 \over {\sqrt {LC} }}

2π(7000)=12×10−6C2\pi (7000) = {1 \over {\sqrt {2 \times {{10}^{ - 6}}C} }}

⇒C=13872F\Rightarrow C = {1 \over {3872}}F

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