An inductor of 0.5 mH, a capacitor of 200 μ F and a resistor of 2 Ω… | JEE Main 2022 (29 Jun, Shift 2)

Q74JEE Main 2022 · 29 JUN · SHIFT 2Easy

Resonance, Bandwidth & Q Factor

An inductor of 0.5 mH, a capacitor of 200 $\mu$ F and a resistor of 2 $\Omega$ are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ____________ $\times$ 102 Hz.

Numerical answer type. Work it out, then open the answer.

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Answer: 5

Current in phase with emf means resonance: $f = \dfrac{1}{2\pi\sqrt{LC}}$
$LC = (0.5\times10^{-3})(200\times10^{-6}) = 10^{-7} \Rightarrow \sqrt{LC} = 3.16\times10^{-4}\text{ s}$
$f = \dfrac{1}{2\pi \times 3.16\times10^{-4}} \approx 503\text{ Hz} \approx 5\times10^{2}\text{ Hz}$
So the answer is 5 (the '102' in the question means $10^2$ ).

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