In a series LCR circuit, C = 2, L = 1 mH and R = 10 Ω. The ratio of… | MHT CET 2023 (11 May, Shift 2)

Q69MHT CET 2023 · 11 MAY · SHIFT 2Medium

Resonance, Bandwidth & Q Factor

In a series LCR circuit, $C = 2\ \mu\text{F}, L = 1\text{ mH}$ and $R = 10\ \Omega$ . The ratio of the energies stored in the inductor and the capacitor, when the maximum current flows in the circuit, is

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Answer: (a)

Maximum current flows at resonance: $I = \frac{V}{R}$ , i.e. $V = IR$ .
Energy in inductor $U_L = \frac{1}{2}LI^2$ ; energy in capacitor (taken with the applied voltage $V = IR$ ) $U_C = \frac{1}{2}CV^2 = \frac{1}{2}CI^2R^2$ .
$\frac{U_L}{U_C} = \frac{L}{CR^2} = \frac{10^{-3}}{2\times10^{-6}\times 100} = 5$
So the answer is (a) $5 : 1$ .

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Resonance, Bandwidth & Q Factor question from MHT CET 2023 (11 May, Shift 2)

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