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Topic: Reactance, impedance, LCR series circuit, resonance· Electromagnetic Induction and Alternating Currents

A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant an…

A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be :

1. 25 rad/s and 75 rad/s

2. 50 rad/s and 25 rad/s

3. 46 rad/s and 54 rad/s

4. 42 rad/s and 58 rad/s

1 answer

Best answer

Answer: 3. 46 rad/s and 54 rad/s

Key idea: power falls to half of its resonance value when \(|X_L-X_C|=R\), which happens at \(\omega=\omega_0\pm\dfrac R{2L}\) (for a high-Q circuit).

\(\omega_0=\dfrac1{\sqrt{LC}}=\dfrac1{\sqrt{5\times80\times10^{-6}}}=50\) rad/s.

\(\dfrac R{2L}=\dfrac{40}{10}=4\) rad/s, so \(\omega\approx46\) and \(54\) rad/s. Option 3.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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