A series LCR circuit has resistance 120 Ω and resonance angular frequency 4×10⁵ rad s⁻¹. At resonance, the voltages across R and L are 60 V and 40 V. Find L and C, and the angular frequency at which current lags voltage by 45°.
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Question

A series LCR circuit has resistance 120 Ω and resonance angular frequency 4×10⁵ rad s⁻¹. At resonance, the voltages across R and L are 60 V and 40 V. Find L and C, and the angular frequency at which current lags voltage by 45°.

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G1 Physics · Accepted Answer

At resonance, use the given resistance/voltage relations with ω₀=1/√(LC). Solving the source conditions gives L=0.2 mH, C=1/32 μF and ω₀=8×105 rad/s. Hence A.