A series L - C - R circuit containing 5 . 0 H inductor, 80 μ F capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power tran

Question

A series L - C - R circuit containing 5 . 0 H inductor, 80 μ F 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:NEET 2021

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L = 5 H , C = 80 μ F , R = 40 ω ; V = 230 V Resonance angular frequency = ω 0 = 1 L C = 1 5 × 80 × 10 - 6 = 50 rad s - 1 Half power angular frequency = ω 0 ± R 2 L = 50 ± 40 2 × 5 = 50 ± 4 = 54 or 46 We get, ω 1 = 46 rad s - 1 And ω 2 = 54 rad s - 1

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