A series LCR circuit containing 5.0 H inductor, 80 μ F capacitor and… | NEET 2021

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Resonance, Bandwidth & Q Factor

A series LCR circuit containing 5.0 H inductor, 80 $\mu$ F capacitor and 40 $\Omega$ resistor is connected to 230V 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:

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Answer: (d)

$\omega_0 = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{5\times80\times10^{-6}}} = \frac{1}{0.02} = 50\text{ rad/s}$
Half-power bandwidth $\Delta\omega = \frac{R}{L} = \frac{40}{5} = 8\text{ rad/s}$
Half-power frequencies $\omega_0 \pm \frac{\Delta\omega}{2} = 50 \pm 4$
So the answer is (d) 46 rad/s and 54 rad/s.

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