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Physics · PYQ NEET UG 2021
हिन्दीA series LCR circuit containing \( 5.0 \text{ H} \) inductor, \( 80 \mu\text{F} \) capacitor and \( 40 \,\Omega \) resistor is connected to \( 230 \text{ V} \) 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:
Correct answer · Option 2
\( 46 \text{ rad/s} \) and \( 54 \text{ rad/s} \)
Explanation
Resonant frequency \( \omega_0 = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{5 \times 80 \times 10^{-6}}} = 50 \text{ rad/s} \). Half power frequencies are given by \( \omega \approx \omega_0 \pm \frac{R}{2L} = 50 \pm \frac{40}{2 \times 5} = 50 \pm 4 \Rightarrow 46 \text{ rad/s} \) and \( 54 \text{ rad/s} \).
