Q 12-07-011NEETNEET 2021Top questionHard
A series LCR circuit containing $5.0$ H inductor, $80\ \mu$F capacitor and $40\ \Omega$ 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 :
Answer: (D) $46$ rad/s and $54$ rad/s
Resonance:
$$\omega_0 = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{5 \times 80 \times 10^{-6}}} = \frac{1}{0.02} = 50\ \text{rad/s}$$
The half-power frequencies are $\omega_0 \pm \dfrac{R}{2L}$:
$$\frac{R}{2L} = \frac{40}{10} = 4\ \text{rad/s}$$
$$\omega = 50 \pm 4 = 46\ \text{rad/s and } 54\ \text{rad/s}$$
Solution by Sreeraj P, M.Sc Physics