A series LCR circuit containing $5.0 ext{ H}$ inductor, $80 ext{ }\mu ext{F}$ capacitor and $40 ext{ }\Ome

Question

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

Accepted Answer

The resonance frequency of LCR series circuit is given as $\omega_0 = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{5 	imes 80 	imes 10^{-6}}} = 50	ext{ rad/s}$. Now half power frequencies are given as $\omega = \omega_0 \pm \frac{R}{2L}$. i.e., $\omega_L = 50 - \frac{40}{2 	imes 5} = 46	ext{ rad/s}$ and $\omega_H = 50 + \frac{40}{2 	imes 5} = 54	ext{ rad/s}$.

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