A series LCR circuit is connected to a 220 V variable frequency (a.c) supply. If $L = 20mH, C = (\frac{800}{π^2}) µF$ and $R = 110 Ω$. The frequency of the source, for which the average power absorbed by the circuit is maximum will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 125 Hz
The resonance condition in an LCR circuit is,
$ω_0=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{20×10^{-3}×\frac{800}{\pi^2}×10^{-6}}}$
$=\frac{\pi}{\sqrt{20×10^{-3}×800×10^{-6}}}≃0.785\,rad/s$
and,
Angular frequency, $ω_0=2\pi v_0$ [v = frequency]
$⇒v_0=\frac{ω_0}{2\pi}=\frac{0.785}{0.28}≃125Hz$