Question

A series LCR circuit with R = 20 $\Omega$ , L = 1.5 H and C = 35 $\mu$F is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

Answer 1

At resonance, the frequency of supply power equals to naturan frequency of LCR circuit.

Impedence, $Z=\sqrt{R^2+(\omega L-1/\omega C)}$

${\omega }_L=\frac{1}{{\omega }_C}$

so, $Z=R$

$I=V/R=200/20=10A$

Power, $W=V\times I=200\times 10=2000W$