Question

Two circuits are shown in the figure (a) \& (b). At a frequency of______ $rad / s$ the average power dissipated in one cycle will be same in both the circuits.

Answer 1

For figure (a)
$P_{\text {avg }}=v_{\text {rms }}{ }^{2} R$
$\frac{v_{\text {rms }}{ }^{2}}{Z^{2}} \times R=v_{\text {rms }}{ }^{2} R \times 1$
$R^{2}=Z^{2}$
$25=\left(\sqrt{\left(x_{C}-x_{L}\right)^{2}+5^{2}}\right)^{2}$
$25=\left(x_{c}-x_{L}\right)^{2}+25$
$x_{c}=x_{L} \Rightarrow \frac{1}{\omega C}=\omega L$
$\omega^{2}=\frac{1}{L C}=\frac{10^{6}}{0.1 \times 40}$
$\omega=500$