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

Answer: 500

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