Power dissipated in an L-C-R series circuit connected to an AC...

The emf of an LCR circuit is (\varepsilon). The impedance of a series LCR circuit is given as, (Z=\sqrt{\left[R^2+\left(\omega L-\frac{1}{\omega C}\right)^2\right]}) The power factor in a series LCR circuit is given as, (\cos \phi=\frac{\mathrm{R}}{|\mathrm{Z}|}) The power dissipated in the circuit is given as, ($$\begin{aligned} & \mathrm{P}=\mathrm{V}_{\mathrm{rms}} \mathrm{I}_{\mathrm{rms}} \cos \phi \\ & =\varepsilon \times \frac{\varepsilon}{|\mathrm{Z}|} \times \frac{\mathrm{R}}{|\mathrm{Z}|} \\ & =\frac{\varepsilon^2 \mathrm{R}}{\left[\mathrm{R}^2+\left(\omega \mathrm{L}-\frac{1}{\omega \mathrm{C}}\right)^2\right]} \end{aligned}$$) Thus, the power dissipated in the series $L C R$ circuit is (\frac{\varepsilon^2 R}{\left[R^2+\left(\omega L-\frac{1}{\omega C}\right)^2\right]}).