What is impedance of an $\mathrm{AC}$ circuit? A capacitor $\mathrm{C}$ and a resistor $\mathrm{R}$ are connected in series in an $\mathrm{AC}$ circuit. Derive expression for the impedance $\mathrm{Z}$ of the circuit. Draw phasor diagram.

Show that the average power dissipated in an $\mathrm{AC}$ circuit is, in general, given by

$\mathrm{P}={\mathrm{V}}_{\mathrm{rms}}\times {\mathrm{I}}_{\mathrm{rms}}\times \mathrm{R}/\mathrm{Z}$

where $\mathrm{R}$ is the resistance of the circuit (defined as real part of the complex impedance) and $\mathrm{Z}$ is the impedance.