Obtain an expression for power consumed in an LCR series circuit. Hence, obtain an expression for power factor of the circuit.

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.

A coil of inductance $0.50 \mathrm{H}$ and resistance $100 \mathrm{\Omega }$ is connected to a $240 \mathrm{V}, 50 \mathrm{Hz}$ ac supply. What is the maximum current in the coil?