Explaining the nature of variation. A series L.C.R circuit is connected to an ac source using phasor diagram, derive the expression for the impedance of the circuit. Plot a graph to show the variation of current with the frequency of the source.

A voltage $V=V_0\sin \omega t$ applied to a series LCR circuit drives a current $i=i_0\sin \omega t$ in the circuit. Derive the expression for the average power dissipated in the circuit.

For currents used for transporting electric power, a low power factor implies large power loss in transmission. Explain.

Draw a labelled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of number of turns and current in the two coil. 

A light bulb is rated $100 \mathrm{W}$ for $220 \mathrm{V}$  ac supply of $50 \mathrm{Hz}.$ Calculate