Calculate current and power factor for the given $\mathrm{AC}$ circuit.

In the given circuit, the potential differences across resistance, capacitance and inductance are given. Work out the emf of the source of alternating current and power factor of the circuit.

An alternating emf $\mathrm{V}$ is applied across a series $\mathrm{L}-\mathrm{C}-\mathrm{R}$ circuit. The peak values of the alternating voltage developed across the three components are marked in the figure. Determine the peak value of the applied emf and the phase difference between the applied emf and the current in the circuit.

The main-supply voltage of the alternating-current circuit shown in the figure is constant, but its frequency $\mathrm{f}$ is variable. For what frequency the voltage across the resistance $\mathrm{R}$ will be maximum?