What is the value of power factor for a pure resistor connected to an alternating current source?

Draw a labelled graph showing the variation of impedance $\left(Z\right)$ of a series LCR circuit versus frequency $\left(f\right)$ of an ac supply.

When an alternating emf $e=310 \sin \left(100\pi t\right)V$ is applied to a series $LCR$ circuit, the current flowing through it is $i=5 \sin \left(100\pi t+\pi /3\right) \mathrm{A}$. What is the phase difference between the current and the emf?

When an alternating emf $e=310 \sin \left(100\pi t\right)V$ is applied to a series $LCR$ circuit, the current flowing through it is $i=5 \sin \left(100\pi t+\pi /3\right) \mathrm{A}$. Calculate the average power consumed by the circuit.

Obtain an expression for the resonant frequency $\left(f_o\right)$ of a series LCR circuit.