A capacitor $\left(\mathit{C}\right)$ and resistor $\left(\mathit{R}\right)$ are connected in series with an ac source of voltage of frequency $50\mathrm{Hz}$. The potential difference across $\mathit{C}$ and $\mathit{R}$ are respectively $120\mathrm{V},90\mathrm{V}$, and the current in the circuit is $3\mathrm{A}$. Calculate (i) the impedance of the circuit (ii) the value of the inductance, which when connected in series with $\mathit{C}$ and $\mathit{R}$ will make the power factor of the circuit unity.
OR
The figure shows a series LCR circuit connected to a variable frequency $230\mathit{V}$ source.
(a) Determine the source frequency which drives the circuit in resonance.
(b) Calculate the impedance of the circuit and amplitude of current at resonance.
(c) Show that potential drop across LC combination is zero at resonating frequency.