(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase: current or voltage?

(ii) Without making any other change, find the value of the additional capacitor $C_1$, to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.

A resistor $R$ and an element $\mathrm{X}$ are connected in series to an ac source of voltage. The voltage is found to lead the current in phase by $\pi /4$. If X is replaced by another element$Y$, the voltage lags behind the current by $\pi /4$.
(i) Identify elements $X$ and $Y$.

(ii) When both $X$ and $Y$are connected in series with $R$ to the same source, will the power dissipated in the circuit be maximum or minimum? Justify your answer.