(a) (i) You are given three circuit elements $\mathrm{X}, \mathrm{Y}$ and $Z$. They are connected one by one across a given ac source. It is found that V and I are in phase for element $X$. V leads I by $\left(\frac{\pi}{4}\right)$ for element $Y$ while I leads $V$ by $\left(\frac{\pi}{4}\right)$ for element $Z$. Identify elements X, Y and $Z$.

(ii) Establish the expression for impedance of circuit when elements $X, Y$ and $Z$ are connected in series to an ac source. Show the variation of current in the circuit with the frequency of the applied ac source.

(iii) In a series LCR circuit, obtain the conditions under which (i) impedance is minimum and (ii) wattless current flows in the circuit.

OR

(b) (i) Describe the construction and working of a transformer and hence obtain the relation for $\left(\frac{v_s}{v_p}\right)$ in terms of number of turns of primary and secondary.

(ii) Discuss four main causes of energy loss in a real transformer.