(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.

(a) (i) A plane light wave propagating from a rarer into a denser medium, is incident at an angle $i$ on the surface separating two media. Using Huygen's principle, draw the refracted wave and hence verify Snell's law of refraction.

(ii) In a Young's double slit experiment, the slits are separated by 0.30 mm and the screen is kept 1.5 m away. The wavelength of light used is 600 nm . Calculate the distance between the central bright fringe and the $4^{\text {th }}$ dark fringe.

OR

(b) (i) Discuss briefly diffraction of light from a single slit and draw the shape of the diffraction pattern.

(ii) An object is placed between the pole and the focus of a concave mirror. Using mirror formula, prove mathematically that it produces a virtual and an enlarged image.