(a) (i) With the help of a labelled diagram, explain the working of an ac generator. Obtain the expression for the emf induced at an instant 't'. (ii) A long, straight horizontal wire X'X is held stationary and carries a current of $3.0\text{ A}$. A square loop MNPS of side $10\text{ cm}$, carrying a current of $1.0\text{ A}$ is kept near the wire X'X as shown in the figure. Find the magnitude and direction of the net magnetic force acting on the loop due to the wire. OR (b) (i) State Faraday's law of electromagnetic induction and mention the utility of Lenz's law. Obtain an expression for self-inductance of a coil in terms of its geometry and permeability of the medium. (ii) A resistance of $20\text{ }\Omega$, a capacitance of $80\text{ }\mu\text{F}$ and an inductor of $50\text{ mH}$ are connected in series. This combination is connected across a $220\text{ V}$ ac supply of variable frequency. When the frequency of supply equals the natural frequency of the circuit, calculate: (1) angular frequency of supply (2) impedance of the circuit