(a) (i) Define the terms (I) resonant frequency, and (II) power factor of a series LCR circuit. For what value of the power factor will the power dissipated in the circuit be maximum ? (ii) An inductor of $\frac{5}{\pi}\text{ H}$, a capacitor of $\frac{50}{\pi}\text{ }\mu\text{F}$ and a resistor of $400\text{ }\Omega$ are connected in series across an ac voltage $v = 140\text{ sin}$100\pi\text{ t}$\text{ V}$. Calculate : (I) impedance of the circuit, and (II) rms value of current that flows in the circuit. (Take $\sqrt{2} = 1\cdot 4$) OR (b) (i) Draw a labelled diagram of a step-up transformer. Obtain the ratio of secondary voltage to primary voltage in terms of number of turns in the two coils. (ii) The number of turns in the primary and the secondary coil of an ideal transformer are $100$ and $5000$ respectively. If $3\cdot 3\text{ kW}$ power is supplied to the transformer at $220\text{ V}$, find (I) current in the primary coil, and (II) output voltage.