(a) (i) A light bulb and an open coil inductor are connected in series across an ac source of variable frequency. How will the glow of the bulb be affected when : (I) an iron bar is inserted inside the coil, and (II) the frequency of the source is decreased ? Justify your answers. Assume that in each above case other factors remain unchanged. (ii) An ac voltage $V = 280 \sin $100\pi \text{ t}$ \text{ volt}$ is connected across a series LCR circuit in which $R = 400 \ \Omega$, $L = \frac{5}{\pi} \text{ H}$ and $C = \frac{50}{\pi} \mu\text{F}$. Taking $\sqrt{2} = 1\cdot4$, calculate : (I) impedance of the circuit. (II) rms value of current that flows in the circuit. (III) power factor of the circuit.