(a) A $20\text{ }\mu\text{F}$ capacitor is connected to a $220\text{ V}$, $\frac{125}{\pi}\text{ Hz}$ ac source. (i) Find the capacitive reactance and the peak value of current in the circuit. (ii) If the frequency of the ac source is doubled, by what factor will the capacitive reactance and the current be changed ? OR (b) An electron (mass $9 \times 10^{-31}\text{ kg}$ and charge $1.6 \times 10^{-19}\text{ C}$) is moving in a circle with a speed of $3.2 \times 10^7\text{ m/s}$ in a magnetic field of $4.5 \times 10^{-4}\text{ T}$ perpendicular to it. Calculate : (i) the radius of the circular path, (ii) its frequency of rotation, and (iii) its energy.