An a.c. source generating a voltage `v=v+(m) sin omega t ` is connected to a capacitor of capacitor of capacitance C. Find the expression for the current, I, flowing through it. Plot a graph of `v` and I versus `omega` t to show that the current is `pi//2` ahead of the voltage.
A resistor of `200 Omega` and a capacitor of `15.0 mu F` are connected in series to a 220 V, 50 Hz a.c. source. Calculate the current in the circuit and the rms voltage across the resistor and the capacitor. Is the algebraic sum of these voltages more than the source voltages ? If yes, resolve the paradox.

Explanation

To solve the given problem step by step, we will break it down into two parts as per the question.

### Part 1: Finding the expression for current through the capacitor

1. **Understanding the Voltage Equation**:
The voltage across the capacitor is given as:
\[
v(t) = V + M \sin(\omega t)
...