[UPSC CSE 2007] Electrostatics and Magnetostatics (Q189, 20M)

In an a.c. circuit, a resistance (R = 100\ \Omega) and a capacitance (C = 100\ \mu\text{F}) in series are connected to an a.c. source V = 200 \sin(100\ \pi t). Calculate the current through the circuit and the voltages across R and C. Draw a vector diagram representing the magnitudes and phases of the voltages.