Problem 2: Charging of a capacitor (9 Marks) In the circuit shown in the figure, at t = 0 there is no charge on the capacitor and the switch S is closed. Express your results in terms of V1, R1, R2, and C. (a) We first consider what happens at t -> co. What is the current in the capacitor? What is the po- W tential difference on R2 and the charge on the R1 capacitor, Qoo? (b) Now for t > 0, derive the differential equation Va C R2 governing the time evolution of the capacitor's charge Q(t). (c) Solve it to determine Q(t) for t > 0 and plot/sketch it as a function of t. (e) What is the maximum current, imax, in the capacitor during its charge? (f) Calculate Q and imax for a typical flash capacitor circuit with V1 = 300 V, R1 = 100, R2 = 10MQ, C = 100/F