Problem 3. Consider the following R. L, C circuit. Initially switches S, and S, are both open. The capacitor is uncharged. & = 12V, R1 = 20, R2 = 40, R3 = 60, C =4/F, and L = 4mH. a) The switch S1 is closed at t = 0, find the currents at t = 0+. b) Find the currents a long time after switch S1 is closed. c) After switch S1 is closed for a long time switch $2 is closed. At the instant So is closed, find all currents. d) Find all currents after after both S, and $2 are both closed a very long time. e) Find the maximum charge on the capacitor. f) (Bonus) After both $1 and $2 are both closed for a very long time, S1 is opened. Find the currents as a function of time once S1 is opened. R , C Sy L S2