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In the circuit above, R = 100$\Omega$ and C = 1$\mu$Farad, and V = 10 volts. The capacitor is initially uncharged. To simplify arithmetic to the finger and toe level, answers given algebraically in terms of powers of $e$ are acceptable - no calculators should be strictly necessary although you can smoke 'em if you got 'em.

a) At time $t = 0$, switch 1 is closed. What is the charge on the capacitor as a function of time?

b) At time $t = 300$ microseconds, switch 1 is opened and switch 2 is closed. What is the voltage across the capacitor as a function of time.

c) At time $t = 500$ microseconds (from $t = 0$ in part a) switch 2 is opened. How much energy is stored in the capacitor at that time?