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A pair of capacitors $C_1$ and $C_2$ is connected as shown, with a resistance $R$ in between them. Initially, the first capacitor carries a total charge $Q_{1i}$ and the second one is uncharged, $Q_{2i} = 0$. At $t = 0$ the switch is closed. Find:

a) The equilibrium ($t = \infty$) charges on the two capacitors, $Q_{1f}$ and $Q_{2f}$.

b) Using Kirchoff's laws for this arrangement, find the time constant for the equilibration process. Note that you do NOT have to solve the DE, just formulate it with $dt$ and some arrangement of $R$, $C_1$, and $C_2$ on the other side.

c) For extra credit, either solve the DE (it is integrable, although a bit messy) or GUESS what its solution is, based on your answers to a) and b). To do the latter, try visualizing what $Q_1(t)$ and $Q_2(t)$ will formally look like - it is just a matter of setting the various constants so that the asymptotic (final) and initial conditions are correctly represented and the approach to those conditions has the right time dependence.