What does the resistor do when the second switch is closed?
Since this is clearly a homework question, I won't provide a complete answer, but rather some hints. You are currently way off track.


Pay attention to the polarity of the voltage across the capacitor. It cannot change when one set of switches opens and the other closes.
Keep in mind that when the second set of switches is closed, the voltage across the resistor is the same as the voltage across the capacitor. How much current is flowing, and how does it change with time?




A more interesting question: What happens if you connect a second capacitor, say, 10 nF, in parallel with the resistor?



Here's a simulatable copy of the circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

Run the simulation to get a feel for what's happening qualitatively, and this should give you some insight into what you're doing wrong with the equations. Try it with SW5 both open and closed.