RC Trouble

We have a circuit as shown in the figure with resistance RR,capacitance CC, a Battery of EMF VV volt. Initially the key was connected to point 22.

At t=0t=0 the key was connected to point 11. Now after one time constant τ\tau the key is connected to point 22. After another time constant the key is connected back to point 11 and we say that a cycle is completed.

If the charge on the capacitor as the number of cycles completed tend to infinity is given by =xCV=xCV than find 100x\left\lfloor 100x \right\rfloor

Details and assumptions

1)The conductor is connected to only point at a time.

2)τ=RC\tau=RC

3)There is no time lag between consecutive cycles that is as soon as one cycle is completed the other cycle is started

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