# RC Trouble

**Electricity and Magnetism**Level 4

We have a circuit as shown in the figure with resistance \(R\),capacitance \(C\), a Battery of EMF \(V\) volt. Initially the key was connected to point \(2\).

At \(t=0\) the key was connected to point \(1\). Now after one time constant \(\tau\) the key is connected to point \(2\). After another time constant the key is connected back to point \(1\) 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 \(=xCV\) than find \(\left\lfloor 100x \right\rfloor\)

**Details and assumptions**

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

2)\(\tau=RC\)

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