Charging & discharging of capacitor

As soon as the switch is closed, the battery is connected across the capacitor, current flows and the potential difference across the capacitor begins to rise but, as more and more charge builds up on the capacitor plates, the current and the rate of rise of potential difference both fall. Finally no further current will flow when the p.d. across the capacitor equals that of the supply voltage V_o. 
The capacitor is then fully charged. 

Current starts to flow and the potential difference across the capacitor drops. As charge flows from one plate to the other through the resistor the charge is neutralised and so the current falls and the rate of decrease of potential difference also falls. Eventually the charge on the plates is zero and the current and potential difference are also zero - the capacitor is fully discharged.

Vbattery = Vresistor + Vcapacitor

Vbattery = IR + Q/C