The voltage of capacitor across battery never reaches battery voltage
you have to understand one the thing for eg,if you connect a capacitor across a 9V PP3 battery or some other battery (not fruit or vegetable battery) the capacitor would get immediately charged to the battery voltage (but it would take a certain time because of the presence of internal resistance would reduce the flow of charge Q; C=Q/V) and the current through the capacitor would get immediately reduced.

Click here and simulate the circuit by giving different R values like a)0.1 ohm b)1 ohm c)100 ohm d)1K and observe the volatge and current of capacitor for different values of resistor.