Capacitance and battery and no resistor and time
If you know that T = RC, then you know that when T gets to RC the capacitor will only be charged up to about 63% of the battery voltage. 

Then, after another RC passes the capacitor will have charged up to about 63% of the difference between the battery voltage and the voltage across the capacitor at the end of the last RC. 

Then, after another RC passes the capacitor will have charged up to about 63% of the difference between the battery voltage and the voltage across the capacitor at the end of the last RC. 

And so on, forever, so you can see that since the charge is exponential the capacitor never really charges up to the battery voltage completely.

This sketch pretty much says it all for the first RC, and if there's no intended resistance in there, then R is equal to the sum of the battery's internal resistance, the wiring resistance, and the capacitor's equivalent series resistance: