Time it takes for a RC circuit to fully charge

[mathnoobie]

Homework Statement

How much time does an RC circuit require to become fully charged assuming that the capacitor was initially uncharged.
resistance = R
capacitance = C
Voltage = V

Homework Equations

Q=CV(1-e^(-t/RC)

The Attempt at a Solution

so T = -ln(Q/(CV) - 1)RC
but Q = 0 since it's initially uncharged?
so T=-ln(0-1)RC

I'm not quite sure what to do for this problem because this error isn't in the domain of the natural log. Honestly, I don't even understand the formula, if CV is the final possible charge, then is Q=CV?

 

[CWatters]

Consider the current through the resistor...

I = V_R/R

where the voltage V_R across the resistor = Source Voltage - Capacitor voltage

So as the capacitor voltage rises the current through the resistor falls. This reduces the rate at which the capacitor charges. In theory the capacitor never becomes fully charged because the current falls towards zero.

The voltage on the capacitor looks like this..

http://www.interfacebus.com/RC-Time-Constant-Rising-Voltage-Chart.jpg

After "5 time constants" (eg 5 * RC) the voltage will be within 1% of the supply voltage.