The Capacitor Charge Time

Hi,
I am learning Filter circuit and there is problem on the time to charge capacitor fully.
As the formula:
Vc = V(1 - e-t/RC)
the time is only depend on RC time constant but in a website I read they said that the time is depend on 2 things:
- time constant
-the current throught the capacitor
Would you tell me why it is depended on the current throught the capacitor?
Thanks in advance.

If we have a RC circuit then the charging current (current through the capacitor) is determine by a resistor.
So the small charging current (high resistance) means slow charging.
But if current charging current is larger the the capacitor will charge faster.
For the constant current this equation hold
C = Q/V = (I * t)/V ----> V = (I *t)/C

I think that website is trying to say something that is relevant, but not doing a very good job of it. This is how I would put it:

In an RC circuit (series-connected voltage source, resistor, and capacitor), the time it takes to bring the capacitor to some fraction of its total charge (meaning the capacitor voltage is equal to the source voltage and the current in the resistor is zero) is dependent on two things:

1) The capacitance, C, since this determines how much charge must be accumulated on the capacitor to reach a desired fraction of the total charge. The larger the resistor, the longer it will take to accumulate the necessary charge, all else being equal.

and

2) The current, since this determines how fast that charge is accumulating. The larger the resistor, the smaller the current and, hence, the longer it will take to accumulate the necessary charge, all else being equal.

At any given instant during the charging process, the current will be dictated by the resistor as follows: The capacitor will have some fraction of the supply voltage across it and the voltage across the resistor will therefore be the difference between the supply voltage and the voltage already on the capacitor. This voltage, divided by the resistance, gives the current.

Cranking through the math shows that the these two effects can be expressed by a single quantity, the product of R and C, known as the RC time constant. In essence, if you double one, you can compensate for it by halving the other.