Capacitor charge time calculator
A capacitor charging through a resistor reaches 63.2% of the supply in one time constant (R × C) and 99% after five. A 470 µF capacitor through 1 kΩ has τ = 470 ms, so it is effectively full after 2.35 seconds.
How to work out charge time
The exponential shape is the thing to internalise: charging is fastest at the start and slows continuously, so the last few per cent take as long as the first sixty. That is why inrush limiters work; a resistor in series limits the initial surge into a large reservoir capacitor, and is then shorted out by a relay once the capacitor is mostly charged. Without it, an empty capacitor looks like a dead short at the instant of switch-on, which is what welds contacts and blows fuses on large supplies.
Questions
Five time constants to 99%. One time constant is resistance times capacitance.
The curve is exponential and approaches the supply asymptotically. Five tau leaves under 1% remaining, which is below component tolerance.
Same time constant through whatever resistance is across it, but a capacitor with nothing across it can hold charge for a very long time.
A large one at high voltage certainly is. Always confirm discharge with a meter rather than assuming, especially in mains equipment.
Only the series resistance. An empty capacitor behaves like a short circuit at the first instant, which is what inrush limiters exist to control.