The time constant
When a capacitor charges through a resistor, its voltage rises quickly at first and then more slowly. The time constant, τ = R × C, is the time to reach 63% of the supply. After 3τ it's at 95% and after 5τ over 99%, which is usually taken as fully charged. Discharging follows the same curve in reverse. With R in ohms and C in farads, τ comes out in seconds, so 10 kΩ and 100 nF give 1 ms.
RC filters
The same pair makes a simple filter. With the capacitor to ground, it's a low-pass filter. Swap them and it's a high-pass filter. Either way, the −3 dB cutoff frequency is f = 1 ÷ (2πRC), and the response falls at 6 dB per octave beyond it. RC filters are used for tone controls, audio filters on a receiver's output, decoupling and anti-aliasing before an analogue-to-digital converter.
For sharper filters with inductors, see the low-pass and bandpass filter calculators, and for oscillators and timers, the 555 timer calculator.
Questions
What is the RC time constant formula?
τ = R × C, in seconds when R is in ohms and C in farads.
How long does a capacitor take to charge?
About 5 time constants to reach over 99%. After one time constant it's at 63%.
What is the cutoff frequency of an RC filter?
f = 1 ÷ (2πRC). With 10 kΩ and 100 nF, it's about 159 Hz.
Is a low-pass or high-pass filter the same RC values?
Yes, the cutoff is the same. Only the positions of R and C are swapped.