RC Time Constant

Charging from 0 towards $V_s$:

$v_C(t) = V_s \left(1 - e^{-t/RC}\right)$

Discharging from $V_0$:

$v_C(t) = V_0\, e^{-t/RC}$

Time	Charged to
1τ	63.2 %
2τ	86.5 %
3τ	95.0 %
5τ	99.3 % ("fully" charged)

Example: 10 kΩ and 100 µF give τ = 1 s. RC circuits set delays, debounce buttons, form filters and generate the timing in 555 oscillators.