Charge a capacitor through a resistor and the voltage does not rise linearly. It approaches the supply asymptotically, fast at first and then ever more slowly, with the whole shape set by a single number: the time constant.
Ohms times farads gives seconds. 10 kΩ with 100 µF is 1 second. After one time constant the capacitor has reached 63.2% of the supply; after five it is at 99.3%, which is close enough that most engineering treats 5τ as fully charged.
Discharge is the same curve mirrored
Discharging follows V(t) = V₀ · e^(−t/τ) with the same τ, provided the discharge path has the same resistance. It often does not — a capacitor charged through a large resistor and discharged through a transistor empties far faster than it filled. That asymmetry is exactly how a 555 timer produces a duty cycle other than 50%.
Where you use it
- Debouncing a mechanical switch, where a few milliseconds of τ smooths the contact bounce.
- Power-on reset circuits that hold a line low until the rail has stabilised.
- Setting the blink rate of a 555 or the ramp time of a simple oscillator.
- Choosing decoupling capacitors, where you want τ short enough to respond to load steps.
Percentage to time constants
| Charged to | Time |
|---|---|
| 50% | 0.69 τ |
| 63.2% | 1 τ |
| 90% | 2.30 τ |
| 95% | 3.00 τ |
| 99% | 4.61 τ |
| 99.9% | 6.91 τ |