What is the RC time constant?
When a resistor feeds a capacitor, the capacitor charges quickly at first and then more and more slowly. The time constant τ = R × C (in seconds) sets the pace: after 1τ the capacitor reaches 63.2% of the supply voltage, or drops to 36.8% when discharging. For 10 kΩ and 100 nF, τ = 10,000 × 0.0000001 = 1 ms.
Typical uses are reset delays, switch debouncing, simple timers and filters.
Charge and discharge formulas
- Charging: VC = VS × (1 − e−t/τ), so reaching X% takes t = −τ × ln(1 − X/100)
- Discharging: VC = V0 × e−t/τ, so falling to X% takes t = −τ × ln(X/100)
When switch S closes, the capacitor charges through R from 0 V; connect the top of R to ground instead and it discharges through R. The chart shows Vc as a percentage of Vs (or of the starting voltage) against time in τ.
| Time | Charged to | Left when discharging |
|---|---|---|
| 0.693τ | 50% | 50% |
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 2.303τ | 90% | 10% |
| 3τ | 95.0% | 5.0% |
| 4τ | 98.2% | 1.8% |
| 5τ | 99.3% | 0.7% |
Cutoff frequency
The same R and C used as a low-pass or high-pass filter have a cutoff frequency of fc = 1 / (2π × R × C), where the signal is 3 dB down (about 70.7%). For 10 kΩ and 100 nF that is about 159 Hz.
Frequently asked questions
How long does a capacitor take to fully charge?
In theory it never quite gets there. In practice 5τ (99.3%) is treated as fully charged, and 3τ (95%) is often close enough.
How do I enter the capacitance?
1 µF = 1,000 nF = 1,000,000 pF. You can type 100n, 0.1u, 100nF or 4u7; a plain number is read as µF. A ceramic capacitor marked “104” is 10 × 104 pF, which is 100 nF.
Why does my circuit not match the calculation?
Capacitors often have a tolerance of ±10% to ±20%, and electrolytics more. The source resistance, the load and the input impedance of your meter or scope also change the result. If the timing matters, use a tight-tolerance capacitor such as C0G or film, and measure.