How it works
When a capacitor charges through a resistor, the voltage rises exponentially. The resistor limits the current and the capacitor stores charge, so a bigger R or C makes the process slower. The product R × C is the time constant τ.
After one τ a charging capacitor is at 63.2% of its final voltage; after five τ it is above 99%. The same τ sets the corner (−3 dB) frequency of a simple RC low-pass or high-pass filter.
Worked example
A 10 kΩ resistor charging a 100 µF capacitor to 95%:
- τ = R × C = 10 kΩ × 100 µF = 1 s
- Time to 95% = −τ × ln(1 − 0.95) = 2.996 s
- Cutoff f = 1 ÷ (2π τ) = 159.155 mHz
- Rise time (10–90%) = 2.197 × τ = 2.197 s
| Input | Value |
|---|---|
| Resistance | 10 |
| Resistance unit | kΩ |
| Capacitance | 100 |
| Capacitance unit | µF |
| Target charge level | 95 % |
| Result | Value |
|---|---|
| Time constant τ | 1 s |
| Time to reach target | 2.996 s |
| Cutoff frequency (−3 dB) | 159.155 mHz |
| 10–90% rise time | 2.197 s |
Assumptions and limits
- Ideal resistor and capacitor with no leakage, series resistance, or source impedance.
- Step input with the capacitor initially fully discharged.
- Electrolytic capacitors can be ±20% or worse, so real timing varies.
Common questions
What is the RC time constant?
It is the time for a capacitor charging through a resistor to reach about 63.2% of its final voltage, equal to R times C in seconds.
How long does a capacitor take to fully charge?
In theory never, but after 5τ it is at 99.3% and is treated as fully charged.
How do I find the cutoff frequency of an RC filter?
f = 1 ÷ (2π R C). At this frequency the output is 70.7% (−3 dB) of the input.
Sources
- Standard first-order RC circuit theory: τ = RC, V(t) = V(1 − e^(−t/τ)), f_c = 1 ÷ (2πRC), 10–90% rise time = 2.197 τ.
Updated 2026-09-30