How it’s calculated
When a resistor charges a capacitor (or a voltage is applied to an inductor through a resistor), the voltage or current approaches its final value exponentially. The time constant τ is the time to reach 63.2% of the change; after 5τ the transient is over 99% complete.
| Elapsed time | Rising (charging) | Decaying |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 4τ | 98.2% | 1.8% |
| 5τ | 99.3% | 0.7% |
Example: 10 kΩ and 100 µF give τ = 10,000 × 100 × 10⁻⁶ = 1.0 s. After 1 s the capacitor is at 63.2% of the supply voltage, after 5 s at 99.3%; f_c = 1 ÷ (2π × 1) = 0.159 Hz. An RL circuit with 100 mH and 50 Ω has τ = 0.1 ÷ 50 = 2 ms.
Frequently asked questions
How long does a capacitor take to fully charge?
In theory never exactly; in practice 5τ (99.3%) is treated as fully charged.
Why does an RL time constant use L/R, not L×R?
A larger resistance damps the inductor’s current change faster, so τ gets shorter as R increases: τ = L/R.
Which resistance do I use?
The total resistance seen by the capacitor or inductor, including source and wiring resistance (the Thevenin resistance).
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Sources
- University Physics Vol. 2, 10.5 RC Circuits — OpenStax
- University Physics Vol. 2, 14.4 RL Circuits — OpenStax
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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