Electrical and electronics
RC and RL time constant calculator
Time constant τ = RC or L/R with the charge and discharge percentages at 1τ to 5τ, the value at any time and the −3 dB cut-off frequency.
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Result
| Time | Elapsed | Rising (charging) | Falling (discharging) |
|---|---|---|---|
| 1τ | 1 s | 63.21% | 36.79% |
| 2τ | 2 s | 86.47% | 13.53% |
| 3τ | 3 s | 95.02% | 4.979% |
| 4τ | 4 s | 98.17% | 1.832% |
| 5τ | 5 s | 99.33% | 0.6738% |
Method and limits
A step applied to a series RC circuit charges the capacitor as v(t) = V (1 − e−t/τ) with τ = R C; in a series RL circuit the current rises as i(t) = (V/R)(1 − e−t/τ) with τ = L / R. After one time constant the response has covered 63.2% of the step, after 5τ 99.3%. Discharge follows e−t/τ. The same τ sets the −3 dB corner frequency of the matching first-order filter, fc = 1 / (2π τ).
Worked example: 10 kΩ and 100 µF give τ = 1 s; the capacitor reaches 63.2% of the supply after 1 s and 99.3% after 5 s; fc = 0.159 Hz.
Limits
Ideal components and a perfect step from a zero-impedance source are assumed. Real capacitors leak and have series resistance, inductors have winding resistance (add it to R) and cores that saturate.
References
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