RC / RL time constant calculator
Pick RC (a capacitor charging through a resistor) or RL (current building in a coil). Enter the parts and get τ, the full five-time-constant table, and — if you give a time — how far along it is.
| Después de | Alcanzado | Tiempo |
|---|---|---|
| 1τ | 63.2 % | — |
| 2τ | 86.5 % | — |
| 3τ | 95.0 % | — |
| 4τ | 98.2 % | — |
| 5τ | 99.3 % | — |
Se carga desde cero hacia el valor final. La descarga es la imagen en espejo: después de 1τ, queda el 36.8 %. Un capacitor que parece descargado todavía puede darle un choque — mídalo.
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How it works
- τ = R × Cohms × farads = seconds
- τ = L ÷ Rhenries ÷ ohms = seconds
- 1 − e−t/τfraction reached at time t
A capacitor does not charge instantly: the resistor limits how fast current can fill it, and as it fills the push left to drive more current shrinks. The result is a curve that is steep at first and flattens out. A coil is the same shape turned round — its current climbs toward V ÷ R, fast at first and then slowly. The time constant τ is the yardstick for both: in each τ the circuit closes 63.2 % of the gap that is left.
Worked examples
RC: 10 kΩ and 100 µF
- τ = 10,000 × 0.000 1 = 1 s.
- Fully charged, for practical purposes, at 5τ = 5 s.
- At 2 s: 1 − e−2 = 1 − 0.135 = 86.5 % of the supply voltage.
RL: a 500 mH coil with 100 Ω of winding
- τ = 0.5 ÷ 100 = 0.005 s = 5 ms.
- On 24 V DC the current heads for 24 ÷ 100 = 0.24 A, and gets 63.2 % of the way (0.152 A) in 5 ms.
- It is all but there at 5τ = 25 ms.
Preguntas frecuentes
Why 63.2 %?
Charging follows the curve 1 − e−t/τ. At t = τ that is 1 − e−1 = 0.632. Each further time constant closes 63.2 % of whatever gap is left, which is why the steps are 63.2, 86.5, 95.0, 98.2 and 99.3 %.
Is it really finished after five time constants?
Mathematically it never quite gets there; practically, at 5τ it is within 0.7 % of the final value, and that is the rule of thumb everyone uses for “fully charged” or “fully built up”. The same numbers apply to discharging: after 5τ less than 0.7 % is left — which is not the same as safe on a big capacitor. Measure before you touch.
What does the time constant mean for an RL circuit?
For a coil, τ = L ÷ R is how long the current takes to reach 63.2 % of its final value (V ÷ R) after the switch closes. A bigger inductance or a smaller resistance makes it slower.
Ver también
- Capacitance — the lesson behind this tool.
- Inductance — the lesson behind this tool.
- Capacitive & inductive reactance — the same parts on AC.
- Motor control: timers — where time delays show up on the job.
- Hojas de fórmulas
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