Capacitor Charge Time
RC time constant — charging and discharging formulas with 5τ rule of thumb.
Reference
Formulas
- Time constant τ
- = R · C
- Charging
- V(t) = V_f · (1 − e^(−t/τ))
- Discharging
- V(t) = V₀ · e^(−t/τ)
- Fully charged (≥99%)
- ~ 5 τ
- Current during charge
- I(t) = (V_f / R) · e^(−t/τ)
Charge progress
| Time | % of V_f | % of V remaining to go |
|---|---|---|
| 1 τ | 63.2% | 36.8% |
| 2 τ | 86.5% | 13.5% |
| 3 τ | 95.0% | 5.0% |
| 4 τ | 98.2% | 1.8% |
| 5 τ | 99.3% | 0.7% |
| 7 τ | 99.9% | 0.1% |
Example τ values
| R | C | τ | 5τ |
|---|---|---|---|
| 1 kΩ | 1 µF | 1 ms | 5 ms |
| 10 kΩ | 10 µF | 100 ms | 500 ms |
| 100 kΩ | 100 µF | 10 s | 50 s |
| 1 MΩ | 1 µF | 1 s | 5 s |
| 50 Ω | 10 nF | 0.5 µs | 2.5 µs |
Notes
- For big bulk caps on power rails, check soft-start of upstream regulator — infinite inrush current attempts to charge C instantly.
- PTC inrush limiters (NTC thermistors) limit startup current then drop to low R once warm.
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