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.
Was this article helpful?