What Is the RC Time Constant? (Charge/Discharge)
The RC time constant (τ, tau) is the value that sets how fast a capacitor charges or discharges in a circuit containing a resistor (R) and a capacitor (C). The formula is very simple: τ = R × C.
What Is the Time Constant (τ)?
The time constant is how long it takes the capacitor to reach about 63% of its final value. Multiplying R (ohms) by C (farads) gives a result in seconds.
Charge and Discharge Curve
A capacitor charges not linearly but exponentially (as a curve). With each time constant it steps closer to the final value:
| Time | Charge level |
|---|---|
| 1τ | 63% |
| 2τ | 86% |
| 3τ | 95% |
| 5τ | ~99% (taken as fully charged) |
Worked Example
If R = 10 kΩ and C = 100 µF: τ = 10,000 × 0.0001 = 1 second. So the capacitor reaches about 63% in ~1 second and is fully charged in ~5 seconds.
Where Is It Used?
In timing circuits, button debouncing, soft-start and RC filters; the cutoff frequency is directly related to τ.
Common Mistakes
- Skipping unit conversion: multiplying without converting µF to farads and kΩ to ohms gives a wildly wrong result.
- Assuming linear charging: charging is exponential — fast at first, slowing toward the end.
- Not waiting 5τ: "fully charged" in practice takes about 5 time constants.
Frequently Asked Questions
Why 63%?+
How do I speed up charging?+
Search related parts in our catalog
Find the right part by comparing price, stock and distributors.