Library / Electrical / ELE-12
Electrical
Capacitor time constant
Characteristic time for a capacitor to charge or discharge through a resistor.
- Ref
- ELE-12
- Rev
- v1
- Field
- Electrical
- Result
- τ [ms]
τ in seconds, R in ohms, C in farads. With R in kΩ and C in µF the product comes out directly in milliseconds, which is what the calculator uses.
The time constant is the resistance times the capacitance. A bigger resistor limits the current, and a bigger capacitor needs more charge, so both make the process slower. After one time constant a discharging capacitor has fallen to about 37% of its starting voltage.
Calculator
- Time constant in seconds1 s
- Five time constants (about 99% settled)5 s
- Half time 0.693 RC693.1 ms
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- τ is simply R × C, so doubling either doubles the time. Because it is a product, the sweep over R or C is a straight line.
- After one τ a charging capacitor reaches about 63% of its final voltage, and a discharging one falls to about 37%. After 5τ it is within 1% of its final value.
- Use τ to design delays, filters and debouncing. An RC low-pass filter has a cutoff frequency f = 1/(2πRC).
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (ms) | Local step | Change in result |
|---|---|---|---|---|---|---|
| C Capacitance | 0.1 to 10,000 µF | 1 | 100,000 | 100,000 | +10% | +10 % |
| R Resistance | 0.1 to 1,000 kΩ | 10 | 100,000 | 99,990 | +10% | +10 % |
Sweep of Capacitance
| Capacitance (µF) | Time constant (ms) |
|---|---|
| 0.1 | 1 |
| 0.4217 | 4.217 |
| 1.778 | 17.78 |
| 7.499 | 74.99 |
| 31.62 | 316.2 |
| 133.4 | 1,334 |
| 562.3 | 5,623 |
| 2,371 | 23,710 |
| 10,000 | 100,000 |
Sweep one variable
Variables and how each one contributes
Time constant
What the equation gives you. Everything else feeds it.
Resistance
Resistance the capacitor charges or discharges through. Directly proportional: doubling R doubles the time constant.
Capacitance
Capacitance of the capacitor. Directly proportional: doubling C doubles the time constant.
Worked example with the values above
- Check the units: kΩ × µF = ms.
- τ = RC = 10 × 100 = 1,000 ms.
- That is 1 s. After one time constant a discharging capacitor is at 37% of its starting voltage, and after 5τ at less than 1%.
Assumptions and limits
- Ideal resistor and capacitor, with no leakage and no series resistance in the capacitor.
- Constant supply voltage when charging.
- Linear RC circuit, so charge and discharge are exponential.
Common mistakes
- Entering R in kΩ and C in µF but reading the answer in seconds. It is in milliseconds.
- Expecting the capacitor to be fully charged after one τ. It is at 63%.
- Forgetting the source resistance, which adds to R.
Statistics and uncertainty
Capacitors and resistors both have tolerances, and capacitance also drifts with temperature and voltage. For independent errors, δτ/τ ≈ √[(δR/R)² + (δC/C)²]. A 5% resistor and a 20% electrolytic capacitor give about 21%, so timing circuits that need accuracy use film or ceramic capacitors and 1% resistors.
Where it is used
- Timing and delay circuits.
- RC filters and smoothing.
- Discharge time of stored charge after power-off (safety).
Maths you need
- Exponentials: e−x describes the charging and decay curves
- Prefixes: kΩ × µF = ms