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| R | Calculated C | Actual Time Constant (τ) | Error (%) |
|---|
| C | Calculated R | Actual Time Constant (τ) | Error (%) |
|---|
Given: R = 10 kΩ, C = 1 μF, Vin = 5 V
Given: R = 47 kΩ, C = 2.2 μF, V0 = 12 V
Given: R = 1 kΩ, C = 100 nF, f = 10 kHz square wave
The time constant of a resistor-capacitor circuit is τ = R × C, in seconds when resistance is in ohms and capacitance in farads. A 10 kΩ resistor with a 100 µF capacitor gives τ = 1 second.
Charging follows an exponential that never quite finishes, so the convention is to treat five time constants as complete:
| Elapsed | Charged to | Discharged to |
|---|---|---|
| 1τ | 63.2% | 36.8% |
| 2τ | 86.5% | 13.5% |
| 3τ | 95.0% | 5.0% |
| 5τ | 99.3% | 0.7% |
An RC network is also a first-order filter, and its −3 dB cutoff is fc = 1/(2πRC) = 1/(2πτ). Time-domain response and frequency-domain response are two views of one circuit: a long time constant means a slow response and a low cutoff frequency, and the two cannot be chosen independently.
This is why a filter that removes noise effectively will also slow down the signal it is filtering — a trade that has to be made deliberately rather than discovered later.
One practical caution: the capacitor’s actual value may differ substantially from its nominal one. Electrolytics are often ±20% or worse and lose capacitance as they age, while Class 2 ceramics lose value under DC bias. Timing that depends on absolute accuracy should use a film or C0G capacitor rather than relying on a bulk part.
τ = R × C, in seconds with resistance in ohms and capacitance in farads. A 10 kΩ resistor with 100 µF gives a one-second time constant.
Strictly it never does, since the approach is exponential. Five time constants reaches 99.3% and is the normal engineering definition of fully charged.
fc = 1/(2πRC) = 1/(2πτ). They describe the same circuit, so a long time constant necessarily means a low cutoff frequency and a slow response.
Long enough to outlast the mechanical bounce, typically a few milliseconds. Too short lets bounces through; too long makes the switch feel unresponsive.
Usually capacitor tolerance. Electrolytics are often ±20% and degrade with age, and Class 2 ceramics lose capacitance under DC bias. Use film or C0G parts where timing accuracy matters.
Only if the resistance is the same in both directions. Circuits that charge through one path and discharge through another — such as a diode-steered network — have different constants each way.