RC Circuit Time Constant
RC Circuit Time Constant
When a capacitor charges through a resistor, the voltage rises exponentially. The time constant τ sets how fast: after one τ the capacitor reaches about 63 % of the supply, and after five τ it is essentially fully charged.
For a series RC circuit τ = RC.
Inputs
R := 10 kOhm=10000 Ω
C := 100 uF=1e-04 A^2·s^4/kg/m^2
Time constant and settling time
tau := R·C=1 s
t_settle := 5·tau=5 s
Results
The time constant has units of seconds (ohm × farad = second). Use τ to size timing, debounce and filter networks: the –3 dB corner frequency of an RC low-pass filter is f = 1/(2πτ). The settling time shown is the practical “fully charged” point.
Assumptions & limitations
- Ideal resistor and capacitor, single time constant.
- Step input from a stiff source; no load on the capacitor.
- Linear (no dielectric or leakage effects modelled).