Exponential circuit response
What is an RC time constant?
The RC time constant describes how quickly a capacitor charges or discharges through a resistor.
It is represented by the Greek letter tau, written τ, and is measured in seconds.
Main RC relationship
RC time constant formula
Time constantτ = RC
- τ is time constant in seconds.
- R is resistance in ohms.
- C is capacitance in farads.
Increasing either resistance or capacitance increases the time needed for the capacitor voltage to change.
Capacitor charging
Charging voltage formula
Charging voltageV(t) = Vₛ(1 − e⁻ᵗ/τ)
After one time constant, the capacitor reaches approximately 63.2% of the source voltage.
Capacitor discharging
Discharging voltage formula
Discharging voltageV(t) = V₀e⁻ᵗ/τ
After one time constant, approximately 36.8% of the initial capacitor voltage remains.
Worked example
Calculate an RC time constant
Suppose a circuit has a resistance of 10,000 Ω and a capacitance of 0.0001 F.
- Use τ = RC.
- Substitute R = 10,000 and C = 0.0001.
- τ = 10,000 × 0.0001.
- The RC time constant is 1 second.
Practical approximation
The five-time-constant rule
- After 1τ, charging reaches about 63.2%.
- After 2τ, charging reaches about 86.5%.
- After 3τ, charging reaches about 95.0%.
- After 5τ, charging exceeds 99%.
Engineers often treat five time constants as effectively fully charged or fully discharged.
SI unit guidance
RC circuit units
- Time constant: seconds (s).
- Resistance: ohms (Ω).
- Capacitance: farads (F).
- Voltage: volts (V).
- Elapsed time: seconds (s).
Model limitations
Assumptions and limitations
- The resistor and capacitor are treated as ideal components.
- Capacitor leakage is not included.
- Equivalent series resistance is ignored.
- Source voltage is assumed constant during charging.
- All calculations use positive magnitudes.
Common questions
RC time constant calculator FAQ
What formula does the RC time constant calculator use?
The basic RC time constant formula is τ = RC, where resistance is measured in ohms and capacitance is measured in farads.
What happens after one RC time constant?
During charging, capacitor voltage reaches about 63.2% of the source voltage. During discharging, about 36.8% of the initial voltage remains.
How long does a capacitor take to charge?
An ideal capacitor approaches full charge exponentially. After about five time constants, it is commonly treated as more than 99% charged.
How do I calculate capacitor charging voltage?
Use V(t) = Vs(1 − e⁻ᵗ/τ), where Vs is source voltage, t is elapsed time, and τ is the RC time constant.
How do I calculate capacitor discharging voltage?
Use V(t) = V₀e⁻ᵗ/τ, where V₀ is the initial voltage, t is elapsed time, and τ is the RC time constant.