Capacitance and inductance
RC time constant
- where
- time constant (s)
- resistance (Ω)
- capacitance (F)
Explain this equation
Works out the time constant of a resistor–capacitor circuit. Sets how quickly a capacitor charges or discharges through a resistance.
τ (tau) is the time constant in seconds. R is the resistance the capacitor charges or discharges through, in ohms. C is the capacitance in farads.
More resistance limits the current, and more capacitance needs more charge, so both slow things down. Ohms times farads comes out in seconds.
Sense check: 1 kΩ with 100 µF gives 0.1 s. After one τ a charging capacitor reaches about 63% of its final voltage; a discharging one falls to about 37%. After about 5τ it is treated as complete.
Watch out: 5τ is a rule of thumb, not proof that a real capacitor is safe.
The time constant sets the pace of a first-order RC response. After one time constant, an initially uncharged capacitor reaches about 63.2% of its final charging voltage.
After one discharging time constant about 36.8% remains. Five time constants is an approximation, never proof that a real capacitor is safe to touch.
Enter your values to see the result.
Common mistake
Calling one time constant a full charge or discharge.
Limits
Ideal first-order RC network; equivalent resistance seen by capacitor.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.