Capacitance and inductance
Capacitor discharge voltage
- where
- capacitor voltage at time t (V)
- initial voltage (V)
- elapsed time (s)
- resistance (Ω)
- capacitance (F)
Explain this equation
Works out the voltage left on a capacitor after it has discharged through a resistance for a set time. Useful for judging discharge times and bleed resistors.
V(t) is the voltage after time t. V₀ is the starting voltage. R is the discharge resistance and C the capacitance; RC is the time constant. e is the base of natural logarithms, about 2.718.
The discharge current is proportional to the voltage still there, so the voltage falls fast at first and then ever more slowly. That pattern is an exponential decay, set by t/RC.
Sense check: 12 V after one time constant leaves about 4.4 V (37%). After 3RC about 5% remains; after 5RC under 1%.
Watch out: the model never quite reaches zero, and real capacitors can recover some voltage. Always test before touching.
Voltage falls exponentially through a fixed discharge resistance. Work out RC in seconds, divide elapsed time by it, change the sign and evaluate the exponential.
The model approaches zero asymptotically. Real leakage, dielectric absorption and failed discharge components require practical verification.
Enter your values to see the result.
Common mistake
Using base 10 instead of e.
Limits
Ideal isolated capacitor discharging through R; no additional supply.
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.