Capacitor Discharge Time Formulas

Capacitor discharge formulas: the time constant of a discharge resistor, the voltage after a time, the time to fall to a safe voltage and the stored energy.

The formulas

R is the discharge resistance in ohms, C the capacitance in farads and V0 the starting voltage in volts. The discharge is exponential, so it never reaches zero in theory, and the time to a safe voltage depends on the starting voltage and the limit. The voltage that is safe and the time allowed come from the standard or the equipment rules you work to, so use your own. The values here are examples. A capacitor bank can also hold a charge in the dielectric after a short discharge, so follow the maker's rules for shorting it.

Worked example: 500 µF with a 100 kΩ discharge resistor from 400 V

1. τ = 100,000 × 500e-6 = 50 s
2. Time to fall to 50 V: t = 50 × ln(400 / 50) = 104 s
3. Voltage after 60 s: 400 × e^(−60 / 50) = 120.5 V
4. E = ½ × 500e-6 × 400² = 40 J and the starting power is 400² / 100,000 = 1.6 W

Time to fall from 400 V (same circuit)

Frequently asked questions

Why does the discharge never finish?

The current falls with the voltage, so the voltage falls by the same fraction in each time constant. It becomes small but never exactly zero.

How many time constants to fall to a safe voltage?

It depends on the ratio of the start to the limit. A fall to 1/8 of the starting voltage takes ln(8) = 2.08 time constants.

How is the discharge resistor chosen?

A smaller resistor discharges faster but loses more power when the capacitor is live. Pick the value that meets the time in your standard with a power loss you can accept.

Does the resistor have to survive the discharge?

Yes. It must handle the starting power and the stored energy, which this page gives.

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