Capacitor Safe-Discharge Time

t = −R · C · ln(Vsafe / V0)

Quick answer

This calculator solves t = −R × C × ln(Vsafe / V0) for Discharge Time. With Bleeder Resistor 10 kΩ, Capacitance 100 µF, Safe Voltage 12 V, Initial Voltage 26.4 V, the result is 0.7885 s. It solves in 5 directions, so you can enter the values you have and get the one you need.

Calculator

Discharge Time (s)
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Formula

t = −R × C × ln(Vsafe / V0)

Description

A bleeder resistor discharges a capacitor exponentially, and this gives the time for the voltage to fall from its initial value to a safe touch level. It is essential for safety design in power supplies and high-voltage equipment: the resistor must drain the stored charge to under ~50 V within a required time (often 1–5 seconds) after power is removed.

Variables

  • t — Time to reach the safe voltage (s)
  • R — Bleeder/discharge resistance (Ω)
  • C — Capacitance (F)
  • Vsafe — Target safe voltage (V)
  • V0 — Initial charged voltage (V)

Practical Notes

Safety standards (e.g. IEC) often require discharge to ≤ 50 V within 1 s (or 5 s for larger equipment). Smaller R discharges faster but wastes more standby power; size it to meet the time limit with margin.

Symbols and units

Symbol Meaning Default unit Accepted units
t Discharge Time s ps, ns, µs, ms, s, min, h
R Bleeder Resistor kΩ mΩ, Ω, kΩ, MΩ
C Capacitance µF pF, nF, µF, mF, F
Vsafe Safe Voltage V pV, nV, µV, mV, V, kV
V0 Initial Voltage V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Bleeder Resistor 10 kΩ, Capacitance 100 µF, Safe Voltage 12 V, Initial Voltage 26.4 V
  2. 2. The relation: t = −R × C × ln(Vsafe / V0)
  3. 3. Substitute: R = 10 kΩ, C = 100 µF, Vsafe = 12 V, V0 = 26.4 V
  4. 4. Result: Discharge Time = 0.7885 s

Related quantities from the same inputs

  • P = V² / R = 14.4 mW
  • I = V / R = 1.2 mA

Worked examples

Minimum range

Given: Bleeder Resistor 100 Ω, Capacitance 100 nF, Safe Voltage 0.33 V, Initial Voltage 0.726 V

Result: Discharge Time = 7.885 µs

Low range

Given: Bleeder Resistor 1 kΩ, Capacitance 1 µF, Safe Voltage 3.3 V, Initial Voltage 7.26 V

Result: Discharge Time = 0.7885 ms

Typical

Given: Bleeder Resistor 10 kΩ, Capacitance 100 µF, Safe Voltage 12 V, Initial Voltage 26.4 V

Result: Discharge Time = 0.7885 s

High range

Given: Bleeder Resistor 100 kΩ, Capacitance 1 mF, Safe Voltage 0.23 kV, Initial Voltage 0.506 kV

Result: Discharge Time = 1.314 min

Maximum range

Given: Bleeder Resistor 1 MΩ, Capacitance 10 mF, Safe Voltage 2.3 kV, Initial Voltage 5.06 kV

Result: Discharge Time = 2.19 h

Solving for each variable

Solve for Discharge Time

Bleeder Resistor 100 Ω, Capacitance 100 nF, Safe Voltage 0.33 V, Initial Voltage 0.726 V → 7.885 µs

Solve for Bleeder Resistor

Discharge Time 100 µs, Capacitance 100 nF, Safe Voltage 0.33 V, Initial Voltage 0.726 V → 1.268 kΩ

Solve for Capacitance

Discharge Time 100 µs, Bleeder Resistor 100 Ω, Safe Voltage 0.33 V, Initial Voltage 0.726 V → 1.268 µF

Solve for Safe Voltage

Discharge Time 100 µs, Bleeder Resistor 100 Ω, Capacitance 100 nF, Initial Voltage 0.726 V → 32.96 µV

Solve for Initial Voltage

Discharge Time 100 µs, Bleeder Resistor 100 Ω, Capacitance 100 nF, Safe Voltage 0.33 V → 7.269 kV

How Discharge Time changes with Bleeder Resistor

Bleeder Resistor (input) Discharge Time (result)
1 kΩ 78.85 ms
2.5 kΩ 0.1971 s
5 kΩ 0.3942 s
7.5 kΩ 0.5913 s
10 kΩ 0.7885 s
15 kΩ 1.183 s
20 kΩ 1.577 s
40 kΩ 3.154 s
70 kΩ 5.519 s
100 kΩ 7.885 s

The same result in other units

Unit Value
µs 788500
ms 788.5
s 0.7885
min 0.01314
h 0.000219

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Frequently asked questions

How do you calculate Capacitor Safe-Discharge Time?

Use t = −R × C × ln(Vsafe / V0). With Bleeder Resistor 10 kΩ, Capacitance 100 µF, Safe Voltage 12 V, Initial Voltage 26.4 V, Discharge Time works out to 0.7885 s.

What is the formula for Capacitor Safe-Discharge Time?

The formula is t = −R × C × ln(Vsafe / V0). A bleeder resistor discharges a capacitor exponentially, and this gives the time for the voltage to fall from its initial value to a safe touch level.

How do you find Bleeder Resistor when you know the other values?

Rearrange for Bleeder Resistor: with Discharge Time 100 µs, Capacitance 100 nF, Safe Voltage 0.33 V, Initial Voltage 0.726 V, Bleeder Resistor is 1.268 kΩ.

How do you find Capacitance when you know the other values?

Rearrange for Capacitance: with Discharge Time 100 µs, Bleeder Resistor 100 Ω, Safe Voltage 0.33 V, Initial Voltage 0.726 V, Capacitance is 1.268 µF.

What units does Capacitor Safe-Discharge Time use?

Discharge Time is shown in µs, ms, s, min, h. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

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