Calculation
uC(t) = U0·exp(−t/(R·C))
After one time constant τ=RC, capacitor voltage has decayed to about 36.8% of its initial value.
Busch 2006, Abschnitt 6.2
RC capacitor discharging
After one time constant τ=RC, capacitor voltage has decayed to about 36.8% of its initial value.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Capacitor voltage uC(t) — Remaining capacitor voltage at the selected time after discharge begins.
- Initial voltage U0 — Capacitor voltage immediately before the discharge resistor is connected at t=0.
- Discharge resistance R — Total resistance in the discharge path, including relevant wiring and switch resistance.
- Capacitance C — Effective capacitance of the initially charged capacitor.
- Time since discharge began t — Elapsed time from the idealised connection of the discharge resistor at t=0.
Example
U0=12 V, R=10 kΩ, C=100 µF and t=1 s give τ=1 s and uC≈4.41 V.
Assumptions and limits
Initially fully charged capacitor, no additional charging path and linear components; leakage, ESR and switching thresholds are excluded.
Understand RC capacitor discharging
This calculator mirrors RC charging: it determines how far the voltage on a previously charged capacitor has decayed after a given time through a resistor.
What does this quantity describe?
If a charged capacitor is short-circuited through resistor R at t=0, voltage decays exponentially as uC(t)=U0·exp(−t/(RC)). Time constant τ=RC sets the decay speed; after one τ about 36.8% of U0 remains.
Formula and variables
uC(t) = U0·exp(−t/(R·C))
uC(t) = U0·exp(−t/(R·C))τ = R·C
| Symbol / input | Meaning |
|---|---|
| Capacitor voltage uC(t) | Remaining capacitor voltage at the selected time after discharge begins. |
| Initial voltage U0 | Capacitor voltage immediately before the discharge resistor is connected at t=0. |
| Discharge resistance R | Total resistance in the discharge path, including relevant wiring and switch resistance. |
| Capacitance C | Effective capacitance of the initially charged capacitor. |
| Time since discharge began t | Elapsed time from the idealised connection of the discharge resistor at t=0. |
Choose the inputs correctly
U0 is the capacitor voltage immediately before discharge begins. R is the total discharge resistance including wiring and switch resistance. C is the effective capacitance, t the time elapsed since R was idealised as connected.
How to use the calculator
Measure U0 in the charged state or take it from a prior charging calculation. Use R and C as for charging; evaluate several values of t to sketch the decay curve.
Worked example
U0=12 V, R=10 kΩ, C=100 µF and t=1 s give τ=1 s and uC≈4.41 V; after about 5τ=5 s the voltage has practically decayed to zero.
Understand the result and units
A larger time constant τ=RC means slower decay. For discharge times well beyond 5τ the formula gives essentially zero, though real leakage and ESR can affect the final value.
U0 and uC(t) are voltages, R a resistance, C a capacitance and t a time. All values are converted internally to coherent SI units.
Typical applications
Estimating discharge times for buffer capacitors, safety discharge after switching off equipment, and sizing timer or delay circuits.
Assumptions, limits and common mistakes
Ideal, initially fully charged capacitor with no additional charging path and a linear, temperature-independent R; leakage current, ESR frequency response and switching thresholds are excluded.
Common mistake: Do not use the charging formula (with factor 1−exp(...)) for discharge; the two processes differ in the sign of the exponent. Do not enter R and C in mismatched prefix units.
Frequently asked questions
What is “RC capacitor discharging” used for?
Estimating discharge times for buffer capacitors, safety discharge after switching off equipment, and sizing timer or delay circuits.
Where do the input values come from?
U0 is the capacitor voltage immediately before discharge begins. R is the total discharge resistance including wiring and switch resistance. C is the effective capacitance, t the time elapsed since R was idealised as connected.
What does the result not cover?
Ideal, initially fully charged capacitor with no additional charging path and a linear, temperature-independent R; leakage current, ESR frequency response and switching thresholds are excluded.