Calculation
uC(t) = Uq·[1−exp(−t/(R·C))]
After one time constant τ=RC, capacitor voltage reaches about 63.2% of the applied step.
Busch 2006, Abschnitt 6.2
RC capacitor charging
After one time constant τ=RC, capacitor voltage reaches about 63.2% of the applied step.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Capacitor voltage uC(t) — Voltage directly across the capacitor at the selected time after switching.
- Applied step voltage Uq — Constant source voltage applied at t=0 to the previously uncharged RC circuit.
- Charging resistance R — Total series resistance in the charging path, including relevant source and wiring resistance.
- Capacitance C — Effective capacitance of the initially uncharged capacitor.
- Time since switching t — Elapsed time from the idealised voltage step at t=0.
Example
Uq=12 V, R=10 kΩ, C=100 µF and t=1 s give τ=1 s and uC≈7.59 V.
Assumptions and limits
Initially uncharged capacitor, ideal constant source and linear components; leakage, ESR, current limiting and switching thresholds are excluded.
Understand RC capacitor charging
This calculator shows voltage across an initially uncharged capacitor after a DC voltage step and makes the RC time constant directly tangible.
What does this quantity describe?
Capacitor voltage cannot jump at switching. It approaches Uq exponentially: uC=Uq(1−e^(−t/RC)). τ=RC is the time to 63.2%; after about 5τ more than 99% is reached.
Formula and variables
uC(t) = Uq·[1−exp(−t/(R·C))]
τ = R·CuC(t) = Uq·(1−e^(−t/τ))i(t) = (Uq/R)·e^(−t/τ)
| Symbol / input | Meaning |
|---|---|
| Capacitor voltage uC(t) | Voltage directly across the capacitor at the selected time after switching. |
| Applied step voltage Uq | Constant source voltage applied at t=0 to the previously uncharged RC circuit. |
| Charging resistance R | Total series resistance in the charging path, including relevant source and wiring resistance. |
| Capacitance C | Effective capacitance of the initially uncharged capacitor. |
| Time since switching t | Elapsed time from the idealised voltage step at t=0. |
Choose the inputs correctly
Uq is constant post-switch voltage. R is total charging-path resistance including relevant source resistance, C effective capacitance, and t starts at switching with an uncharged capacitor.
How to use the calculator
Identify the real charging path, add its series resistances, obtain C from rating or measurement, and enter the required time. Compare uC with any switching threshold.
Worked example
12 V, 10 kΩ and 100 µF give τ=1 s. After exactly 1 s, uC=12·(1−e⁻¹)≈7.59 V.
Understand the result and units
Charging is fastest initially; during each further time constant the remaining gap to Uq shrinks by the same factor e⁻¹.
R and C are converted to Ω and F so τ results in seconds. Enter t in ms, s, min or h; Uq and uC are voltages.
Typical applications
Power-on delays, reset networks, simple timers, sensor filters and first-order transient laboratory exercises.
Assumptions, limits and common mistakes
Initially uncharged capacitor and ideal voltage step only. ESR, leakage, source current limit, tolerances, tap loading and nonlinear thresholds are excluded.
Common mistake: Time starts at switching and an existing initial voltage cannot be ignored. R must include the actual path, and a µF value must not be entered numerically as farads.
Frequently asked questions
What is “RC capacitor charging” used for?
Power-on delays, reset networks, simple timers, sensor filters and first-order transient laboratory exercises.
Where do the input values come from?
Uq is constant post-switch voltage. R is total charging-path resistance including relevant source resistance, C effective capacitance, and t starts at switching with an uncharged capacitor.
What does the result not cover?
Initially uncharged capacitor and ideal voltage step only. ESR, leakage, source current limit, tolerances, tap loading and nonlinear thresholds are excluded.