RC timing and transient capacitor voltage
The time constant controls how quickly the ideal voltage approaches its final state. A 99% transition means reaching 99% of the charging supply or falling to 1% of the initial discharge voltage. It is a threshold, not exact completion.
For the initial current of a specified resistive charging path, the Ohm’s Law Calculator provides a separate voltage-resistance calculation.
The formula
The charge model begins with an uncharged capacitor connected through the resistor to an ideal DC source. The discharge model begins at the entered initial voltage and decays through the resistor toward zero. Capacitance in microfarads is converted to farads.
Worked example
A 10,000 Ω resistor and 100 µF capacitor have τ = 1 s. Charging from zero toward 5 V gives 3.160603 V after 1 s. Discharging from 5 V gives 1.839397 V after the same time. A 99% transition takes 4.605170 s.
How to use this calculator
- Enter resistance, capacitance using the units shown.
- Set supply or initial capacitor voltage, elapsed time, transient mode.
- Calculate and review rc time constant alongside the supporting quantities.
One time constant is a reference point
After one τ, ideal charging has completed about 63.2% of its voltage transition and discharging retains about 36.8% of its initial voltage. The curve approaches its final value exponentially, so exact completion takes no finite time in this mathematical model. Use a required threshold rather than expecting an exact zero or full supply voltage.
Equivalent resistance seen by the capacitor
The entered resistance must describe the relevant charging or discharging path. Source resistance, other branches, leakage, and a measuring instrument can change that effective value. Complex networks may have several time constants and cannot be reduced to a single RC pair without analysis. Component tolerances and capacitance variation also alter the observed timing.
Assumptions & limitations
What this calculation assumes
- One ideal resistor and one constant capacitor determine the transient.
What to keep in mind
- Excludes leakage, multiple time constants, dielectric behavior, and source or switching limits.
Common questions
Is five time constants exactly full charge?
No. It is about 99.326% of the voltage transition. The ideal curve reaches the exact final value only asymptotically.
Why is discharge still above zero?
Exponential decay approaches zero gradually. A practical circuit uses a specified voltage threshold to define completion.
What is the initial condition for charging?
The capacitor starts at zero volts and charges toward the entered supply through the entered resistance.
Sources & further reading
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