Define what “charged enough” means
An ideal capacitor charging through a resistor approaches supply voltage gradually. To decide how long to wait, specify a threshold: 90%, 99% or a particular voltage. Saying only “charged” is ambiguous.
Start with a discharged capacitor, a constant 5 V supply and a series resistor. Initial voltage is 0 V. Changing that initial condition changes the curve even if R and C stay fixed.
A 47 µF capacitor with a 10 kΩ resistor
Vc(t) = Vs (1 − e^(−t/τ))
Time to fraction f: t = −τ ln(1 − f)
| Threshold | Voltage | Time |
|---|---|---|
| 63.21 % | 3.1606 V | 0.4700 s |
| 90 % | 4.5 V | 1.0822 s |
| 99 % | 4.95 V | 2.1644 s |
One time constant is not 90%. At five time constants—2.35 s here—the voltage reaches about 99.326%. Exact 100% is an asymptotic limit; real circuits are evaluated using tolerances.
Doubling R and doubling C match the timing, but not everything else
20 kΩ with 47 µF and 10 kΩ with 94 µF both give τ = 0.94 s. Their voltage curves match under the same initial conditions. Initial current is Vs/R, however: 0.25 mA in the first case and 0.5 mA in the second. At equal voltage, doubling C also doubles stored energy, E = C V²/2.
An absolute threshold also depends on supply voltage. Reaching 4.5 V from zero with a 5 V supply requires 90%; a 3 V supply never reaches it in this model. The ratio t/τ depends only on the chosen fraction.
Leakage, capacitor ESR, supply changes and tolerances are omitted. The related discharge model starts at Vs with a resistor connected and the source removed: Vc = Vs e^(−t/τ).
Predict the time, then inspect the curve
Double R or C in the experiment and check voltage at a specific instant. Record the fraction reached before changing another value, so you can separate the effect of time from the effect of the circuit.
With τ = 0.47 s, how long does discharge to 10% take?
t = −0.47 ln(0.1) = 1.0822 s. This matches the time to 90% under the stated initial conditions.
Does doubling the supply double the time to 90%?
No. At fixed R and C, the fraction reached depends on t/τ. The voltage corresponding to 90% doubles, not the time to reach it.
Further reading: OpenStax: RC circuits ↗. Accessed October 24, 2026. The numerical cases in this guide are original teaching examples, not component measurements.