RC Circuit Charge Time Calculator
Calculate the voltage across a capacitor at any time during charging.
Shows the time constants (63%, 87%, 95%, 99%) for RC circuit charging.
When a capacitor charges through a resistor, the voltage across the capacitor rises exponentially toward the source voltage. It never reaches the source voltage instantaneously — instead it follows:
V(t) = V₀ × (1 − e^(−t/RC))
where τ = RC is the time constant — the fundamental timing parameter of the circuit.
What is the time constant τ = RC?
The time constant τ (tau) is the time it takes the capacitor to charge to about 63.2% of the source voltage. It depends on:
- Resistance R in ohms (Ω) — more resistance = slower charging
- Capacitance C in farads (F) — more capacitance = slower charging
Charging milestones:
| Time | Charge % | Notes |
|---|---|---|
| 1τ | 63.2% | One time constant |
| 2τ | 86.5% | Two time constants |
| 3τ | 95.0% | Three time constants |
| 4τ | 98.2% | Four time constants |
| 5τ | 99.3% | “Fully charged” in practice |
Why does this matter?
RC time constants are everywhere in electronics:
- Camera flash circuits charge a capacitor through a resistor
- Audio tone controls use RC networks to boost or cut frequencies
- Digital circuits use RC delays to debounce switches and set timing
- Power supplies use large RC time constants for smooth filtering
Example: An RC circuit with R = 10 kΩ and C = 100 μF has τ = 10,000 × 0.0001 = 1 second. It takes about 5 seconds to fully charge a capacitor from 0 V to nearly the supply voltage.