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Time constants
How quickly RC and RL circuits charge and decay.
How quickly RC and RL circuits charge and decay.
A capacitor cannot change voltage instantly, and an inductor cannot change current instantly. Connect either through a resistor to a supply and the change builds up smoothly. The time constant, τ (tau), says how quickly.
An empty capacitor is a short circuit for an instant, so the full supply voltage appears across the resistor and the current is large. As the capacitor fills, its voltage opposes the supply, the voltage left across the resistor shrinks, and so does the current. The capacitor then fills more slowly. Every interval closes the same fraction of what is left, never a fixed amount, which is what makes the curve exponential.
| Time | Charging (of final) | Discharging (left) |
|---|---|---|
| 1 τ | 63.2% | 36.8% |
| 2 τ | 86.5% | 13.5% |
| 3 τ | 95.0% | 5.0% |
| 4 τ | 98.2% | 1.8% |
| 5 τ | 99.3% | 0.7% |
An RL circuit is the same shape with current in place of voltage. A coil resists the current change, and the resistor limits how far it can go. Note that τ = L ÷ R means a larger resistance makes an RL circuit faster, the opposite of an RC circuit.
Resistance in ohms and capacitance in farads give τ in seconds. Keep the units straight: Units and metric prefixes helps with the prefixes.