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Calculate the RC time constant and charging time for any resistor-capacitor combination.
V(t) = Vcc × (1 − e^(−t/τ))
V(t) = Vcc × (1 − e−t/τ)
When you apply a voltage to an RC circuit, the capacitor doesn't charge instantly. Current flows through the resistor and gradually builds up charge on the capacitor plates. The rate of charging follows an exponential curve, getting slower as the capacitor voltage approaches the supply voltage.
The time constant τ = R × C tells you how fast the circuit responds. A 10kΩ resistor with a 100µF capacitor gives τ = 1s. After one time constant the capacitor is at 63.2% of Vcc. After five time constants it's at 99.3%, which is close enough to call it fully charged for most purposes.
One practical note: the capacitor voltage at any moment is V(t) = Vcc × (1 − e^(−t/τ)). If you need to reach a specific voltage, use the target voltage field above. This is useful when designing timing circuits, power supply filters, or debounce circuits where you need to hit a threshold voltage at a precise time.
Time Constant
τ = R × CCharging Voltage
V(t) = Vcc × (1 − e^(−t/τ))RC charge and discharge:
Charging: Vc(t) = Vs × (1 – e^(–t/τ))
Discharging: Vc(t) = V₀ × e^(–t/τ)
Time constant: τ = R × C
Key time points:
t = 1τ: 63.2% charged (36.8% discharged)
t = 2τ: 86.5% charged
t = 3τ: 95.0% charged
t = 5τ: 99.3% charged ← considered 'fully charged'
Charge stored: Q = C × V Energy stored: E = ½ × C × V²| R | C | τ | 5τ (full charge) | Application |
|---|---|---|---|---|
| 1kΩ | 1µF | 1ms | 5ms | Audio coupling |
| 10kΩ | 100nF | 1ms | 5ms | Debounce filter |
| 47kΩ | 10µF | 470ms | 2.35s | Power-on delay |
| 1MΩ | 1µF | 1s | 5s | Timer circuit |
| 100Ω | 100µF | 10ms | 50ms | Power supply filter |
| 10kΩ | 47nF | 470µs | 2.35ms | RC oscillator |
τ needed ≥ 10ms / 5 = 2ms.
Use R=10kΩ, C=220nF: τ = 2.2ms, 5τ = 11ms ✓
Firmware reads GPIO after 10ms delay after interrupt — noise suppressed.
τ = 100ms/5 = 20ms.
R=100kΩ, C=220nF: τ = 22ms, 5τ = 110ms ✓
Capacitor holds RESET low while power supply stabilizes.
For precision timing, use 1% resistors and ±5% or better capacitors. Electrolytic capacitors have ±20% tolerance — avoid for precision RC timing. Leakage current in electrolytic caps causes slow drift in long time constants (> 1s). Use film capacitors (polyester, polypropylene) for timing circuits above 1ms.
Did you know? Capacitors were invented in 1745 by Ewald Georg von Kleist and independently by Pieter van Musschenbroek (the Leyden jar). Early capacitors were glass jars filled with water and wrapped in tin foil — a far cry from today's ceramic SMD components.