Capacitor Charging Calculator
Understanding Capacitor Charging
1. Basic Theory
A capacitor charging through a resistor follows an exponential curve. The voltage across the capacitor increases according to:
V(t) = Vs(1 - e^(-t/RC))
2. Time Constant
The RC time constant determines the charging rate:
- τ = R × C (in seconds)
- 63.2% of final voltage at 1τ
- 86.5% at 2τ
- 95% at 3τ
- 98.2% at 4τ
- 99.3% at 5τ
3. Voltage Response
The charging behavior exhibits key characteristics:
- Initial rapid rise
- Gradual approach to final value
- Never theoretically reaches supply voltage
- Practically full at 5τ
Energy Storage
Energy storage in capacitors:
| Parameter | Formula | Units |
|---|---|---|
| Energy | E = ½CV² | Joules (J) |
| Power | P = VI | Watts (W) |
| Charge | Q = CV | Coulombs (C) |
Quick Reference
Key Formulas
V(t) = Vs(1 - e^(-t/RC))
τ = R × C
t = -RC × ln(1 - V/Vs)
Key Points
- Exponential charging curve
- 5τ for practical full charge
- Current decreases exponentially
- Energy stored = ½CV²
Best Practices
- • Use high-quality components
- • Consider temperature coefficients
- • Allow for component tolerances
- • Include discharge path
- • Monitor power dissipation
- • Verify voltage ratings