Capacitor Discharge Calculator
Understanding Capacitor Discharge
1. Basic Theory
A capacitor discharging through a resistor follows an exponential decay curve. The voltage across the capacitor decreases according to:
V(t) = V₀e^(-t/RC)
2. Time Constants
The discharge characteristics at different time constants (τ = RC):
| Time | Voltage | Energy |
|---|---|---|
| 1τ | 36.8% of V₀ | 13.5% of E₀ |
| 2τ | 13.5% of V₀ | 1.8% of E₀ |
| 3τ | 5% of V₀ | 0.25% of E₀ |
| 4τ | 1.8% of V₀ | 0.034% of E₀ |
| 5τ | 0.7% of V₀ | 0.004% of E₀ |
3. Applications
Understanding capacitor discharge characteristics is essential for various applications:
- Power supply smoothing and filtering
- Timing circuits and delay functions
- Energy storage and transfer systems
- Protection circuits and crowbar applications
- Motor braking and energy recovery
- Emergency power systems
4. Design Optimization
Key factors to consider when designing discharge circuits:
- Discharge resistor power rating requirements
- Temperature effects on discharge characteristics
- ESR and its impact on discharge rate
- Voltage coefficient considerations
- Physical layout and safety spacing
- Environmental factors affecting discharge
5. Discharge Time Calculation
How to calculate capacitor discharge time:
Step by Step Process
- Identify initial voltage (V₀)
- Define target discharge voltage (V)
- Calculate RC time constant
- Apply discharge time formula
Quick Reference
Key Formulas
V(t) = V₀e^(-t/RC)
τ = RC
t = -RC × ln(V/V₀)
Key Points
• Exponential decay curve
• 5τ for practical discharge
• Current decreases exponentially
• Energy dissipated in resistor
Best Practices
- • Include discharge resistors
- • Monitor temperature rise
- • Consider safety requirements
- • Verify voltage ratings
- • Calculate power dissipation
- • Regular maintenance checks