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Capacitor Charge / Discharge
Calculate RC time constant and voltage milestones during capacitor charging/discharging.
Capacitor Transient Response defines how voltage rises or falls across a capacitor as it charges or discharges through a resistor.
Formulas:
- Time Constant:
tau (τ) = R * C - Charging Voltage:
Vc(t) = Vs * (1 - e^(-t / τ)) - Discharging Voltage:
Vc(t) = V_initial * e^(-t / τ)
Usage: Input supply voltage, resistance, and capacitance to calculate the time constant and watch how the voltage evolves over key time milestones (e.g. 99% charge at 5τ).
When you need it: Computing RC charge or discharge time to a target voltage — power-on delays, soft-start, debounce, or sizing a hold-up capacitor for a brief supply dropout.
Worked example: R = 10 kΩ, C = 100 µF → τ = RC = 1 s. Charging reaches 63.2% of the supply in one τ and ~99% in 5τ = 5 s. To hold a rail above Vmin through a dropout, C ≈ I × t / ΔV.
Tips & gotchas:
- Five time constants is "fully" charged (99.3%); design timing around τ, not a vague "instant".
- Real capacitors have ESR (which heats under ripple) and wide tolerance — electrolytics run ±20% and age.
- Derate the voltage rating to about 50% of the working voltage for lifetime, especially on electrolytics.
- Class-2 ceramics (X7R/Y5V) lose capacitance with DC bias and temperature — the applied value can be far below the marking.