Capacitor Charge / Discharge

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.