Calculate Capacitor Voltage at Any Time During Charge or Discharge
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Resistance R (Ω)
Capacitance C (F)
Supply/Initial V₀ (V)
Time t (s)
Result
Voltage V(t)
Time Constant τ
Step-by-Step Calculation
Charge/Discharge Formulas
Time Constant: τ = R × C
Charging: V(t) = V₀ × (1 - e^(-t/τ))
Discharging: V(t) = V₀ × e^(-t/τ)
% of steady state: 1τ=63.2%, 3τ=95%, 5τ=99.3%
The exponential charge and discharge curves are fundamental to RC circuit behavior. During charging, the capacitor voltage rises quickly at first then slows as it approaches the supply voltage. During discharge, the voltage drops quickly then tapers off.
⚠After 1τ: 63.2% charge / 36.8% discharge. After 5τ: 99.3% charge / 0.67% discharge. For practical purposes, a capacitor is fully charged/discharged after 5τ.
How Capacitor Charge/Discharge Works
When voltage is applied to an RC circuit, current flows into the capacitor, storing energy in its electric field. The voltage rises exponentially toward the supply voltage. During discharge, the stored energy is released through the resistor. The time constant τ=RC determines how fast this process occurs.
Charging Curve
V(t) = V₀(1-e^(-t/τ)). Fast initial rise, slows near V₀. Current decreases exponentially. Energy stored in electric field.
Discharge Curve
V(t) = V₀×e^(-t/τ). Fast initial drop, slows near zero. Current reverses direction. Energy released as heat in R.
Time Constant Effect
Large τ = slow (big R or C). Small τ = fast (small R or C). τ sets the timescale for all exponential changes.
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