Circuit Parameters
Understanding the Concepts
What is Capacitor Discharge?
When a charged capacitor is connected to a resistor, it begins to release its stored electrical energy, creating a current that flows through the resistor. This process is called discharging. The voltage across the capacitor doesn't drop instantly; it decreases exponentially over time. This interactive tool helps you visualize and calculate this decay.
The Time Constant (τ)
The time constant, represented by the Greek letter tau (τ), is a crucial measure in an RC circuit. It's calculated as the product of resistance (R) and capacitance (C): τ = R × C. The time constant represents the time it takes for the capacitor's voltage to drop to approximately 36.8% of its initial value. It effectively defines the speed of the discharge process.
Simple RC Discharge Circuit
Capacitor (C) discharging through a Resistor (R).
The Discharge Formula
The voltage V across the capacitor at any given time t during discharge is calculated using the formula:
Where V₀ is the initial voltage, R is the resistance, C is the capacitance, and 'e' is the base of the natural logarithm (approximately 2.718).
Capacitor Discharge Formula, RC Time Constant, and Resistor Selection
This capacitor discharge calculator is based on the exponential decay behavior of an RC circuit. For a charged capacitor connected through a resistor, the voltage follows V(t) = V0 x e^(-t/RC). To calculate the time required to reach a target voltage, use t = -RC x ln(V/V0).
| Design item | What to check | Why it matters |
|---|---|---|
| Design item Time constant | What to check tau = R x C | Why it matters After 5 tau, the capacitor is usually near fully discharged |
| Design item Initial power | What to check P = V0^2 / R | Why it matters Sets the required resistor power rating |
| Design item Residual voltage | What to check Target voltage after discharge | Why it matters Defines safe handling or restart conditions |
| Design item Capacitor energy | What to check E = 0.5 x C x V0^2 | Why it matters Shows the total stored energy to dissipate |
When selecting a discharge resistor, consider target discharge time, maximum resistor power, capacitor voltage rating, and the safe residual voltage required by the circuit.
