Capacitor Discharge Curve Calculator

Capacitor Discharge Equation:

\[ V(t) = V_0 \times e^{-t / (R \times C)} \]

Initial Voltage (V0):

Time (t):

Resistance (R):

Capacitance (C):

Voltage at Time t (V(t)):

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1. What is the Capacitor Discharge Equation?

The capacitor discharge equation describes how the voltage across a capacitor decreases over time when it discharges through a resistor. This exponential decay follows the natural exponential function and is fundamental to understanding RC circuits.

2. How Does the Calculator Work?

The calculator uses the capacitor discharge equation:

\[ V(t) = V_0 \times e^{-t / (R \times C)} \]

Where:

\( V(t) \) — Voltage at time t (V)
\( V_0 \) — Initial voltage (V)
\( t \) — Time since discharge began (s)
\( R \) — Resistance (Ω)
\( C \) — Capacitance (F)
\( e \) — Euler's number (~2.71828)

Explanation: The equation shows that the voltage decreases exponentially with time, with the rate of decay determined by the RC time constant (τ = R×C).

3. Importance of Capacitor Discharge Calculation

Details: Understanding capacitor discharge is essential for designing timing circuits, filter networks, power supply systems, and many other electronic applications where controlled energy release is required.

4. Using the Calculator

Tips: Enter initial voltage in volts, time in seconds, resistance in ohms, and capacitance in farads. All values must be positive (time can be zero).

5. Frequently Asked Questions (FAQ)

Q1: What is the RC time constant?
A: The RC time constant (τ = R×C) is the time required for the voltage to decrease to approximately 36.8% of its initial value.

Q2: How long does it take for a capacitor to fully discharge?
A: Technically, a capacitor never fully discharges, but after 5 time constants (5τ), the voltage drops to less than 1% of its initial value.

Q3: Can this equation be used for charging capacitors?
A: No, the charging equation is different: V(t) = V0 × (1 - e^{-t/RC}) for a capacitor charging through a resistor.

Q4: What happens if the resistance is zero?
A: The equation becomes undefined as resistance approaches zero. In practice, very low resistance causes rapid discharge, potentially damaging components.

Q5: How does temperature affect capacitor discharge?
A: Temperature can affect both resistance and capacitance values, which would alter the discharge characteristics, especially with certain capacitor types.