RC Circuit Capacitor Voltage Calculator

Capacitor Discharge Formula:

\[ V_c = V e^{-t / RC} \]

Initial Voltage (V):

volts

Time (t):

seconds

Resistance (R):

ohms

Capacitance (C):

farads

Capacitor Voltage (Vc):

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1. What is the RC Circuit Capacitor Voltage Formula?

The RC circuit capacitor voltage formula describes how the voltage across a capacitor changes over time during discharge. It's a fundamental equation in electronics that shows exponential decay behavior.

2. How Does the Calculator Work?

The calculator uses the capacitor discharge equation:

\[ V_c = V e^{-t / RC} \]

Where:

\( V_c \) — Voltage across capacitor at time t (volts)
\( V \) — Initial voltage (volts)
\( t \) — Time since discharge began (seconds)
\( R \) — Resistance (ohms)
\( C \) — Capacitance (farads)
\( e \) — Euler's number (~2.71828)

Explanation: The equation shows how the voltage decays exponentially with a time constant (τ = RC), which is the time it takes for the voltage to drop to ~36.8% of its initial value.

3. Importance of Capacitor Voltage Calculation

Details: Understanding capacitor discharge is crucial for designing timing circuits, filters, power supplies, and many other electronic applications where controlled voltage decay is needed.

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 numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the time constant (τ) in an RC circuit?
A: The time constant τ = RC represents the time required for the voltage to decay to 36.8% of its initial value (1/e ≈ 0.368).

Q2: How long does it take for a capacitor to fully discharge?
A: In theory, a capacitor never fully discharges, but after 5τ it's considered effectively discharged (~0.7% of initial voltage remains).

Q3: What happens if R or C is zero?
A: The equation breaks down mathematically - zero resistance would cause instantaneous discharge, while zero capacitance means no storage capacity.

Q4: Can this formula be used for charging capacitors?
A: No, the charging formula is different: \( V_c = V(1 - e^{-t/RC}) \) for charging through a resistor.

Q5: What are typical RC circuit applications?
A: Common uses include timing circuits, filters, debouncing switches, analog-to-digital converters, and signal processing.