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Capacitor Output Voltage Calculator

Formula

The formula to calculate the output voltage of a capacitor (V(t)) is:

$V(t) = V₀ \cdot e^{\left(-\frac{t}{R \cdot C}\right)}$

Where:

$V(t)$ is the output voltage across the capacitor at time $t$ (V)
$V₀$ is the initial voltage across the capacitor (V)
$t$ is the time elapsed since the start of the discharge (seconds)
$R$ is the resistance in the circuit (ohms)
$C$ is the capacitance of the capacitor (farads)

Definitions

Capacitor Output Voltage (V(t)): The voltage across a capacitor at a specific time during its discharge through a resistor.
Initial Voltage (V₀): The initial voltage across the capacitor before it starts discharging.
Time Elapsed (t): The time elapsed since the start of the discharge.
Resistance (R): The resistance in the circuit through which the capacitor discharges.
Capacitance (C): The capacitance of the capacitor.

Example

Let's say the Initial Voltage (V₀) is 10 V, the Time Elapsed (t) is 5 seconds, the Resistance (R) is 100 ohms, and the Capacitance (C) is 0.01 farads. Using the formula:

$V(t) = 10 \cdot e^{\left(-\frac{5}{100 \cdot 0.01}\right)}$

We get:

$V(t) \approx 6.07 \text{ V}$

So, the output voltage of the capacitor after 5 seconds is approximately 6.07 V.