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.

How to Calculate Voltage Across a Capacitor

Definition: This calculator helps determine the voltage across a capacitor.

Formula: \( V = \frac{1}{C} \int I \, dt \)

V: Voltage across the capacitor
C: Capacitance of the capacitor (in farads)
I: Current flowing through the capacitor (in amperes)

Example: \( V = \frac{1}{2} \int 10 \, dt \)

C: 2 F
I: 10 A

Voltage Formula for Capacitor

Definition: This formula calculates the voltage across a capacitor based on its capacitance and the current flowing through it.

Formula: \( V = \frac{q}{C} \)

V: Voltage across the capacitor
q: Charge stored in the capacitor (in coulombs)
C: Capacitance of the capacitor (in farads)

Example: \( V = \frac{20}{4} \)

q: 20 C
C: 4 F

Capacitor Voltage Current Equation

Definition: This equation relates the voltage across a capacitor to the current flowing through it.

Formula: \( V = \frac{1}{C} \int I \, dt \)

V: Voltage across the capacitor
C: Capacitance of the capacitor (in farads)
I: Current flowing through the capacitor (in amperes)

Example: \( V = \frac{1}{3} \int 15 \, dt \)

C: 3 F
I: 15 A

Capacitor Voltage in Series Calculator

Definition: This calculator determines the voltage across capacitors connected in series.

Formula: \( V = \frac{V_{total}}{n} \)

V: Voltage across each capacitor
V_total: Total voltage applied to the series
n: Number of capacitors in series

Example: \( V = \frac{12}{3} \)

V_total: 12 V
n: 3