How the Capacitor Discharge Calculator Works

This calculator determines the remaining voltage across a capacitor discharging through a series resistor after a specific period of time. It is based on the fundamental RC circuit discharge formula.

The Discharge Formula

The calculator uses the following exponential decay equation to estimate the voltage:

$V(t) = V_0 \times e^{-\frac{t}{RC}}$

Where:

• $V(t)$: The Remaining Voltage across the capacitor at time t.
• $V_0$: The Initial Voltage across the capacitor before discharge begins.
• $t$: The Time elapsed since the discharge started.
• $R$: The Resistance of the resistor in series ($\Omega$).
• $C$: The Capacitance of the capacitor ($F$).

How to Use This Calculator

To measure the voltage across the capacitor, simply enter the known values for the circuit.

1. Initial Voltage ($V_0$): Enter the voltage level of the capacitor at the very beginning ($t=0$).
2. Resistance ($R$): Enter the resistance value of the resistor connected in series.
3. Capacitance ($C$): Enter the capacitance value.
4. Time ($t$): Enter the duration for which the discharge has occurred.
5. Result: The calculator will output the Remaining Voltage ($V_c$) after the specified time.

Understanding the Variables

Three key factors influence how quickly the initial voltage drops to zero: Time, Resistance, and Capacitance.

1. Time ($t$)

• Relationship: As time passes, the energy stored in the capacitor depletes.
• Effect: The longer the time ($t$), the lower the remaining voltage. Conversely, a shorter time means less charge has drained, resulting in a higher remaining voltage.

2. Resistance ($R$)

• Relationship: Resistance restricts the flow of current in the circuit.
• Effect: A higher resistance slows down the current flow, causing the capacitor to discharge more slowly. Therefore, after a specific amount of time, a circuit with high resistance will have a higher remaining voltage compared to one with low resistance (which drains quickly).

3. Capacitance ($C$)

• Relationship: Capacitance represents the storage capacity ("bucket size") of the capacitor.
• Effect: A higher capacitance means the capacitor holds more charge. It takes longer to drain a large reservoir than a small one. Therefore, a larger capacitor discharges more slowly, resulting in a higher remaining voltage after a set period compared to a smaller capacitor.