A capacitor’s discharge curve illustrates the decrease in voltage over time as the capacitor releases its stored electrical energy.

When a capacitor is fully charged, it accumulates electrical energy in the form of electric potential energy. Upon connecting the capacitor to a circuit, it begins to discharge, leading to the release of this stored energy. Consequently, the voltage across the capacitor diminishes over time as the charge on its plates decreases.

The discharge curve of a capacitor typically follows an exponential pattern, indicating that the voltage drops at a consistent rate over time. The rate of discharge is influenced by several factors, including the capacitance of the capacitor, the resistance in the circuit, and the initial voltage across the capacitor.

The time constant, denoted by $\tau$, is a key parameter that represents the time required for the voltage across the capacitor to decrease to approximately $37\%$ of its initial value. This time constant is mathematically expressed as the product of the capacitance $C$ (in farads) and the resistance $R$ (in ohms) in the circuit, given by the formula:

This discharge curve is not only useful for visualizing how voltage decreases but also serves as a tool for calculating the time constant $\tau$ and determining either the capacitance or resistance in the circuit.

In summary, a capacitor’s discharge curve effectively demonstrates the gradual decline of voltage over time during discharge. The exponential nature of this curve allows for the calculation of the time constant and aids in determining the capacitance or resistance within the circuit.