What percentage change in current occurs when charging a capacitor during each time constant?

When charging a capacitor in an RC (resistor-capacitor) circuit, the current and voltage across the capacitor change over time according to the exponential function defined by the time constant (τ). During the first time constant, approximately 63.2% of the maximum charge that the capacitor can hold is achieved. This phenomenon is governed by the formula for the charging of a capacitor, where the voltage across the capacitor rises approximately to 63.2% of the supply voltage within one time constant.

This percentage is derived from the mathematical expression associated with the charging process, and it demonstrates how the capacitor's charging rate slows down as it approaches its maximum capacity. This characteristic is crucial in understanding how circuits operate over time, particularly in transient analysis, where knowing the time it takes for charging and discharging is essential for circuit design and analysis.

Thus, the percentage change in current when charging a capacitor during each time constant is accurately represented by 63.2%.