What does the time constant of a capacitor refer to?

The time constant of a capacitor, often denoted as τ (tau), is a specific measure that indicates how quickly a capacitor charges or discharges in an RC (resistor-capacitor) circuit. It is defined as the time required for the voltage across the capacitor to reach approximately 63.2% of its maximum value when charging, or to drop to approximately 36.8% of its initial value when discharging.

This concept is critical because it allows engineers and technicians to understand the behavior of capacitors in circuits over time. For example, in a charging scenario, after one time constant, a capacitor will have charged to about 63.2% of the supply voltage, while after about five time constants, it will nearly be fully charged, reaching over 99% of its maximum voltage.

The other options do not accurately define the time constant. The charging and discharging to 100% or 0% of the voltage does not encapsulate the exponential nature of the charge curve. Similarly, while reaching a steady state is relevant to circuit behavior, it doesn't specifically pertain to the defined time constant of the capacitor. Thus, the focus on the 63.2% figure underscores a fundamental characteristic of capacitors in