What does the term "time constant" of an RC circuit specifically refer to?

The term "time constant" in an RC (resistor-capacitor) circuit specifically refers to the time required for the capacitor to charge to approximately 63.2% of the supply voltage when charging. This value is denoted by the Greek letter tau (τ) and is calculated as the product of the resistance (R) and the capacitance (C) in the circuit (τ = R × C).

At time equal to one time constant, the voltage across the capacitor reaches 63.2% of the maximum voltage (the supply voltage) if it is charging, or it discharges to 36.8% of its initial charge if it is discharging. This property makes the time constant a fundamental concept in analyzing the charging and discharging behavior of capacitors in circuits.

The significance of the 63.2% figure is derived from the mathematical equations governing exponential growth (charging) and decay (discharging) processes, allowing engineers and technicians to predict how long it will take for a capacitor to approach certain voltage levels within the circuit dynamics.