How many time constants does it take to fully charge a capacitor?

The full charging of a capacitor in an RC (resistor-capacitor) circuit is described by the time constant, which is the product of the resistance (R) and the capacitance (C) in the circuit, denoted as τ (tau). The time constant τ indicates the time it takes for the voltage across the capacitor to rise to about 63.2% of its maximum value after a step change in voltage.

Typically, the charging of a capacitor is considered to be effectively complete after about five time constants. At this point, the voltage has risen to over 99% of its maximum value, which is a practical threshold for most applications. Thus, it’s standard practice to state that it takes five time constants to fully charge a capacitor to a level that can be considered close enough to fully charged for most practical purposes.

The concept of time constants is fundamental in understanding capacitor behavior in circuits, as it helps predict how quickly a capacitor will charge or discharge depending on the resistance and capacitance values in the circuit.