Approximately how many time constants does it take to charge or discharge a capacitor fully?

The concept of time constants is crucial in understanding the charging and discharging processes of capacitors in RC (resistor-capacitor) circuits. A time constant, represented by the symbol τ (tau), is defined as the time taken for the voltage across the capacitor to either charge up to about 63.2% of its maximum voltage (during charging) or to discharge to about 36.8% of its maximum voltage (during discharging).

In practice, while the voltage curve approaches its final value asymptotically, it is generally accepted that a capacitor is considered to be fully charged or discharged after about 5 time constants. At this point, the capacitor is typically over 99% charged to its maximum voltage or discharged to near zero, which is functionally equivalent to being fully charged or discharged for most applications.

Thus, the range of approximately 5 time constants provides a reliable benchmark for most engineers and practitioners when performing calculations or assessing capacitor behavior in circuits.