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

A capacitor typically charges or discharges according to an exponential curve governed by the time constant, which is denoted by the symbol τ (tau). This time constant is determined by the resistance (R) in the circuit and the capacitance (C) of the capacitor, calculated as τ = RC.

During the charging process, the capacitor reaches approximately 63.2% of its maximum voltage (the supply voltage) after one time constant. At each subsequent time constant, the capacitor charges further until it effectively reaches its maximum charge. By around five time constants, the capacitor will reach over 99% of its maximum charge, which is generally considered close enough to be effectively fully charged for most practical applications. This principle also applies symmetrically when discharging; a capacitor will also reach about 99% discharge in approximately five time constants.

Choosing five as the correct answer acknowledges this exponential behavior of charging and discharging in electronic circuits, where it’s widely accepted that around five time constants is sufficient for a capacitor to be regarded as fully charged or completely discharged.