How many time constants are required to charge a capacitor to 100 percent of the source voltage?

To understand the number of time constants required to charge a capacitor to 100 percent of the source voltage, it’s essential to know how a capacitor charges through a resistor in an RC (resistor-capacitor) circuit.

The charging process of a capacitor is described by the exponential function, specifically the equation:

[ V(t) = V_{source}(1 - e^{-t/RC}) ]

where:

• ( V(t) ) is the voltage across the capacitor at time ( t ),

• ( V_{source} ) is the source voltage,

• ( R ) is the resistance,

• ( C ) is the capacitance,

• ( e ) is the base of the natural logarithm.

During the charging process, a capacitor will never actually reach the source voltage, but it can get very close. After one time constant (RC), the capacitor charges to about 63.2% of the source voltage. After two time constants, it reaches approximately 86.5%, and after three time constants, it is around 95%.

By the time five time constants have passed, the capacitor charges to over 99%, essentially considered fully charged for most practical purposes. Therefore, while the theoretical