Capacitor Discharging Graph

A voltage-time graph for a discharging capacitor. The target voltage and time constant are labelled.

Capacitor, C charges up through the resistor until it reaches an amount of time equal to 5 time constants or 5T and then remains fully charged. If this fully charged capacitor was now disconnected from its DC battery supply voltage it would store its energy built up during the charging process indefinitely (assuming an ideal capacitor and ignoring any internal losses), keeping the voltage across its terminals constant. If the battery was now removed and replaced by a short circuit, when the switch was closed again the capacitor would discharge itself back through the resistor, R as we now have a RC discharging circuit. As the capacitor discharges its current through the series resistor the stored energy inside the capacitor is extracted with the voltage Vc across the capacitor decaying to zero.

The RC time constant, also called tau, the time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e.

T = RC

It is the time required to charge the capacitor, through the resistor, by ≈ 63.2 percent of the difference between the initial value and final value or discharge the capacitor to ≈36.8 percent. This value is derived from the mathematical constant e, specifically 1 - e ^-1, more specifically as voltage to charge the capacitor versus time

Charging:       V(t) = V_o(1 - e^-t/T)

Discharging:  V(t) = V_o(e^-t/T)

RC Discharging Table:

Note that as the discharging curve for a RC discharging circuit is exponential, for all practical purposes, after five time constants a capacitor is considered to be fully discharged.

So a RC circuit’s time constant is a measure of how quickly it either charges or discharges.