The figure below shows a Capacitor, (C) in series with a Resistor, (R) forming a RC Charging Circuitconnected across a DC battery supply (Vs) via a mechanical switch. When the switch is closed, the capacitor will gradually charge up through the resistor until the voltage across it reaches the supply voltage of the battery. The manner in which the capacitor charges up is also shown below.
Let us assume that the Capacitor, C is fully "discharged" and the switch is open. When the switch is closed the time begins at t = 0 and current begins to flow into the capacitor via the resistor. Since the initial voltage across the capacitor is zero, (Vc = 0) the capacitor appears to be a short circuit and the maximum current flows through the circuit restricted by resistor R. This current is called the Charging Current and is found by using the formula: i = Vs/R.
The capacitor now starts to charge up with the actual time taken for the charge on the capacitor to reach63% of its maximum possible voltage, in our curve 0.63Vs is known as the Time Constant, (T) of the circuit and is given the abbreviation of 1T.
So we can say that the time required for a capacitor to charge up to one time constant is given as: