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# Charging and Discharging of Capacitors

The processes of charging and discharging a capacitor are already familiar from the treatment of *DC circuits*: Connecting a capacitor via a charging resistor *R* to a direct voltage *U*_{0} causes the capacitor to be charged to this voltage. The potential rises exponentially from 0 V to the final value of *U*_{0}. The charging current drops, also according to an exponential function, from an initial maximum value to zero (the capacitor's charging curve is shown on the left in the following diagram). If the capacitor is then disconnected from the voltage source and short-circuited, a discharging process takes place that is the converse of charging (shown on the right in the following diagram).

Charging and discharging currents flow in opposite directions. The rate at which the capacitor is charged or discharged depends on its capacitance and the resistance *R *of the circuit branch in which it is located (here represented by the equivalent resistor). It is characterised by a *time constant **T* = *R*·*C*. After this amount of time, the capacitor attains exactly 63% of its final voltage during charging or loses 63% of its initial voltage during discharging. Once the capacitor is fully charged, current ceases to flow, i.e. the capacitor *blocks direct current*.

If, after charging, the capacitor is disconnected from the voltage source without being short-circuited, it retains its charge and potential for a theoretically indefinite period of time. Under real circumstances, however, the capacitor always undergoes a certain amount of intrinsic self-discharging.