- Capacitor Definition: A capacitor is defined as a device with two parallel plates separated by a dielectric, used to store electrical energy.
- Working Principle of a Capacitor: A capacitor accumulates charge on its plates when connected to a voltage source, creating an electric field between the plates.
- Charging and Discharging: The capacitor charges when connected to a voltage source and discharges through a load when the source is removed.
- Capacitor in a DC Circuit: In a DC circuit, a capacitor initially allows current flow but eventually stops it once fully charged.
- Capacitor in an AC Circuit: In an AC circuit, a capacitor charges and discharges continuously as the voltage polarity alternates.
The question how does a capacitor work is easiest to answer with its basic structure. A parallel plate capacitor has two conducting plates separated by an insulating dielectric. When a battery, which is a DC Voltage Source, is connected across the capacitor, plate I connects to the positive terminal and plate II connects to the negative terminal. Electrons move through the external circuit from one plate to the other, but an ideal dielectric prevents conduction directly across the gap. The charging current falls as the capacitor voltage approaches the battery voltage.
The separated charges create an electric field in the dielectric. Plate I loses electrons and becomes positively charged, while plate II receives electrons from the battery circuit and becomes negatively charged. The capacitor charge follows Q = CV, where C is capacitance and V is the applied voltage. The interval needed to approach this final charge is the charging time of this capacitor.
When the battery is disconnected and no conductive path joins the terminals, an ideal capacitor retains its separated charge. A real capacitor loses charge gradually through leakage. Its stored energy remains in the electric field until a discharge path is provided.
If plate I and plate II are connected through a load, charge flows through the external circuit and the capacitor voltage falls. In a resistive circuit, the current and voltage decay exponentially rather than stopping at a fixed instant. This interval is described by the discharging time of the capacitor.
Capacitor in a DC Circuit
Suppose a capacitor is connected across a battery through a switch and a finite circuit resistance.
Immediately after the switch closes, at t = +0, an initially uncharged capacitor has zero voltage across it and the charging current is at its largest value. As the capacitor charges, its voltage rises and the current falls. The circuit resistance limits the initial current.
At DC steady state, the capacitor voltage equals the source voltage, so there is no potential difference across the series resistance and no current flows. An ideal uncharged capacitor can therefore be approximated as a short circuit at the switching instant and as an open circuit after a long time when connected to a battery or DC source.
Capacitor in an AC Circuit
When a capacitor is connected across an AC source, the applied voltage changes continuously. During a positive half-cycle, plate I becomes positive relative to plate II and opposite charges accumulate on the two plates.
During the negative half-cycle, the voltage reverses, so plate I becomes negative relative to plate II. Electrons still do not cross an ideal dielectric. Instead, charge moves through the external circuit as the electric field and plate polarity reverse. This repeated charging and discharging produces alternating current whose size depends on capacitance, frequency and applied voltage.
