A capacitor is an electrical device that is used to store electrical energy in the form of an electric field. Adding electrical energy to the capacitor is called “charging” and taking energy from a capacitor is called “discharging”. It is a passive device and does not provide any gain.
A typical capacitor consists of two metal plates separated by some insulator material or vacuum called a dielectric. Dielectric used in capacitors can be glass, paper, ceramic, vacuum, or semiconductor depletion region. The ability of a capacitor to store charge is called capacitance and this capacitance depends on the type of dielectric material used during the manufacturing of the capacitor. Also, the capacitance is directly proportional to the area of metal plates and inversely proportional to the distance between the metal plates that are part of the capacitor.
C= ɛ A/d
A= Area of a capacitor plate
d = distance between plates
ɛ = dielectric constant
Ideally, the capacitance of the capacitor is considered to be a constant and is equal to the charge stored on either plate of the capacitor to the voltage applied between the capacitor plates .
Q = charge
Since capacitors are energy storing elements, the operation of capacitors as an energy-storing element can be understood by thinking of gravity. Suppose you are standing near the stairs and you need to climb up, for that you have to work against the gravitational field and energy is required. Once you apply the required energy and climb the stairs the energy you used is not lost it is actually stored as gravitational potential energy.
Similarly, when a capacitor is connected across a voltage source, energy is stored in the capacitor due to work done by the voltage source or battery.
As soon as the source is connected, electrons are pulled away from one capacitor plate causing net positive charge on that plate and to have equilibrium the same number of electrons are pushed to other plates causing net negative charge on that plate, as a result, the potential difference is created between the two plates.
As soon as the capacitor remains connected to the battery these positively and negatively charged plates retain their state of charge. However, as the battery is removed and due to open circuit charges cannot move and there is already a potential difference, an electric field is established between the plates and the energy stored in the capacitor remains there.
When a resistor or any other device is connected across the capacitor, now charges have a path to flow which causes current. Hence energy stored in the capacitor is converted to the heat or some form of work. As the current flows through the capacitor charge is returned to its equilibrium position, the potential difference decreases, the strength of the electric field weakens, and the capacitor is said to have discharged.
A capacitor can only store a finite amount of energy which depends on the dielectric strength of the dielectric material which sets the capacitor breakdown voltage. Work required to move charge dQ from positive plate to negative plate is VdQ, where V is the force that is required to move the charge.
So the work done will be
dW= V dQ
dW = work done
dQ = Charge
dQ = C dV
dW = VC dV
to find the total work done we have to integrate the above equation for a voltage ranging from zero to V
W = ∫_0^V▒〖VC dV〗
W = ½ CV2
From the above-mentioned equation it can be told that energy stored in the capacitor is in joules if the capacitance of the capacitor is in farad and potential difference applied is in volts.