The Parallel Plate Capacitor

An electrical component that keeps the energy stored in an electric field is called a Capacitor. The capacitor consists of two metalized foil or metal plates separated by a dielectric material. An increase in voltage across the plates builds up the electric field and more charge can be stored. The capacitance is a measure of the ability of the capacitor to store charge and is proportional to the surface area of the plates and the thickness of the dielectric material. The simplest form of the capacitor is the parallel plate capacitor.

What is a Parallel Plate Capacitor?

A setup where two parallel metal plates are charged by connecting across a battery to establish an electric field is called a parallel plate capacitor. 

Arrangement of a Parallel Plate Capacitor:

• Electrodes- The two metal plates.

• Dielectric Medium- The insulating medium (vacuum, air, electrolyte gel, mica, paper wool, or gas) between the electrodes.

• Battery- Power supply. 

The parallel plate capacitor consists of two electrodes, also known as conducting metal plates fixed parallel to each other, separated by a dielectric medium that works as an insulator. The arrangement includes a battery that works as a power supply to create charges.

The conducting plate connected to the positive terminal traps positive charges and the plate connected to the negative terminal traps negative charges. Thus, the attraction charges keep the energy trapped and stored between the electrodes (two plates). 

The Principle of Parallel Plate Capacitor

Due to its non-conductive nature, the dielectric does not allow any flow of electric current. But the principle of the parallel plate capacitor involves polarising the dielectric material with the help of a battery (the power supply or electricity). The polarisation of the atoms results in the formation of positive and negative charges on the two parallel plates or electrodes of the capacitors. The cumulation of opposite charges on the metal plates stimulates the flow of a charging current through the parallel plate capacitor until the difference between the metal plates is equal to the source potential. 

The field allows a parallel plate capacitor to store finite energy.

The applied voltage should not exceed the threshold to avoid any short circuit due to the dielectric breakdown. Therefore, make sure to keep the working voltage within the threshold limit. 

Dependence of Charge Stored in a Capacitor

The amount of charge stored in a capacitor depends on the gap between the two plates. Therefore, the amount of charge stored in the metal plates of a capacitor is directly proportional to the difference between the plates.

Dependence of charge stored in a Capacitor can be seen as:

Q ∝ V

Thus, Q= (constant) x V = CV

C= Capacitance

Q= The Amount of Charge stored

V= the difference between the two metal plates

The Parallel Plate Capacitor Formula

The capacity of the capacitor to store charge is called the Capacitance. Every capacitor has its limitation to store the body. Therefore the following formula is used to calculate the capacitance of the parallel plate capacitor:

C=k∈0A/d

C= capacitance of the capacitor

K= relative permittivity of the dielectric medium

∈0= 8.854 × 10−12 F/m which is the permittivity of space

A= area of metal plates

d= distance between plates

Derivation of the Formula

The two metal plates of the parallel plate capacitor carry opposite and equal charges. So, let us consider that one plate carries +Q and the other carries -Q. ‘A’ denotes the area of the plates and the distance between the plates is shown as ‘d’. Suppose the distance between the plates is much lesser than the area of the respective plates, d<<A which denotes the effect of plates as an infinite plane sheet. Therefore, the electric field generated by the plates will be treated as the electric field of an infinite plane sheet having uniform surface charge density.

The density can be denoted as:

σ= Q/A

Similarly, the surface charge density in the case of plate 2 having the charge -Q can be shown as,

σ= – Q/A

The regions surrounding the parallel plate capacitor can be distributed into the following three parts:

REGION I (Area left of the plate):

Since both the infinite plane sheets and the magnitude of the electric field remain the same in any part of this region, the direction stays opposite to each other. As the opposite forces cancel each other out, the electric field can be shown as:

E= σ/2∈0 – σ/2∈0 = 0

REGION II (Area between the two plates):

Here, in both plates 1 and 2, the magnitude, as well as the direction of the electric field, remain the same. Thus, the electric field can be shown as:

E= σ/2∈0 + σ/2∈0 = σ/∈0

REGION III (Area covering the right of the plate):

As in region I, the opposite direction of the electric field in this region cancels out the charges whereas the magnitude remains the same. Hence, the effect can be denoted as:

E= σ/2∈0 – σ/2∈0 = 0

Hence, the flow of electric field from positive to negative plate remains uniform.

The potential difference of the capacitor multiplies the electric field by the distance between the two plates: V=Exd = (1/∈0)Qd/A

Therefore, the capacitance of the parallel plate capacitor can be denoted as:

C = Q/V=∈0A/d

Applications

Parallel plate capacitors are used in rechargeable energy systems like batteries, dynamic digital memory systems, pulsed laser circuits, radars, and signal suppression, among others.

Conclusion

A capacitor is an electrical component that stores energy in an electric field. It consists of two conductors (plates) separated by a dielectric material. The capacitance or stored energy per unit voltage is a function of the size, shape, and spacing of the plates, and the type of dielectric material. In addition to capacitors used in electronic equipment, there are also very large capacitors used in power transmission and distribution.