The Capacitance Of A Parallel Plate

Introduction

The topic of the capacitance of a parallel plate plays a crucial role in the syllabus of IIT-JEE. This topic includes the functioning of the capacitor according to its different arrangements. This arrangement works according to variable principles and values. This study explains the arrangements and flow of current with more clarity. The notes include the formulas for the various arrangements and suitable examples to explain their use.

Concept Of A Parallel Plate Capacitor

In a Parallel Plate Capacitor, the two conducting plates act like electrodes, and there is a dielectric among them. That dielectric acts as the separator of the plates. The two plates of this parallel plate capacitor are totally of the same dimension. They are connected with the power supply, and which plate connects with the battery’s positive terminal relieves positive charge. The plate that connects with negative terminals releases a negative charge. 

In another word, it can be said that a parallel plate capacitor is an organized arrangement of electrodes  and insulating material also known as dielectric.  A parallel capacitor can have storage of some small amount of energy before the occurrence of dielectric breaks down. As a definition, when both the parallel plates get connected  accordingly across a battery, the plates get easily charged and create an electric field between them. This setup is also called a Parallel Plate Capacitor.

Principle Of A Parallel Plate Capacitor 

Some charge can easily be provided in the plate of the object. It can further create leakage in the energy but only when you increase the amount of charge in the plates. However, with a new placement of the 2d plate next to the positively charged plate, a new formation can occur where the negative charge will move to the side of this plate, which is somehow too close to the positively charged plate. 

With the charging of both plates, the negative charge that is present on plate 2 will decrease as there remains some potential difference of plate 1. Likewise, plate 2 filled with a positive charge will automatically grow its energy due to the difference on plate 1. However, the negative charge always aims to be more powerful than the positive. Due to this, more charge will be present in plate 1, and the difference of negative charge will be less. However, these rules are defined as the main principles of a Parallel Plate Capacitor. 

Parallel Plate Capacitor Formula 

The direction of the electric field is known as the direction of the flow of positive charge. Capacitance is called the limitation of the storage capacity of the electric charge. Every capacitor has its individual capacitance. There are two metallic plate areas A in a typical parallel plate capacitor, separated by the distance D.

C  = k0Ad

Here, 0 is the permissive space. (8.854 × 10⁻¹² F/m)

k represents the similar permittivity of dielectric material

d is the separation between the plates.

A is the area of plates. 

This is the Parallel Plate Capacitor Formula.

Parallel Plate Capacitor Derivation 

The Parallel Plate Capacitor can be created by two large plates placed parallel to each other at a very small distance which is d. The dielectric medium fills up the space between two plates.  However, the two plates present here can carry equal energy and opposite charge. 

The first plate carries the charge + Q, and the second one carries -Q. The area of plates is A, and the distance between them is d. The area of d is much smaller than the area of plates. Therefore, we can represent it as d < A. The plates’ effect is considered infinite plane sheets; the generated electrical field is treated as the field generated by infinite plane sheets having uniform surface charge density. The total charge of plate 1 is +Q, and the area is A. Therefore, the surface charge density can be represented as  

=QA

Similarly, for plate 2, the charge is -Q and areas A and can be represented as the density charge, 

=-QA

Concept Of Capacitor And Capacitance 

The capacitor is known as an electric condenser. It is a two-terminal electronic component. It has the capacity or ability to store energy in the electric charge form.  It is usually designed to enhance the effect of capacitance. This is the relation between Capacitor and Capacitance. The storage capacity of capacitance can be different from small to high storage. 

Capacitance is nothing but the ability of capacitors to store energy in the form of electric charge.  In simpler words, capacitance is the storing unit of the capacitor.  Farad is the measuring unit of capacitance. 

Most capacitors usually contain two electrical conductors, and metallic plates separate them. Conductors can be in the form of electrolytes, a bead of metal or thin film, etc. 

Sometimes the shape of the capacitor also affects the capacitance. It depends on the distance between the plates and also the area between the plates. The more distant the plates are, the more negative power will be charged. And positive plates will get easier to charge if the area is larger.  

Some factors  can affect capacitance. Such as plate spacing, area of plates, and dielectric. There are two types of variable capacitors. One is a tuning capacitor, and the other one is a trimming capacitor.

Conclusion

Thus we can conclude that the Capacitance is influenced by three factors: the size of the conductors, the size of the gap between them, and the substance used to connect them (the dielectric). The capacitance increases with the size of the conductors.