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Parallel Plate Capacitor: Basics ,Apllication&Formula

Author: Apogeeweb
Date: 26 Aug 2021
 324
parallel plate capacitor formula

Catalog

ⅠIntroduction

Ⅱ Brief introduction of a Capacitor

Ⅲ What is Parallel Plate Capacitor ?

Ⅳ The Working Principle and Application of Parallel Plate Capacitor

4.1 Construction & Principle

4.2 The Application of Parallel Plate Capacitor

Ⅴ Parallel Plate Capacitor Formula

5.1 The formula

5.2 How to Derivate Parallel Plate Capacitor

Ⅵ Solved Examples

6.1 Exemplification 1

6.2 Exemplification 2

Ⅶ Frequently Questions about Parallel Plate Capacitor

 

ⅠIntroduction

We are so reliant on mobile applications and devices for entertainment and work in the digital electronic platform. Laptops and mobile phones have rechargeable batteries to make them more convenient. These batteries are subject to the charging and discharging phenomena. When these are charged, they become mobile. Capacitors are used in all rechargeable circuits. These capacitors are filled with various dielectrics, resulting in various capacitor types. Paper capacitors, for example, mica capacitors, and so on. Similarly, a parallel plate capacitor is a type of capacitor that can increase capacitance. These are the most common energy-storing elements.

 

 

Ⅱ Brief introduction of a Capacitor

The capacitor, a component, like a small rechargeable battery, has the ability or "capacity" to store energy in the form of an electrical charge that produces a potential difference (Static Voltage) across its plates.

Capacitors contain various sizes and shapes, ranging from very small capacitor beads used in resonance circuits to large power factor correction capacitors, but they all do the same thing: they store charge.

A capacitor, in its most basic form, is made up of two or more parallel conductive (metal) plates that are not connected or touching each other, but are electrically separated by air or some form of good insulating material such as waxed paper, mica, ceramic, plastic, or some form of a liquid gel as used in electrolytic capacitors. The Dielectric is the insulating layer that exists between the plates of a capacitor.

 

Ⅲ What is Parallel Plate Capacitor ?

 

A parallel plate capacitor consists of two parallel metal conductor plates that are separated in the middle by a dielectric material. There will be an electrostatic field distribution between the two plates when there is a certain potential difference between them. The area between the two plates has a uniform electric field distribution. The electric field lines at the capacitor's edge are curved and divergent due to the edge effect. The parallel plate capacitor is the most basic type of capacitor. Any non-parallel plate capacitor can be thought of as a series and parallel connection of a number of small parallel plate capacitors.

A parallel plate capacitor is an arrangement of two plates that are parallel to each other and separated by a dielectric material. These plates perform the function of electrodes.

 

capacitor-lab-basics

Figure1: basics of a parallel plate capacitor

 

Ⅳ The Working Principle and Application of Parallel Plate Capacitor

 

This section will be divided into two parts. The first section introduces construction steps. Another section will demonstrate how a parallel plate capacitor works.

 

4.1 Construction & Principle

 

The parallel plate capacitor can be built by following the steps outlined below:

  • The plates used to build the parallel plate capacitor must have the same dimensions.
  • The power supply for these plates has to be provided.
  • Positive charges are necessary for a plate to connect the positive side of the battery.
  • Similarly, the plate connected to the supply's negative terminal is charged with negative charges.
  • As a result, an electric field is formed between those plates.

As a result, an electric field is formed between those plates.

 

Parallel-Plate-Capacitor-Construction

Figure2: the construction of parallel plate capacitor

 

The parallel plate capacitor operates on the following principle:

• A plate in the capacitor is charged to a specific value.

• As the number of charges applied to the plate increases, so does the potential.

• The charges may leak due to the increase in potential.

• To overcome such a situation, another plate is placed next to the first positively charged plate.

• The negative charges are transferred to the next plate that is placed.

• Both plates are now charged.

• Because of the presence of negative charges on the second plate, the potential difference on the first plate tends to be reduced.

• Similarly, the presence of positive charges on the opposite side of the second plate tends to increase the potential difference on the first plate.

• However, the effect of potential difference due to negative charges on the second plate is significant. As a result, the first plate receives a greater number of charges.

 

principle-of-capacitor

Figure3: the principle of parallel plate capacitor

 

4.2 The Application of Parallel Plate Capacitor

Capacitors, in addition to storing electricity, play an important role in electricians and electronic circuits. Capacitors are used in the control of current and voltage in an alternating current circuit, the generation of oscillating current in a transmitter, tuning in a receiver, filtering in a rectifier circuit, time delay in an electronic circuit, and so on.

Parallel plate capacitors operate in the following applications:

• This type of capacitor works in batteries (Rechargeable Energy System).

• Such capacitors are applied to dynamic digital memory systems.

• Such capacitors are used in radars and Pulsed LASER circuits.

• Parallel plate capacitors are used in signal suppression or signal coupling.

 

Ⅴ Parallel Plate Capacitor Formula

The electric field's direction is defined as the direction in which the positive test charge would flow. Capacitance is the body's inability to store an electric charge. Each capacitor has its own capacitance. A typical parallel-plate capacitor is made up of two metallic plates of area A separated by d.

 

5.1 The formula

The parallel plate capacitor formula is given by

C=kϵ0Ad

Where,

ϵo is the permittivity of space (8.854 × 10−12 F/m)

k is the relative permittivity of dielectric material

 

parallel_plate_capacitorFigure4:Parallel Plate Capacitor Formula

 

5.2 How to Derivate Parallel Plate Capacitor

 

A parallel plate capacitor is depicted in the diagram below. Two large plates are parallel to each other and separated by a small distance d. As shown by the dotted array, the space between the plates is filled with a dielectric medium. The two plates are charged in opposite directions.

 

Parallel-Plate-CapacitorFigure5:Two plates

 

We can see that the first plate has a charge +Q and the second plate has a charge –Q. Each plate's area is A, and the distance between these two plates is d. The distance d is much smaller than the area of the plates, and we can write dA, so the effect of the plates is treated as that of an infinite plane sheet with uniform surface charge density, and the electric field generated by them is treated as that of an infinite plane sheet with uniform surface charge density. Because the total charge on plate 1 is Q and the plate area is A, the surface charge density can be calculated as :

Similarly, for plate 2 with a total charge of –Q and area A, the surface charge density can be calculated as follows:

The regions surrounding the parallel plate capacitor are divided into three sections, with area 1 being the area to the left of the first plate, area 2 being the area between the two planes, and area 3 being the area to the right of plate 2.

Let's compute the electric field in the vicinity of a parallel plate capacitor.

Region I: The magnitude of the electric field due to infinite plane sheets I and II is the same at any point in this region, but the direction is opposite. The two forces cancel each other out, and the overall electric field is given as,

step-3

Region II: The magnitude and direction of the electric field due to plane sheets I and II in these regions are the same, and the overall effect is as follows:

step-4

Region III: As in Region I, the magnitude of the electric field generated by plane sheets I and II is the same, but the direction is opposite, yielding the same result as,

step-5

The electric field is uniform throughout and runs from the positive plate to the negative plate in this case.

 

The potential difference across the capacitor can be calculated by multiplying the electric field by the distance between the planes, as shown in the equation.

step-6

The following is the  capacitance  of parallel plate capacitor:

 

step-7

 

Ⅵ Solved Examples

 

6.1 Exemplification 1

A parallel plate capacitor is kept in the air and has an area of 0.50m2 and a distance of 0.04m between them. Determine the parallel plate capacitor.

Solution:

Given:

Area A = 0.50 m2,

Distance d = 0.04 m,

relative permittivity k = 1,

ϵo = 8.854 × 10−12 F/m

The parallel plate capacitor formula is as follows:

C=k0Ad = 8.8541092 0.50 / 0.04

4.427 x 1012 / 0.04

As a result, C = 110.67 x 1012 F.

 

6.2 Exemplification 2

If the capacitance is 25 nF and the separation between the plates is 0.04m, calculate the area of a parallel plate capacitor in the air.

Solution:

Given:

Capacitance is equal to 25 nF.

d = 0.04 m distance

k = relative permittivity

8.854 1012 F/m = o

 

The parallel plate capacitor formula is as follows:

C=k0Ad A=dCk0 = 0.04 25109 / 18.5541012

A = 1 x109/ 8.854 1012

As a result, the area of the parallel plate capacitor is 112.94 m2.

 

Ⅶ Frequently Questions about Parallel Plate Capacitor

1. What happens to the charge on A parallel plate capacitor?

What happens to the charge on a parallel-plate capacitor if the potential difference doubles? The charge on each plate doubles. You want to increase the maximum potential difference of a parallel-plate capacitor. Describe how you can do this for a fixed plate separation.

 

2. When a battery is connected to a capacitor Why do the two plates?

Explanation: In any circuit, electrons are neither created nor destroyed according to the laws of conservation of charge, but are transferred from one point to another on the circuit. When the plates of a capacitor are connected to battery, the battery pushes the electron to move due to its potential difference.

 

3. How do you find the charge on each plate of a capacitor?

The amount of charge that moves into the plates depends upon the capacitance and the applied voltage according to the formula Q=CV, where Q is the charge in Coulombs, C is the capacitance in Farads, and V is the potential difference between the plates in volts.

 

4. How can we increase the capacitance of a parallel plate capacitor?

Hence the capacitance can be increased by either increasing the plate area or decreasing the spacing between plates. Hence, by decreasing the plate separation, the capacitance of a parallel-plate capacitor can be increased. Thus, option (E) is the correct answer.

 

5. How many types are there for increasing the capacitance of parallel plate capacitor?

If you want to increase the Capacitance of Parallele Plate Capacitor then increase the surface area, reduce the separation between the plate and use a dielectric material in between the plate which have higher dielectric breakdown strength.

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