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Capacitor and Capacitance

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Capacitor and Capacitance are related to each other as capacitance is nothing but the ability to store the charge of the capacitor. Capacitors are essential components in electronic circuits that store electrical energy in the form of an electric charge. They are widely used in various applications, including power supplies, filtering circuits, timing circuits, and coupling circuits. The ability of a capacitor to store electrical energy is determined by its capacitance, which is a measure of the amount of charge that can be stored per unit of the voltage applied. Understanding the fundamentals of capacitors and capacitance is important for anyone working with electronic circuits or interested in electronics. 

In this article, we will learn about Capacitors, the Working of Capacitors, Capacitance, and others in detail.

Capacitor

A Capacitor is a two terminal electronic device that has the ability to store electrical energy in the form of electric charge in an electric field. It is a physical object. 

It consists of two conductors generally plates and an insulator (air, mica, paper, etc.) separated by a distance. The space between the conductors is filled by a vacuum or with an insulator known as a dielectric. It stores energy by taking pairs of opposite charges. The dielectric material allows each plate to hold an equal and opposite charge. It is also called electric condensers. Capacitors are a simple passive device that is used to store electrical charge and they are invented by Ewald Georg von Kleist in 1745.

How Does a Capacitor Work?

Capacitor is one of the basic components of the electric circuit, which can store electric charge in the form of electric potential energy. It consists of two conducting surfaces such as a plate or sphere, and some dielectric substance(air, glass, plastic, etc.) between them.

Working of Capacitor

 

A capacitor is an electronic component that is designed to store electric charge. It consists of two conductive plates that are separated by a dielectric material, such as air or a plastic film. When a voltage is applied across the plates, electrons build up on one plate and are drawn away from the other, causing an electrical charge to accumulate. The amount of charge that a capacitor can store is determined by its capacitance, which is measured in farads (F). The capacitance of a capacitor depends on the surface area of its plates, the distance between them, and the dielectric constant of the material between them.

Capacitors are used in a variety of electrical and electronic circuits. For example, they can be used to filter out unwanted noise or voltage spikes, to store energy in power supplies, or to tune resonant circuits in radios and other electronic devices. They can also be used in timing circuits, where they are charged and discharged at specific intervals to create precise timing signals.

Capacitor Symbol

The symbol of a capacitor in an electric circuit is given in the following diagram:

Capacitor Symbol

 

Energy Stored in Capacitor

Once a capacitor is connected to the power source, it started to accumulate electrons on one surface and the opposite charges on the other surface. The work done by the power source for this is  stored in the capacitor in the form of electrical potential energy and this energy stored in a capacitor is given by the equation:

U = (1/2)CV2

Where

  • U is the energy stored in joules (J), 
  • C is the capacitance of the capacitor in farads (F), and 
  • V is the voltage across the capacitor in volts (V).

Derivation of Energy Stored in Capacitor

Consider a capacitor of capacitance C, which is charged to a potential difference V. 

The charge Q on the capacitor is given by the equation Q = CV, where C is the capacitance and V is the potential difference.

The work done in charging the capacitor from an uncharged state (where Q = 0) to a charged state dQ with potential V is given by the equation:

dW =  VdQ

As V = Q/C, the equation can be written as

dW = Q dQ/C

Integrating both sides of the equation,

W = ∫ Q dQ/C

W = (1/2)Q2/C      {Q = CV}

W = (1/2)CV2 

This work done is stored in the capacitor as the electric potential energy.

Thus, U = (1/2)CV2 

Capacitance

The capacity of a capacitor to store charge in it is called its capacitance. It is an electrical measurement. It is the property of the capacitor.

Capacitance Formula

When two conductor plates are separated by an insulator (dielectric) in an electric field. The quantity of charge stored is directly proportional to the voltage applied and the capacitance of the capacitor. 

Q ∝ V

or

Q = CV

where, 

  • Q is charge stored.
  • C is Capacitance of the capacitor.
  • V is voltage applied.

Unit of Capacitance

The standard unit OR the SI unit of capacitance is Farad, but 1 farad is a very large unit of capacitance. So, capacitance is measured in milifarads, microfarads, picofarads, nanofarads, etc.

As mili, micro, pico, and nano are the standard prefixes representing the following relations:

  • 1 millifarad (mF) = 10-3 Farads
  • 1 microfarad (μF) = 10-6 Farads
  • 1 nanofarad (nF) = 10-9 Farads
  • 1 picofarad (pF) = 10-12 Farads

Series and Parallel Combination of Capacitor

  • When the capacitors are connected in a series combination i.e one after the other, the total capacitance of the capacitors is

1/Ctotal = 1/C1 + 1/C2

Ctotal  = (C1C2)/(C1+C2)

Ctotal = C1+C2

Capacitance of Parallel Plate Capacitor

A parallel plate capacitor is shown in the image added below,

Parallel Plate Capacitor

 

The capacitance of a parallel plate capacitor is directly proportional to the area (A) of the two parallel plates and inversely proportional to the distance of separation between the two plates (d)

C ∝ A/d

or

C = ∈oA/d

where 

  • o = permittivity of free space = 8.854 × 10-12

Capacitance of Spherical Capacitor

A Spherical Capacitor is shown in the image added below,

Spherical Capacitor

 

Spherical Capacitor is made up of two hollow concentric conducting shells of radii R1 and R2 with a dielectric substance between them. These shells have equal and opposite charge Q. Capacitance of this capacitor is given by 

\bold{C = 4\pi \epsilon_o \frac{R_1R_2}{R_1 - R_2}}

where 

  • εo = permittivity of free space = 8.854 × 10-12

Factors affecting Capacitance

There are some factors that can affect the capacitance of capacitors, which are,

  • Dielectric
  • Distance Between Surfaces
  • Area of the Surfaces

Now let’s learn about each in detail.

Dielectric

The dielectric material between both surfaces can affect the capacitance of capacitors drastically. The capacitance of any capacitor is proportional to the permittivity of the dielectric i.e., the higher the permittivity of the dielectric higher the capacitance of that capacitor. 

The dielectric constant and permittivity of various dielectrics materials are given as follows:

Dielectric

Permittivity of Dielectric

Vacuum

1

Air

1.0006

Teflon 

2.1-2.3

Glass

4.5-10

Water

80.4

Ethanol

24.3

Glycerol

42.5

Silicon Dioxide

3.7-4.9

Distance Between Surfaces

Distance between the surface of the capacitor is inversely proportional to its capacitance i.e., a higher distance between the surfaces implies a lesser capacitance of the capacitor. If the capacitance of a capacitor is C and the distance between the surface is d then, 

C ∝ 1/d

Area of the Surfaces

The area of the surface building up the capacitor can affect the capacitance of that capacitor in a direct proportion i.e., a higher surface area capacitor produces a higher capacitance capacitor. If C is the capacitance and A is the surface area of one side of the capacitor, then.

C ∝ A

Uses of a Capacitor

Capacitors are important components in electronic circuits. They can store electrical energy and release it as needed, which makes them useful for powering devices and stabilizing voltage. Capacitors can also filter out unwanted signals, create timing circuits, transfer signals between circuits, and isolate circuits from each other to prevent interference. They are used in various fields, including telecommunications, automotive, aerospace, and consumer electronics.

Applications of Capacitors

Capacitors are electronic devices that have various applications and some of the applications of capacitors are,

  • Capacitors are used for Energy Storage
  • Capacitors are used for Power Conditioning
  • Capacitors are used as Sensors
  • Capacitors are used for Signal Processing

Now let’s learn about them in detail,

Capacitors are used for Energy Storage

The major application of the capacitor is as energy storage, the capacitor can hold a small amount of energy which can power the electric circuit in case of power outages. Various appliances use capacitors as energy sources, that include,

  • Audio equipment
  • Camera Flashes
  • Power supplies
  • Magnetic coils
  • Lasers

Capacitors are used for Power Conditioning

Capacitors are also used for Power Conditioning as they only allow only AC current to pass when they are charged, blocking DC current.

Capacitors are used as Sensors

Capacitors are used as sensors which are used to measure a variety of things such as humidity, mechanical strain, and fuel levels. 

Capacitors are used for Signal Processing

In modern electronics, capacitors are also used as signal processors, they are used to build DRAM and other electronic devices.

Difference between Capacitor and Capacitance

As, capacitor and capacitance both are related in some manner but there are some differences between them, which are as follows:

Capacitor

Capacitance

A Capacitor is a two-terminal electronic device that can store electrical energy in the form of electric charge in an electric field.The capacity of the capacitor to store charge in it is called capacitance
It is a physical object or deviceIt is an electrical measurement.
The capacitor is a passive device.It is not a device. It is the property of a capacitor.
It is also called electric condensers.It is only called capacitance.
It does not depend on size, shape, and distance.The capacitance of a capacitor depends on the geometrical configuration like size, shape, and distance between the conductor plates.
It does not depend on the nature of the insulating material.It depends on the nature of the insulating material.
It depends on the nature of the material of the conductor.It doesn’t depend on the nature of the material of the conductor.

Sample Questions on Capacitor and Capacitance

Question 1: What are the uses of capacitors?

Answer: 

Uses of capacitors are:

  • They are used to store energy. 
  • It is used in A.C to D.C converter circuits.
  • It is used in tuners.
  • It is used in low pass filters and high pass filters.

Question 2: How much charge is deposited on each plate of 6pF when it is connected to a 24V battery?

Answer:

Given ,

V = 24V

C =6pF

Formula Q = CV

Q = 6  × 10-12 × 24

= 144  ×  10-12C

Therefore, the charge required is 144 × 10-12C.

Question 3: The voltage applied is 15 V between the capacitors having a charge of 3μC. Find the capacitance.

Answer:

Given,

V = 15V

Q = 3 μC

Formula: Q= CV

3  × 10-6 = C  ×  15

C = 3 × 10-6/15

= 0.2 × 10-6F

Therefore, the capacitance of the capacitor is 0.2 × 10-6F

Question 4: A capacitor is constructed from two metal plates with an area of 6m2 and is separated by a distance of 5m apart from each other. Calculate the capacitance of the capacitor.

Answer:

Given 

Area A = 6m2

Distance d = 5 m

Formula, C = ∈oAd

C = 8.854 × 10-12 × 6/5

C = 10.62 × 10-12F

Therefore, the capacitance of the capacitor is 10.62 × 10-12F.

Question 5: If 2 capacitors are connected in series combination with capacitances 15F and 12F. Calculate the total capacitance of the capacitors.

Answer: 

Given,

C1= 15F

C2 = 12F

Formula: Ctotal  = C1C2/C1+C2

Ctotal = (15 × 12)/(15+12)

= 180/27

= 6.66F.

Therefore, the total capacitance of the capacitor is 6.66F

FAQs on Capacitors and Capacitance

Q1: What is Capacitor?

Answer:

Capacitor is the most basic electrical component of circuit which can store charge in the form of electric potential energy.

Q2: What is Capacitance?

Answer:

The ability of capacitor to store charge is known as capacitance.

Q3: How can the capacitance of a capacitor be increased?

Answer:

To increase the capacitance of a capacitor, we can increase the surface area of the plates, reduce the separation between plates, and also use dielectric material that has a higher dielectric constant.

Q4: What are Ultracapacitors?

Answer:

Ultracapacitors also called supercapacitors, are high-capacity capacitors with a capacitance value much higher than other capacitors but they have a lower voltage limit.

Q5: What are the factors on which the capacitance of a capacitor depends?

Answer:

The factors on which the capacitance of a capacitor depends are,

  • Dielectric Material Used
  • Distance Between Surfaces
  • Area of the Surfaces


Last Updated : 04 Feb, 2024
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