# Basic Physics Lesson - 19: Capacitance

Umesh is a freelance writer contributing his creative writings on varied subjects in various sites and portals in the internet.

## Introduction

In earlier lessons in this series, we learnt a great deal about voltage, current, resistance etc and their inter-relations. We learnt that when a voltage was applied across a resistor, some current flowed through the resistor depending on its resistance. The mathematical relationships between the three entities voltage (V), resistance (R), and current (I) was understood in terms of Ohm's law which stated that V = I R.

Now in this lesson, we will learn and understand another important entity that is the electrical capacitance.

## Charge, the carriers of electrical current

If we recollect the design of an electrical cell or battery then we find that it contains two metallic plates called positive and negative terminals and in between them some electrolytic material is placed. The electrical charges which are deposited on these plates are the source of electrical current whenever these two terminals are connected to a resistor say like an electrical bulb or LED light or connected to an electric circuit for a specific purpose. When an electrical circuit is completed the current starts to flow in it which is nothing but flow of the electrical charges.

The negatively charged subatomic particles called electrons can move across the metallic and conducting paths and this is the main framework under which the flow of current is ascertained and understood. The electrons come from the atoms only and wherever they come from or technically speaking dislodged, becomes a positive charge (lacking electrons). So, the presence of the electron is actually negative charge while its absence from an atom, when it leaves an atom and becomes a free electron capable of moving in the metal body, is termed as positive charge. Now we can well understand what does the positive and negative terminal of a cell or battery mean. It is obvious that the terminal at which more electrons are available is the negative terminal and the other terminal where electrons are less becomes a positive terminal. This difference in the charges at the two terminals is the source of electromotive force that is available to us from that battery. We can use it for any purpose from lighting an electrical bulb to starting the engine of a car.

Let us think of a situation where we have two metallic plates separated by each other and not touching each other but connected to the terminals of an electric battery - one plate to one terminal and the second plate to the second terminal. What would happen? The charges which are present on the battery terminals will move to these plates and just stop there itself as there is no further path for them to go ahead. In this process, one plate becomes positively charged and the other becomes negatively charged. As this happens quickly so some current flows momentarily but once the plates are charged, the current stops, and a steady state is reached. In this situation, there are charges on both plates. This charge accumulation is a very important property and these two plates together now constitute to become a capacitor. Remember that these two plates should not touch each other as that would complete the circuit and charges will continuously flow and there will not be a capacitor action available.

## Capacity of a conductor to hold charges

We were talking of two plates but even if a single metal plate or metallic material is connected to a terminal of the battery it will get charged because electrons are ready to move to any metallic or conducting material. So, charges would flow to it and then a steady-state would be reached after which no charges will come to it. How many charges will it be able to accommodate or store in it is governed and decided by its electrical property known as capacitance. This property will of course depend on the particular matter but also on its size as bigger the size it would have more place for those small charge particles to stay in it.

It is interesting to note that if we touch these charged materials with some other metallic object or even with our hands then they will start moving to it. The tendency of charged particles is always to move in an electric voltage gradient.

Have you anytime felt or heard a little spark-type sound and minor electric flow while sitting or touching plastic or polymer furniture like a chair or stool. That happens because some stray static charges present there to try to move through the person or object lying on them. Every person might not experience that type of thing because depending upon the human body's skin resistance to the charges one may get that little electric discharge feeling or simply miss that.

These small charges are the basic elements which constitute a current flow in any material.

## What is a capacitor

Some scientists namely Ewald Georg Von Kleist and Pieter Van Musschenbroek came to know, in the year 1745, about this interesting property called capacitance exhibited by the arrangement of two metal plates placed very near to each other, finally called capacitor. They were actually working with the phenomenon of electrostatic charges.

If we take two conductors and place them close but they do not touch each other and then if we connect them to a battery - one to the positive terminal of the battery and the other to the negative terminal of the battery then charges will move from the battery terminals to these conductors but the circuit is not complete and current does not flow. The charges simply move and sit on these conductors. This is a very interesting situation that two conductors are near each other but not touching but are charged. Now let us disconnect the wires connected from the battery to these and what we find is that charges are still there on the plates and this becomes a device to hold charges and can be used to send these charges to other places in an electrical circuit if they are used in that way. This arrangement is known as a capacitor or condenser. It can hold some charge and give it back when required.

Now, how much charge can a capacitor hold depends on the design and size of plates in it as well as the distance between them, and finally, the dielectric material which is placed between these two conductors to avoid their direct contact with each other.

These separating materials or more technically the dielectric materials are not metals but are actually insulators but have a property such that it helps the capacitor to store more charge depending on the dielectric properties of the material.

The dielectric materials have a property called permittivity and depending upon the value of this they help in increasing or decreasing the capacitance value of a capacitor. The greater the permittivity of the dielectric the greater the capacitance, and lesser the permittivity of the dielectric the lesser the value of the capacitance.

If there is no material present between the plates of a capacitor then air would be there and taking the permittivity of air as a base the permittivity of dielectric materials is considered and that ratio is known as the dielectric constant of the material.

## Charge and capacitance

We will now see how the capacitance is related to the charges which move from one place to other under an applied voltage or electric field. Let us take the example of a single metal piece or metal wire or say a metal spherical ball and we connect it to one of the terminals of a battery or cell. What would happen? Some electrons from the battery terminal will try to start moving to this metal piece or some electrons from the metal piece itself will start to move to battery depending upon which battery terminal we have connected to it. Now interesting thing to note is that depending upon the capacity of the metal piece it will accept or deliver these electrons and then a steady state will come when no further movement will take place. At this moment we say that the metal piece has got some charge.

This charge will depend on the applied voltage and if the voltage is more, charge would be more but again limited by the capacity of the metal piece which is nothing but it's electrical capacitance property.

Scroll to Continue

If q is the charge accumulated on the metal piece when connected to a voltage source of V then q is proportional to V but the exact relation would depend on the value of the capacitance of the metal piece. Mathematically it is shown as -

q is proportional to V.

Which means that q = CV where C is the value of the capacitance. It is the capacity to store charges. It is now obvious that capacitor can hold charges and it also means that some electrical energy can be stored in them. This energy can be used to flow a current through a load in specific cases in which situation we say that capacitor istting discharged through that load or resistor. But once the charges present in the capacitor are discharged then it cannot deliver the electrical energy further unless it gets charged again by an electrical power source like a battery.

The electrical energy (U) stored in a capacitor is given by the following formula -

U = CV2/2

## Parallel plate capacitor

The simplest type of capacitor is the parallel plate capacitor in which two metallic plates are kept at a small distance from each other. More the area of these plates more the charge they can store or retain. That is the reason why in commercial high value parallel plate capacitors long foils of metals are separated by an electrolyte like teflon strip and then rolled in a cylindrical fashion to take less space.

The capacitance of a parallel plate capacitor is proportional to the area of the plate (A) but also inversely proportional to the distance (d) between them. Mathematically it is represented like -

C = εA/d where ε is the permittivity of the dielectric material.

The permittivity of air is represented as ε0 and the relation of dielectric constant k to it is given as -

k = ε / ε0

## Unit of capacitance

The unit of capacitance is Farad. The name farad was given to honour English physicist Michael Faraday.

If a conductor can hold 1 Coulomb of charge on application of 1 volt potential to it then it is said to have a capacitance of 1 Farad. In practice, conductors have very small capacitance and that is why the practical unit is in microfarad (1 Farad = 1000000 microfarad) or picofarad (1 Farad = 1000000000000 picofarad).

Example:

If we take two same sized aluminium foils and isolate them by a thin plastic or teflon sheet and connect two wires one each to one foil then this simple capacitor will have a capacitance of a few picofarad. If we replace these two small foils with the two long strips of foils and roll them and prepare a cylindrical capacitor then its capacitance might reach to hundreds of picofarad. Increasing the length of these strips further might create capacitor having capacitance in the microfarad range. These properties are utilised in manufacturing industrial capacitors.

## DC voltage and capacitor

When a DC voltage is applied to a capacitor the charges from the DC source reach the capacitor and charge its plates. This charging is very fast and for all practical purposes it is quick and immediate.

There are some technical purposes where this charging time can be increased by inserting a resistor in the circuit and it will lower the current flowing during charging of capacitor which eventually means less number of charges are now moving towards the capacitor to charge it and so it takes comparatively longer time to charge. For example there could be a situation where the capacitor was getting charged in say one tenth of a second but inclusion of a resistor in the circuit makes it 2 seconds.

## Discharge of a capacitor

So far we have talked about the charging of the capacitor. Now a charged capacitor will have charges stored on its two plates which are separated by some insulating or dielectric material. So if we connect the two plates of this capacitor through a metal wire or some resistor like an electric bulb then the charges would move through the resistor and negative charges would reach the positively charged plate and soon there will be no charge left on the capacitor and in this situation the capacitor is said to be discharged.

Have you observed in some of your appliances that the indicator lights continue to glow for a short moment even if we turn off the mains power? That is the effect of some capacitor inside the electronic circuitry which takes a small time to discharge and keeps the indicator light alive for a little time as the mains supply is not there.

The discharge time of a capacitor can be made longer by inclusion of a resistor in the circuit so that the charges slowly discharge through it. Charging and discharging of a capacitor is utilised in various electrical and electronic circuits for different technical purposes.

## AC voltage and capacitor

The behaviour of capacitor is different with AC because AC voltage changes its direction many times in a second.

The most important change in the behaviour of capacitor with DC and AC is that though it gets charged with DC but it blocks it for any current flow in the circuit except giving back the charge to circuit if so required but with AC voltage, as AC changes direction (like the mains AC voltage changes direction about 50 or 60 times in a second known as its frequency) the capacitor passes it and an AC current flows in the circuit through this capacitor. Interestingly, capacitor also creates a resistance for the flow of AC current depending upon the value of its capacitance as well as the frequency of the AC voltage applied. This resistance or hindrance created by the capacitor in the path of AC current is called impedance and is a very important parameter to be kept in consideration in electronic circuits where AC is flowing through the capacitor.

The numerical value of this impedance is given by ωC where ω = 2 π f (f is the frequency) and C is the capacitance value of the capacitor.

## Types of capacitor

There are many designs for capacitors. The simplest is parallel plate capacitor. In this type two metallic plates are placed near each other separated by an insulator which acts like an electrolyte to separate the plates.

Other than this, there are many other designs like spherical capacitors, cylindrical capacitors, electrolytic capacitors etc.

## Capacitors connected in series and parallel

Capacitors can be connected in series or parallel depending upon the purpose intended. For example if we have a number of capacitors in our stock each having 2 µF value and we want to put 10 µF in an electrical circuit then we can connect 5 number of capacitors each of 2 µF value in parallel and it would serve the same purpose as a single capacitor of 10 µF. This property of capacitor addition is presented in the following mathematical way -

C = C1 + C2 + C3 + C4

Where C is the total value of the above 4 capacitors having different values from (C1 to C4) connected in parallel.

Similarly capacitors can be connected in series also and in that case the combined capacitance value is governed by the folowing equation -

1/C = 1/C1 + 1/C2 + 1/C3 + 1/C4

We have connected 4 capacitors here as an example but one can connect less or more but the formula would be similar.

## Use of capacitors in industry

Capacitors are utilised in a variety of ways. Some of these are -

1. While converting the AC voltage to DC using rectifier circuits, the capacitors are used for smoothing the output to remove ripples from the DC voltage.

2. They are used in many electrical appliances for phase correction or improving the power factors.

3. They are an integral part of many basic electronic circuits like oscillators, multivibrators, op amplifiers, etc.

4. Capacitors are widely used for filtering out the spurious signals from the circuit which can induce noise or even can damage the electronic circuitry.

5. They are used to couple circuits and assemblies with each other as they pass the frequency signals but block the DC.

6. Capacitors are the important components in a resonant circuit where they are used alongwith a inductor coil. Technically known as LC circuits, they are used to resonate at a particular frequency to create maximum signal at that frequency. In old times the radio equipments invariably had these LC resonant circuits. In fact there used to be a variable parallel plate capacitor and by varying it with a knob we could tune to different radio stations.

1. https://byjus.com/physics/capacitor-and-capacitance/

2. https://www.fluke.com/en-in/learn/blog/electrical/

3. https://www.britannica.com/science/capacitance

4. https://www.electronics-tutorials.ws/capacitor/cap_1.html

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.