Battery Technology

Battery Technology

In the modern era, electrical energy is normally converted from mechanical energy, solar energy, and chemical energy etc. A battery is a device that converts chemical energy to electrical energy. The first battery was developed by Alessandro Volta in the year of 1800. In the year 1836, John Frederic Daniell, a British chemist developed the Daniell cell as an improved version of the voltaic cell. From that time until today, the battery has been the most popular source of electricity in many daily life applications.In our daily life, we generally use two types of battery, one of them is which can be used once before it gets totally discharged. Another type of battery is rechargeable which means it can be used multiple times by recharging it externally. The former is called primary battery and the later is called secondary battery.  
Batteries can be found in different sizes. A battery may be as small as a shirt button or may be so big in size that a whole room will be required to install a battery bank. With this variation of sizes, the battery is used anywhere from small wrist watches to a large ship.

We often see this symbol in many diagrams of electrical and electronics network. This is the most popularly used symbol for battery. The bigger lines represent positive terminal of the cells and smaller lines represent negative terminal of the cells connected in the battery.

We are often confused about the terms battery cell and battery . We generally refer a battery as a single electro-chemical cell. But literally, battery does not mean that. Battery means a number of electro-chemical cells connected together to meet a certain voltage and  current level. Although there may be a single cell battery, literally,  battery and cell are different.

History of Battery

In the year of 1936 during the middle of summer, an ancient tomb was discovered during construction of a new railway line near Bagdad city in Iraq. The relics found in that tomb were about 2000 years old. Among these relics, there were some clay jars or vessels which were sealed at the top with pitch. An iron rod, surrounded by a cylindrical tube made of wrapped copper sheet was projected out from this sealed top. 
When these pots were filled with an acidic liquid, they produced a potential difference of around 2 volts between the iron and copper. These clay jars are suspected to be 2000 year old battery cells.

In 1786, Luigi Galvani, an Italian anatomist and physiologist was surprised to see that when he touched a dead frog’s leg with two different metals, the muscles of the legs contracted. He could not understand the actual reason why, otherwise he would have been known as the first inventor of the battery cell. He thought the reaction might be due to a property of the tissues.
After that, Alessandro Volta realized that same phenomenon could be created by using cardboard soaked in salt water instead of frog's leg. He sandwiched a copper disc and a zinc disc with a piece of cardboard soaked in salt water in between them and found a potential difference between the copper and zinc. After that in 1800, he developed the first Voltaic Pile (battery) constructed of alternating copper and zinc discs with pieces of cardboard soaked in brine between them. This system could produce measurable current. Alessandro Volta's voltaic pile was considered the first "wet battery cell". Thus, the history of battery began.

The main problem with the Voltaic pile was that, it could not deliver current for a long time. This problem was solved by a British inventor John F. Daniell in 1836. He invented a more developed version of the battery cell which is known as the Daniell cell. Here in this cell, one zinc rod is immersed in zinc sulfate in one container and one copper rod is immersed in copper (II) sulfate in another container. The solutions of these two containers are bridged by a U shaped salt bridge. A Daniell cell could produce 1.1 volt and this type of battery lasted much longer than the Voltaic pile.  
In 1839, the fuel cell was designed by Sir William Robert Grove, a discoverer and man of science. He mixed hydrogen and oxygen within an electrolyte solution, and created electricity and water. The fuel cell did not deliver enough electricity, but it is helpful.
Bunsen (1842) and Grove (1839) created enhancements to battery that used liquid electrodes to supply electricity.  

In the year of 1859, Gaston Plante; first developed the lead acid  battery cell. This was the first form of rechargeable secondary battery. The  lead acid  battery   is still in use for many industrial purposes. It is still the most popular to be used as car battery. 
In 1866, the battery was again developed by a French engineer, Georges Leclanche. It was a carbon-zinc wet cell battery known as the Leclanche cell. Crushed manganese dioxide mixed with a bit of carbon forms the positive electrode and a zinc rod is used as the negative electrode. Ammonium chloride solution is used as a liquid electrolyte. After some years, Georges Leclanche himself improved his own design by replacing liquid ammonium chloride solution with ammonium chloride. This was the invention of the first dry cell.
In 1901, Thomas Alva Edison discovered the alkaline accumulator. Thomas Edison's basic cell had iron as the anode material (-) and nickel oxide as the cathode material(+). This is just one portion of an endless history of  battery .

Step by Step Development in History of Batteries

Developer/Inventor

Country

Year

Invention

Luigi Galvani

Italy

1786

Animal Electricity

Alessandro Volta

Italy

1800

Voltaic Pile

John F. Daniell

Britain

1836

Daniell Cell

Sir William Robert Grove

Britain

1839

Fuel Cell

Robert Bunsen

German

1842

used liquid electrodes to supply electricity

Gaston Plante

France

1859

Lead Acid Battery

Georges Leclanche

France

1866

Leclanche Cell

Thomas Alva Edison

United States

1901

Alkaline Accumulator

Working Principle of Battery

To understand the basic principle of battery properly, first, we should have some basic concept of electrolytes and electrons affinity. Actually, when two dissimilar metals or metallic compounds are immersed in an electrolyte, there will be a potential difference produced between these metals or metallic compounds. 
It is found that, when some specific compounds are added to water, they get dissolved and produce negative and positive ions. This type of compound is called an electrolyte. The popular examples of electrolytes are almost all kinds of salts, acids, and bases etc.
The energy released during accepting an electron by a neutral atom is known as electron affinity. As the atomic structure for different materials are different, the electron affinity of different materials will differ. If two different kinds of metals or metallic compounds are immersed in the same electrolyte solution, one of them will gain electrons and the other will release electrons. Which metal (or metallic compound) will gain electrons and which will lose them depends upon the electron affinities of these metals or metallic compounds. The metal with low electron affinity will gain electrons from the negative ions of the electrolyte solution. On the other hand, the metal with high electron affinity will release electrons and these electrons come out into the electrolyte solution and are added to the positive ions of the solution. In this way, one of these metals or compounds gains electrons and another one loses electrons. As a result, there will be a difference in electron concentration between these two metals. This difference of electron concentration causes an electrical potential difference to develop between the metals. This electrical potential difference or emf can be utilized as a source of voltage in any electronics or electrical circuit. This is a general and basic principle of  battery .

All batteries cells are based only on this basic principle. Let’s discuss one by one. As we said earlier, Alessandro Volta developed the first battery cell, and this cell is popularly known as the simple voltaic cell. This type of simple cell can be created very easily. Take one container and fill it with diluted sulfuric acid as the electrolyte. Now immerse zinc and one copper rod in the solution and connect them externally by an electric load. Now your simple voltaic cell is completed. Current will start flowing through the external load. 
Zinc in diluted sulfuric acid gives up electrons as below:

These Zn ^{+ +} ions pass into the electrolyte, and their concentration is very high near the zinc electrode. As a result of the above oxidation reaction, the zinc electrode is left negatively charged and hence acts as cathode. The diluted sulfuric acid and water disassociate into hydronium ions as given below:

Due to the high concentration of Zn ^{+ +} ions near the cathode, the H₃O⁺ ions are repelled towards the copper electrode and get discharged by removing electrons from the copper atoms. The following reaction takes place at the anode:

As a result of the reduction reaction taking place at copper electrode, copper is left positively charged and hence it acts as the anode.
Daniell Battery Cell: The Daniell cell consists of a copper vessel containing copper sulfate solution. The copper vessel itself acts as the positive electrode. A porous pot containing diluted sulfuric acid is placed in the copper vessel. An amalgamated zinc rod dipping inside the sulfuric acid acts as the negative electrode.
When the circuit is completed, diluted sulfuric acid in the porous pot reacts with zinc so as to liberate hydrogen gas. The reaction takes place as below:

The formation of ZnSO₄ in the porous pot does not affect the working of the cell, until crystals of ZnSO₄ are deposited.
The hydrogen gas passes through the porous pot and reacts with the CuSO₄ solution as below:

Copper so formed gets deposited on the copper vessel.

 

 

 

Why Measure Voltage?

Why Measure Voltage?

●        If you are an Electrical Engineering student:

○        Voltage is a fundamental quantity that is important in every phase of electrical engineering from power systems to voltages inside VLSI chips.

●        If you are an Mechanical Engineering student:

○        You will want to measure things like temperature.  If you do that, you will use some sort of temperature sensor, and the odds are high that it will produce a voltage that you have to measure.

●        If you are a Chemical Engineering student:

○        You will want to measure things like pH.  If you do that, you will use some sort of pHsensor, and the odds are high that it will produce a voltage that you have to measure.

●        If you are a Civil Engineering student:

○        You will want to measure things like strain.  If you do that, you will use a strain gage in an electrical circuit, and you will need to know how to measure voltage, and quite possibly you will need to know how to set up the circuit.

●        If you are a Bioengineering student:

○        You may want to measure voltages produced by nerve cells.

Whatever your engineering persuasion, you will need to make measurements that will invariably require you to deal with a voltage from a sensor.  You might not need to be the world's greatest expert on how to measure voltage, but you will need to be knowledgeable even if you just want to talk to the person who designs the measurement system. 

That leads us to the question of what you should know at the end of this lesson.  Consider the following:

●        Given a need for a physical measurement:

○        Be able to select and use basic sensors to measure temperature, strain, etc.

●        Given a voltage output from a sensor:

○        To be able to connect a voltmeter - or other voltage measurement instrument - to the circuit at proper points,Be able to use a voltmeter, oscilloscope or A/D card to measure the voltage

Eventually, you will also want to do the following - even though it is not explicitly covered in this lesson.

●        Given a voltage measurement problem:

○        Be able to record voltage measurements in a computer file, and,

○        Be able to use that file in an analysis program, including Mathcad, Matlab or Excel.

            The conclusion that you have to come to is that everyone who makes measurements - of almost any physical variable - is going to deal with voltages, voltage measurements and digital representations of voltages, whether they are a biologist, a mechanical engineer, an automobile mechanic or any number of other occupations.  Voltage is ubiquitous, and you have to deal with it - whether you want to or not.  You may not want to be an electrical enginer, but you will probably need to understand enough about basic electrical measurements to be able to use modern sensors, instruments and analysis programs in your work.

Using a Voltmeter

            In this section we'll look at how you use a voltmeter.  Here's a representation of a voltmeter.

For our introduction to the voltmeter, we need to be aware of three items on the voltmeter.

●        The display.  This is where the result of the measurement is displayed.  You meter might be either analog or digital.  If it's analog you need to read a reading off a scale.  If it's digital, it will usually have an LED or LCD display panel where you can see what the voltage measurement is.

●        The positive input terminal, and it's almost always red.

●        The negative input terminal, and it's almost always black.

            Next, you need to be aware of what the voltmeter measures.  Here it is in a nutshell.

●        A voltmeter measures the voltage difference between the positive input terminal of the voltmeter and the negative input terminal.

            That's it.  That's what it measures.  Nothing more, nothing less - just that voltage difference.  That means you can measure voltage differences in a circuit by connecting the positive input terminal and the negative input terminal to locations in a circuit.

            We'll show a voltmeter connected to the circuit diagram - a mixed metaphor approach.  Forgive us for that, but let's look at it.

This figure shows where you would place the leads if you wanted to measure the voltage across element #4.

●        Notice that the voltmeter measures the voltage across element #4, +V₄.

●        Notice the polarity definitions for V₄, and notice how the red terminal is connected to the "+" end of element #4.  If you reversed the leads, by connecting the red lead to the "-" terminal on element #4 and the black lead to the "+" end of element #4, you would be measuring -V₄.

            There are some important things to note about taking a voltage measurement.  The most important point is this.

●        Voltage is an across variable.

○        That means that when you measure voltage you measure a difference between two points in space.

○        There are other variables of this type.  For example, if you use a pressure sensor, you measure the pressure difference between two points, much like you measure a voltage difference.

○        There are other kinds of variables.  For example, there are numerous variables that are flow variables.  Current and fluid flow variables are example of flow variables.  They usually have units of something per second.  (Current is couloumbs/sec, while water flow might be in gallons/sec. - for example.)

●        When you measure a voltage the two terminals of the voltmeter (in the figure, the red terminal and the black terminal) are connected to the two points where the voltage appears that you want to measure.  One terminal - say it is the red terminal - will then be at the same voltage as one of the points, and the other terminal - the black terminal - will be at the same voltage as the other point.  The meter then responds to the difference between these two voltages.

            Let's look at an example.  Here are three points.  These points could be anything and may be located in a circuit, for example.  Wherever they are, there is a voltage difference between any two of these points, and you could theoretically measure the voltage difference between any two of these points.  There are actually three different choices for voltage differences.  (Red/Green, Green/Blue, Blue/Red)  Then, for each difference, there are two different ways you can connect the voltmeter - switching red and black leads.

Let's check to see if you understand that.  Here are the same three points, but now they are points within a circuit.  In this particular circuit, the battery will produce a current that flows through the two resistors in series.

This circuit has a schematic representation shown below.

And, here is the same circuit with the measurement points (see above) marked.

Now, if you want to measure the voltage across R_b, here is a connection that will do it.

And, the physical circuit would look like this one.

            Now, the reason for taking this so slowly is that students often have trouble moving between circuit diagrams and the physical circuit and understanding how to translate between them.  What looks clear on a circuit diagram is not always as clear in the physical situation.  We'll get a little closer to physical reality in this exercise.

Exercise 1

            Here's a portion of a circuit board.  You want to measure the voltage across R27.  Click on both places where you should put the voltmeter leads.

            When you measure a voltage difference - whatever the instrument you use - you will always have two leads coming from the instrument that will have to be connected to the two points in your circuit across which the voltage appears.

            And, remember, the voltage might be any of the folowing.

●        The voltage might be across an element embedded in a circuit.

●        The voltage might be the output of a transducer measuring some physical variable like temperature, pH, rotational velocity (a tachometer), etc.

Instruments for Measuring Voltage

            In the material above, we assumed that you would measure voltage with a voltmeter.  Actually, there are often numerous options for the instruments you use to measure voltage.  Here are three common options.

●        A Voltmeter

●        An Oscilloscope

●        An A/D card in a computer

We will examine each of these options separately in the next section.  Before we get there, however, note these common points for each of these three instruments.

●        Each measures voltage.

●        To measure voltage, remember that voltage is an "across" variable.  Each instrument will therefore have two leads to be connected to the circuit where you want to measure voltage, and those leads should be placed across the two points defining the voltage you want to measure.

Internal Resistance

            Voltmeters (including oscilloscopes, etc. as voltmeters) will have an effect on any circuit when they are used.  Any time you take a measurement - no matter what the measurement is - you disturb the thing you are measuring.  Attaching a voltmeter to a circuit will change the circuit - i.e. disturb the circuit - and modify the voltage you are trying to measure.  You just have to ensure that the disturbance is negligible.  That's what we want to look at here.

            Let's examine measuring the outut voltage of a voltage divider circuit.  Here is the circuit.

            Now, the voltmeter is really equivalent to a resistor, so we can - for purposes of analysis - replace the voltmeter by its equivalent resistance.  Here is the circuit with the voltmeter equivalent resistance.  (R_m is the resistance of the voltmeter.)

Now, you should be able to see that this isn't the same circuit that you thought you were measuring.  The addition of the voltmeter resistance changes the circuit and the changed circuit will have a different output voltage than the original circuit.  The question is whether the output voltage of the changed circuit is significantly different from the output voltage of the original circuit.

To determine if the output voltage has changed, you need to consider that the voltmeter and the resistance, R_b, are now in parallel.  That means that the output of the voltage divider is different.  However, you can compute the output without the meter and with the meter.

V_out = V_in R_b/( R_a + R_b) - without the meter

and

V_out = V_in R_e/( R_a + R_e) - with the meter, and

R_e = R_m R_b/( R_m + R_b)

These two expressions are very similar, and the how the close the two voltages will be depends upon how close the equivalent resistance and the original resistance are.  Note that the equivalent parallel resistance is:

R_e = R_m R_b/( R_m + R_b)

R_e = R_b [R_m/( R_m + R_b)]

So, if the factor multiplying R_b is close to one, there won't be much difference between the original voltage and the voltage you have when you attach the voltmeter.  In order to be sure that is true, we need to have the factor multiplying R_b as close to one as possible.

[R_m/( R_m + R_b)] = 1

or at least get as close to 1 as we can.  That's going to happen when the meter resistance is much larger than R_b.

The conclusion that you come to is that you want the resistance of a voltmeter - any voltmeter, including osciloscopes, etc. - to be as large as possible.  We'll look at typical values for instruments that are sold as we examine individual instruments.

Voltmeters

Voltmeters are perhaps the commonest or most widely used instruments for measuring voltage.  While there are still many analog voltmeters, most voltmeters today have digital displays, so that you get an LCD display with several digits of resolution.

            If an instrument has other capabilities (for example being able to measure current and/or resistance) then it is a multimeter.  If it is a digital multimeter it is often referred to as a "DMM".  A digital voltmeter can be referred to as a DVM.

            There are several things you will need to worry about when using a voltmeter or DMM.

●        Voltmeters can often measure either DC or AC voltages.

○        When measuring AC voltages, a voltmeter will give you values for the RMS value - not the peak value of the sine wave.  And, if the signal isn't sinusoidal, you may have trouble getting the measured value(s) you want.

●        In many instances, it is possible to connect the voltmeter to a computer.  That allows you to import your data into a computer and then use analysis programs like Mathcad, Matlab, spreadsheets, etc. to extract information from your data.  You may need to learn how to use those kinds of connections.

●        Voltmeters have range settings.  Some common range settings are 0-0.3v, 0-3v, 0-30v, etc.  On lower ranges you will get more accuracy.  On digital voltmeters, for example these ranges are really:

○        0-3.0000 v

○        0-30.000 v

○        As you go to higher ranges you will get as many significant digits in the measured value.

○        If you want more significant digits in a meter the cost will go up, and each additional digit is more expensive.

●     Voltmeters are not ideal.  The most common aspect of a voltmeter that you need to take into account is the resistance of the voltmeter.  Typically a DMM will have a resistance of 10 MW.  When you connect the voltmeter to a circuit it would be like connecting a 10 MW resistance to the circuit.  In many circuits that won't be a problem because that will be a negligible disturbance to the circuit.

●        Voltmeters measure voltages that are constant or at least do not change rapidly.  A typical digital voltmeter will measure voltage and display the results, then hold the results long enough for you to see the number.

            The last point in the bullets above has a hidden question.  That question is "What if you have a voltage that changes rapidly and you want to see details as it changes?".  If you have that situation, a voltmeter may not be your instrument of choice.  You may need an oscilloscope or an A/D card in a computer.  That's what we will examine next.

Oscilloscopes

       Oscilloscopes can measure time-varying voltages and give you a graph of voltage vs. time.  When you think about how to connect them to a circuit, they are exactly like voltmeters.  You connect an oscilloscope across the two points where you want to measure the voltage.  However, what you get from an oscilloscope is not what you get from a voltmeter.  When you measure a signal with an oscilioscope, you get a scaled picture of the voltage time-function.  That picture might look like this one if you were measuring a sinusoidal voltage.

Currently oscilloscopes will also perform some computations using data taken from the voltage waveform that is presented on the oscilloscope face.  These usually include things like the following.

●        The RMS value of the waveform.

●        The average value of the waveform.

●        The peak-to-peak value of the waveform.

●        The frequency of the waveform.

Also, once those signal parameters are computed and are in numerical form within the oscilloscope, they can be transmitted - using a variety of ways - to a computer where you can use a program to compute other properties you might be interested in.  For example, you might capture a transient temperature and measure the time it takes your temperature control system to reach a steady state by computing a time constant.  You could use any number of analysis programs for that including Mathcad, Matlab and spreadsheets.

            If you want a more complete description of oscilloscopes, you can go to the lesson on oscilloscopes by clicking here.  (That lesson has a number of interesting simulations you can try, so that you can learn a little before you go into lab.  It also has links to laboratories that help you learn to use oscilloscopes.)

A/D Boards

            You can purchase numerous A/D (short for Analog-to-Digital Converter) (Click here to go to the lesson on A/D converters.) converters that come on boards that plug into computers.  And, there are numerous ways to interface with such boards including at least the following.

●        Pre-written programs you can buy

●        Programming in C or C++

●        Programs that allow you to build good-looking GUIs (That's Graphical User Interfaces) including:

○        Programming in Visual C++

○        Programming in LabView

○        Programming in Matlab

○        Programming in Visual Basic

○        and others!

The ability to use these boards to get data into a computer allows you to use analysis programs like Mathcad, Matlab and spreadsheets to analyze your data, plot it, and to extract other information from your data.

            In many cases you may have soft instruments on the computer.  Soft instruments are computer programs that simulate voltmeters and oscilloscopes.  In other words, they look and feel like instruments (except that they are interactive images on a computer screen).  They are often designed to look and act like real instruments as much as possible.

 

 

Classification of Engineering Materials

Classification of Engineering Materials

Basically Engineering Materials Can be classified into two categories-

1.   Metals

2.   Non-Metals

Metals

Metals are polycrystalline bodies which are having number of differentially oriented fine crystals. Normally major metals are in solid states at normal temperature. However, some metals such as mercury are also in liquid state at normal temperature. All metals are having high thermal and electrical conductivity.  All metals are having positive temperature coefficient of resistance. Means resistance of metals increase with increase of temperature.
Examples of metals – Silver, Copper, Gold, Aluminum, Iron, Zinc, Lead, Tin etc.
Metals can be further divided into two groups-

1.   Ferrous Metals – All ferrous metals are having iron as common element. All ferrous materials are having very high permeability which makes these materials suitable for construction of core of electrical machines. Examples: Cast Iron, Wrought Iron, Steel, Silicon Steel, High Speed Steel, Spring Steel etc.

 

2.   Non-Ferrous Metals- All non-ferrous metals are having very low permeability. Example: Silver, Copper, Gold, Aluminum etc.

Non-Metals

Non-Metal materials are non-crystalline in nature. These exists in amorphic or mesomorphic forms. These are in both solid & gases forms at normal temperature.
Normally all non-metals are bad conductor of heat and electricity. 
Examples: Plastics, Rubber, Leathers, Asbestos etc.
As these non-metals are having very high resistivity which makes them suitable for insulation purpose in electrical machines.

Difference between Metals and Non Metals

Sl. No.

Property

Metals

Non-Metals

1.

Structure

All metals are having crystalline structure

All Non-metals are havingamorphic & mesomorphic structure

2.

State

Generally metals are slid normal temperature

State varies material to material. Some are gas state and some are in solid state at normal temperature.

3.

Valance electrons and conductivity

Valance electrons are free to move with in metals which makes them good conductor of heat & electricity

Valence electrons are tightly bound with nucleus which are not free to move. This makes them bad conductor of heat & electricity

4.

Density

High density

Low density

5.

Strength

High strength

Low strength

6.

Hardness

Generally hard

Hardness is generally varies

7.

Malleability

Malleable  

Non malleable

8.

Ductility

Ductile

Non ductile

9.

Brittleness

Generally non brittle in nature

Brittleness varies material to material

10.

Lustre

Metals possess metallic lustre

Generally do not possess metallic lustre (Except graphite & iodine)

Other classification of engineering materials:

Engineering materials can also be classified as below-

1.   Metals and Alloys

2.   Ceramic Materials

3.   Organic Materials

Metals and Alloys

Metals are polycrystalline bodies which are have number of differentially oriented fine crystals. Normally major metals are in solid states at normal temperature. However, some metals such as mercury are also in liquid state at normal temperature.
Pure metals are having very low mechanical strength, which sometimes does not match with the mechanical strength required for certain applications. To overcome this draw back alloys are used.
Alloys are the composition of two or more metals or metal and non-metals together. Alloys are having good mechanical strength, low temperature coefficient of resistance. Example: Steels, Brass, Bronze, Gunmetal, Invar. Super Alloys etc.

Ceramic Materials

Ceramic materials are non-metallic solids. These are made of inorganic compounds such as Oxides, Nitrides, Silicides and Carbides. Ceramic materials possess exceptional Structural, Electrical, Magnetic, Chemical & Thermal properties. These ceramic materials are now extensively used in different engineering fields. 
Examples: Silica, glass, cement, concrete, garnet, Mgo, Cds, Zno, SiC etc.

Organic Materials

All organic material are having carbon as a common element. In organic materials carbon is chemically combined with oxygen, hydrogen and other non-metallic substances. Generally organic materials are having complex chemical bonding. 
Example: Plastics, PVC, Synthetic Rubbers etc.

 

 

Norton Theorem

Norton Theorem

This theorem is just alternative of Thevenin theorem. In Norton theorem, we just replace the circuit connected to a particular branch by equivalent current source. In this theorem, the circuit network is reduced into a single constant current source in which, the equivalent internal resistance is connected in parallel with it. Every voltage source can be converted into equivalent current source.
Suppose, in complex network we have to find out the current through a particular branch. If the network has one of more active sources, then it will supply current through the said branch. As in the said branch current comes from the network, it can be considered that the network itself is a current source. So in Norton theorem the network with different active sources is reduced to single current source that's internal resistance is nothing but the looking back resistance, connected in parallel to the derived source.

The looking back resistance of a network is the equivalent electrical resistance of the network when someone looks back into the network from the terminals where said branch is connected. During calculating this equivalent resistance, all sources are removed leaving their internal resistances in the network. Actually in Norton theorem, the branch of the network through which we have to find out the current, is removed from the network. After removing the branch, we short circuit the terminals where the said branch was connected. Then we calculate the short circuit current that flows between the terminals. This current is nothing but Norton equivalent current I_N of the source. The equivalent resistance between the said terminals with all sources removed leaving their internal resistances in the circuit is calculated and said it is R_N. Now we will form a current source that's current is I_N A and internal shunt resistance is R_N Ω.
For getting clearer concept of this theorem, we have explained it by the following example,
In the example two resistors R₁ and R₂ are connected in series and this series combination is connected across one voltage source of emf E with internal resistance R_i as shown. Series combination of one resistive branch of R_L and another resistance R₃ is connected across the resistance R₂ as shown. Now we have to find out the current through R_L by applying Norton theorem.

First, we have to remove the resistor R_L from terminals A and B and make the terminals A and B short circuited by zero resistance.
Second, we have to calculate the short circuit current or Norton equivalent  current I_N through the points A and B.

The equivalent resistance of the network,

To determine internal resistance or Norton equivalent resistance R_N of the network under consideration, remove the branch between A and B and also replace the voltage source by its internal resistance. Now the equivalent resistance as viewed from open terminals A and B is R_N,


As per Norton theorem, when resistance R_L is reconnected across terminals A and B, the network behaves as a source of constant current I_N with shunt connected internal resistance R_N and this is Norton equivalent circuit. 

Norton Equivalent Circuit

Biot Savart Law

The mathematical expression for magnetic flux density was derived by Jean Baptiste Biot and Felix Savart. Talking the deflection of a compass needle as a  measure of the intensity of a current, varying in magnitude and shape, the two scientists concluded that any current element projects into space a magnetic field, the magnetic flux density of which dB, is directly proportional to the length of the element dl, the current I, the sine of the angle and θ between direction of the current and the vector joining a given point of the field and the current element and is inversely proportional to the square of the distance of the given point from the current element, r. This is Biot Savart lawstatement. 
Where, K is a constant, depends upon the magnetic properties of the medium and system of the units employed. In SI system of unit, 

Therefore, final Biot Savart law derivation is,

Let us consider a long wire carrying an current I and also consider a point p. The wire is presented in the below picture by red color. Let us also consider an infinitely small length of the wire dl at a distance r from the point P as shown. Here, r is a distance vector which makes an angle θ with the direction of current in the infinitesimal portion of the wire.

If you try to visualize the condition, you can easily understand the magnetic field density at that point P due to that infinitesimal length dl of wire is directly proportional to current carried by this portion of the wire. That means current through this infinitesimal portion of the wire is increased the magnetic field density  due to this infinitesimal length of wire, at point P increases proportionally and if the current through this portion of wire is decreased the magnetic field density at point P due to this infinitesimal length of wire decreases proportionally.
As the current through that infinitesimal length of wire is same as the current carried by the wire itself.

It is also very natural to think that the magnetic field density at that point P due to that infinitesimal length dl of wire is inversely proportional to the square of the straight distance from point P to center of dl. That means distance r of this infinitesimal portion of the wire is increased the magnetic field density  due to this infinitesimal length of wire, at point P decreases and if the distance of this portion of wire from point P, is decreased, the magnetic field density at point P due to this infinitesimal length of wire increases accordingly.


Lastly, field density at that point P due to that infinitesimal portion of wire is also directly proportional to the actual length of the infinitesimal length dl of wire. As θ be the angle between distance vector r and direction of current through this infinitesimal portion of the wire. The component of dl directly facing perpendicular to the point P is dlsinθ,

Now combining these three statements, we can write,

This is the basic form of Biot Savart's Law
Now putting the value of constant k (which we have already introduced at the beginning of this article) in the above expression, we get 

Here, μ₀ used in the expression of constant k is absolute permeability of air or vacuum and it's value is 4π10^-7 W_b/ A-m in SI system of units. μ_r of the expression of constant k is relative permeability of the medium.  
Now, flux density(B) at the point P due to total length of the current carrying conductor or wire can be represented as, 


 If D is the perpendicular distance of the point P form the wire, then

Now, the expression of flux density B at point P can be rewritten as,


As per the figure above,

Finally the expression of B comes as,

This angle θ depends upon the length of the wire and the position of the point P. Say for certain limited length of the wire, angle θ as indicated in the figure above varies from θ₁ to θ₂. Hence, flux density at point P due to total length of the conductor is, 

Let's imagine the wire is infinitely long, then θ will vary from 0 to π that is θ₁ = 0 to θ₂ = π. Putting these two values in the above final expression of Biot Savart law, we get,

This is nothing but the expression of Ampere's Law.

 

 

Nature of Electricity

Nature of Electricity

 

Electricity is the most common form of energy. Electricity is used for various applications such as lighting, transportation, cooking, communication, production of various goods in factories and much more. None of us exactly know that what is electricity. The concept of electricity and theories behind it, can be developed by observing its different behaviors. For observing nature of electricity, it is necessary to study the structure of matters. Every substance in this universe is made up of extremely small particles known as molecules. The molecule is the smallest particle of a substance into which all the identities of that substance are present. The molecules are made up of further smaller particles known as atoms. An atom is the smallest particle of an element that can exist.

 

There are two types of substances. The substance, that's molecules are made of similar atoms is known as an element. The matter whose molecules consisting dissimilar atoms, is called a compound. The concept of electricity can be achieved from the atomic structures of substances.

Structure of Atom

An atom consists of one central nucleus. The nucleus is made up of positive protons and charge less neutrons. This nucleus is surrounded by numbers of orbital electrons. Each electron has a negative charge of - 1.602 × 10 ^{- 19}Coulomb and each proton in the nucleus has a positive charge of + 1.602 × 10  ^- 19 Coulomb. Because of the opposite charge there is some attraction force between the nucleus and orbiting electrons. Electrons have relatively negligible mass compared to the mass of the nucleus. The mass of each proton and neutrons is 1840 times the mass of an electron. As the modulus value of each electron and each proton are same, the number of electrons is equal to the number protons in an electrically neutral atom. An atom becomes positively charged ion when it loses electrons and similarly an atom becomes negative ion when it gains electrons. 

Atoms may have loosely bonded electrons in their outermost orbits. These electrons require a very small amount of energy to detach themselves from their parent atoms. These electrons are referred as free electrons which move randomly inside the substance and transferred from one atom to another. Any piece of substances which as a whole contains an unequal number of electrons and protons is referred as electrically charged. When there is more number of electrons compared to its protons, the substance is said to be negatively charged and when there is more number of protons compared to electrons, the substance is said to be positively charged.

The basic nature of electricity is, whenever a negatively charged body is connected to a positively charged body by means of a conductor, the excess electrons of negative body starts flowing towards the positive body to compensate the lack of electrons in that positive body.  
Hope you got the very basic concept of electricity from the above explanation. There are some materials which have plenty of free electrons at normal room temperature. Very well known examples of this type of materials are, silver, copper, aluminium, zinc etc. The movement of these free electrons can easily be directed to a particular direction if the electrical potential difference is applied across the piece of these materials. Because of plenty of free electrons these materials have good electrical conductivity. These materials are referred as good conductor. The drift of electrons in a conductor in one direction is known as the current. Actually electrons flow from lower potential (-Ve) to higher potential (+Ve) but the general conventional direction of current has been considered as the highest potential point to lower potential point, so the conventional direction of current has been just opposite of the direction of flow of electrons. In non-metallic materials, such as glass, mica, slate, porcelain, the outermost orbit is completed and there is almost no chance of loosing electrons from its outermost shell. Hence there is hardly any free electron present in this type of material.
Hence, these materials cannot conduct electricity in other words electrical conductivity of these materials is very poor. Such material are known as non - conductor or electrical insulator. The nature of electricity is to flow through a conductor while an electrical potential difference applied across it, but not to flow through insulator even high electrical potential difference applied across them.