Dual voltage Transformer

Dual voltage Transformer

A dual voltage transformer can be defined as the one which is capable of providing two types of voltages i.e. if the two separate windings are connected in series, they will provide the sum of voltages supplied to the two coils and if the two windings are connected in parallel, then the net voltage will be decreased.
These voltages can be switched within the transformer according to the type of output required, just be using a dual voltage switch.

Construction and working

Suppose we have a dual voltage transformer which has two windings connected in series at the input terminal and two other windings also connected in series at the output terminal at the place of the secondary coils. Then if each of the two primary windings are rated at 120 volts each, the total voltage at the input terminal will be equal to 120 V + 120 V = 240 Volts.
Similarly at the output terminal if both the secondary coils are rated at 12 volts each then the total voltage at the secondary terminal would also be equal to 24 volts. This is evident from the figure below:





Similarly, now if the primary and secondary coils are connected in parallel and each of the two primary windings are still rated 120 volts each then the total voltage at the input terminal would now be equal to 120 volts and 12 volts at the output terminal if it two parallel windings are rated at 12 volt each. In this way we can switch between two types of voltages by just switching the connections of the windings, which can easily be done by a switch as well.
This is shown in the figure below:

Uses of a Dual Voltage Transformer

This reconnection saves the time and cost as well, as much of the power applications require a number of voltage levels for different machines, then in this case, using different types of transformers is not a solution. Just having a Transformer which has reconnect able windings greatly reduces the cost and the switch saves the time as well.
Moreover, this type of transformer can be used in both the American and European countries, where the appliances and all the other electronics operate on a different voltage levels as supplied in those countries, then this transformer is of great use and can be used in both the countries with any inconvenience of changing connections or buying a new one, as all the connections are already made inside the device and offers a great deal of convenience, especially for industrial leaders, who have to use portable devices all over the world.

Identification of a dual Voltage Transformer

Dual voltage transformers are quite easy to recognize as their voltage and power ratings are mentioned on them in a different manner as compare to usual transformers. For example, if a simple transformer supplies 24 volts at 2 A, then it would be written like 24V @ 2 A. But since a dual voltage transformer can give us 12 V as well as 24 V, then it would be mentioned like 12 V – 24 V, from which it can be easily recognized that it this transformer can supply two types of voltages, although we have not seen its internal connections.
In this way, they are really easy to identify, use and are getting quite versatile, especially in the industry nowadays.

Varistor

Varistor

Varistor is a non linear resistor made of semiconductor through which depends non-linearly on the applied voltage across it. The most commonly used form of that is metal oxide varistor or MOV. The current in that device is a function of the applied voltage and given as
I = kV^α
where k is a constant depends upon the quality of the material and size of the device and α is the non linearity exponent depends upon the quality of the material.


Metal oxide varistor or MOV is a simple voltage dependent resistor, whose resistance becomes suddenly very low after a predetermined value of applied voltage. It absorbs and bypasses surge energy for both negative positive cycle of surge voltage pulses and protect the sophisticated electronic circuit elements. Some time during very heavy surge and lightning strike the varistor may be damaged itself to keep the other costly electronic elements safe.
Although this is a non linear resistor but it is mainly used for economical protection against
high voltage transients in different electronic circuits. Transient suppressor diodes are used for same purpose but metal oxide varistor or MOV has some advantages over it. The former absorb much more transient energy and can suppress both positive and negative transients. Actually in this device the electrical resistance varies with voltage across it. Here if voltage crosses a certain predetermined value, then the resistance becomes significantly low. As it is connected across the circuit, the transient is bypassed through the varistor and keep the sensitive costly circuit component safe. Metal oxide varistor is made of non-homogeneous material in such a way that gives a rectifying action at the contact points of two
particles. Many series and parallel connections determine the voltage rating and the current capability of the device.The zinc oxide based non linear resistors are primarily employed to protect solid state power supplies from low and medium surge voltages in the supply line.

Metal Oxide Varistor

Non linear resistors are primarily made from silicon carbide obtained by electrically heating a mixture of quartz sand with carbon to a temperature of about 2000^oC. Elements made by baking discs molded from a mixture of silicon carbide, graphite and water glass serve as a negative resistivity material.

Different characteristics of Varistor

Maximum continuous Voltage of Varistor

The maximum steady voltage that can be applied across a metal oxide varistor continually without any harm is referred as maximum continuous voltage of varistor.

Varistor Voltage

This is the voltage across the MOV for which 1 mA electric current flows through it. The measurement should be done for very short period to avoid heat perturbation. The varistor voltage, is a point on the V – I characteristic, utilized for easy comparing of different models and types.

Maximum Clamping Voltage

The maximum voltage across a metal oxide varistor for which the standard pulse current through it rises in 8 µs and decreases in 20 µs (8 µs to 20 µs)according to IEC 60060-2, (sec 6 ) The specified current for this measurement is referred as class current of varistor.

Maximum non repetitive surge current

The maximum current allowed to flow through a varistor is depended upon its pulse shape, duty cycle and number of pulses. In order to determine the capabiity of withstanding pulse currents, it is normally allowed to warrant a maximum non repetitive surge current. This is given for one pulse characterized by the shape of the pulse current of 8 µs to 20 µs following IEC 60060-2, with such an amplitude that the MOV voltage measured at 1 mA does not change by more than 10 % maximum. This is the specified surge current beyond which the device may rupture with expulsion.

Maximum Energy Rating of Varistor

For one pulse current there will be an energy dissipation in the device. This dissipated energy depends upon


1) The magnitude of the current

2) The magnitude of voltage across the metal oxide varistor corresponding to its peak current

3) The rise time of the pulse front

4) The decrease time of the pulse front;

5) The non-linear characteristics of varistor

Thevenin & Norton Theorem

 Thevenin Theorem

 Suppose we have to calculate the electric current through any particular branch in a circuit. This branch is connected with rest of the circuit at its two terminals. Due to active sources in the circuit there is one potential difference between the points where the said branch is connected. The current through the said branch is caused by this potential difference appears across the terminals. So rest of the circuit can be considered as a single voltage source, whose voltage is nothing but the open circuit voltage between the terminals where the said branch is connected and the internal resistance of the source is nothing but the equivalent electrical resistance of the circuit looking back into the terminals where the branch is connected. So the Thevenin theorem can be stated as follows,

1) When a particular branch is remove from a circuit, the open circuit voltage appears across the terminals of the circuit, is Thevenin equivalent voltage and


2) the equivalent resistance of the circuit network looking back into the terminals, is Thevenin equivalent resistance.


3) If we replace the rest of the circuit network by a single voltage source, then the voltage of the source would be Thevenin equivalent voltage and internal resistance of the voltage source would be Thevenin equivalent resistance which would be connected in series with the source as shown in the figure below.

For better understanding Thevenin theorem, we have shown the circuit below,

Here 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. One resistive branch of R_L is connected across the resistance R₂ as shown. Now we have to calculate the current through R_L.

First we have to remove the resistor R_L from the terminals A and B.

Second we have to calculate the open circuit voltage or Thevenin equivalent voltage V_T across the terminals A and B.

The current through resistance R₂,

Hence voltage appears across the terminals A and B i.e.

 

 

 Third, for applying Thevenin theorem, we have to determine the Thevenin equivalent electrical resistance of the circuit and for that first we have to replace the voltage source from the circuit leaving behind only its internal resistance R_i. Now view the circuit inwards from the open terminals A and B. It is found the circuits now consists of two parallel paths – one consisting of resistance R₂ only and the other consisting of resistance R₁ and R_i in series.

Thus the Thevenin equivalent resistance R_T as viewed from the open terminals A and B is given as. As per Thevenin theorem when resistance R_L is connected across terminals A and B the network behaves as a source of voltage V_T and internal resistance R_T and this is called Thevenin equivalent circuit. The current through R_L is given as

Thevenin Equivalent Circuit

 Norton theorem
 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 to equivalent current source.
Suppose in complex network we have to find out the electrical current through a particular branch. If the network has one of more active sources then it will supply current through the said branch. As the said branch current comes from the network, it can be considered the network itself is a current source. So in Norton theorem the network with different active sources is reduced to single current source whose 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 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 say it is RN. Now we will form a current source whose current is I_N A and internal shunt resistance is R_N Ω.
For getting more clear 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.


 For determining of internal resistance or Norton equivalent resistance R_N of the network under consideration. Remove the 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 electrical 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

Lenz’s law and Faraday’s law of electromagnetic induction

Lenz’s law:-



Lenz’s law is named after the German scientist H. F. E. Lenz in 1834. Lenz’s law obeys Newton’s third law of motion (i.e to every action there is always an equal and opposite reaction) and the conservation of energy (i.e energy may neither be created nor destroyed and therefore the sum of all the energies in the system is a constant)
Lenz law is based on Faraday’s law of induction so before understanding Lenz’s law one should know what Faraday’s law of induction is "When a changing magnetic field is linked with a coil, an emf is induced in it. This change in magnetic field may be caused by changing the magnetic field strength by moving a magnet toward or away from the coil or moving the coil into or out of the magnetic field as desired".

Heinrich Friedrich Emil Lenz

LENZ’S LAW

Lenz law states that when an emf is generated by a change in magnetic flux according to Faraday’s Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it.
The negative sign is used in Faraday’s law of electromagnetic induction, indicates that the induced emf ( ε ) and the change in magnetic flux ( δΦ_B ) have opposite signs.

Where
ε = Induced emf
δΦ_B = change in magnetic flux
N = No of turns in coil

Reason for opposing, cause of induced current in Lenz’s law?

• As stated above Lenz law obeys the law of conservation of energy and if the direction of the magnetic field that creates the current and the magnetic field of the current in a conductor are in same direction, then these two magnetic field would add up and produce the current of twice the magnitude and this would in turn creates more magnetic field, which cause more current and this process continues on and on and thus leads to violation of the law of conservation of energy.
• If the induced current creates a magnetic field which is equal and opposite to the direction of magnetic field that creates it, then only it can resist the change in the magnetic field in the area which is in accordance to the Newton’s third law of motion

EXPLANATION OF LENZ’S LAW

For understanding Lenz’s law consider two cases :

CASE-I When a magnet is moving towards the coil. 



When the north pole of the magnet is approaching towards the coil, the magnetic flux linking the coil increases. According to Faraday’s law of electromagnetic induction, when there is change in flux, an emf and hence current is induced in the coil and this current will creates its own magnetic field . Now according to Lenz law, this magnetic field created will oppose its own cause or we can say opposes the increase in flux through the coil and this is possible only if approaching coil side attains north polarity, as we know similar poles repel each other. Once we know the magnetic polarity of the coil side, we can easily determine the direction of the induced current by applying right hand rule. In this case the current flows in anticlockwise direction.

CASE-II When a magnet is moving away from the coil.


 
When the north pole of the magnet is moving away from the coil, the magnetic flux linking the coil decreases. According to Faraday’s law of electromagnetic induction, an emf and hence current is induced in the coil and this current will creates its own magnetic field . Now according to Lenz’s law, this magnetic field created will oppose its own cause or we can say opposes the decrease in flux through the coil and this is possible only if approaching coil side attains south polarity, as we know dissimilar poles attract each other. Once we know the magnetic polarity of the coil side, we can easily determine the direction of the induced current by applying right hand rule. In this case the current flows in clockwise direction.

NOTE : For finding the directions of magnetic field or electric current use Right hand thumb rule i.e if the fingers of the right hand are placed around the wire so that the thumb points in the direction of current flow, then the curling of fingers will show the direction of the magnetic field produced by the wire.

Right hand thumb rule

The Lenz law can be summarized as under:

• If the magnetic flux Ф linking a coil increases, the direction of current in the coil will be such that it oppose the increase in flux and hence the induced current will produce its flux in a direction as shown below (using right hand thumb rule).

• If magnetic flux Ф linking a coil is decreasing, the flux produced by the current in the coil is such that it aid the main flux and hence the direction of current is as shown below

APPLICATION OF LENZ’S LAW

• Lenz law can be used to understand the concept of stored magnetic energy in an inductor. When a source of emf is connected across an inductor, a current starts flowing through it. The back emf will oppose this increase in current through the inductor. In order to establish the flow of current, the external source of emf has to do some work to overcome this opposition. This work done by the emf is stored in the inductor and it can be recovered after removing the external source of emf from the circuit
• This law indicates that the induced emf and the change in flux have opposite signs which provide a physical interpretation of the choice of sign in Faraday’s law of induction.
• Lenz’s law is also applied to electric generators. When an electric current is induced in a generator, the direction of this induced current is such that it opposes its cause i.e rotation of generator (as in accordance to Lenz’s law) and hence the generator requires more mechanical energy. It also provides back emf in case of electric motors.
• Lenz’s law is also used in electromagnetic braking and induction cook tops.

Faraday’s law of electromagnetic induction

In 1831, Michael Faraday, an English physicist gave one of most basic law of electromagnetism called Faraday’s law of electromagnetic induction. This law explains the working principle of most of electrical motors, generators, electrical transformers and inductors. This law shows the relationship between electric circuit and magnetic field. Faraday performs an experiment with a magnet and coil. During this experiment he found how emf is induced in the coil when flux linked with it changes. He has also done experiments in electrochemistry and electrolysis.

Michael Faraday

Faraday’s Experiment

RELATIONSHIP BETWEEN INDUCED EMF AND FLUX

Faraday’s law

In this experiment Faraday takes a magnet and a coil and connects a galvanometer across the coil. At starting the magnet is at rest so there is no deflection in the galvanometer i.e needle of galvanometer is at centre or zero position. When the magnet is moved toward the coil, the needle of galvanometer deflects in one direction. When the magnet is held stationary at that position, the needle of galvanometer returns back to zero position. Now when the magnet is moved away from the coil , there is some deflection in the needle but in opposite direction and again when the magnet become stationary at that point with respect to coil , the needle of galvanometer return back to zero position. Similarly if magnet is held stationary and the coil is moved away and towards the magnet, the galvanometer shows deflection in similar manner. It is also seen that the faster the change in the magnetic field, the greater will be the induced emf or voltage in the coil.

Position of magnet	Deflection in galvanometer
Magnet at rest	No deflection in galvanometer
Magnet moves towards the coil	Deflection in galvanometer in one direction
Magnet is held stationary at same position (near the coil)	No deflection in galvanometer
Magnet moves away from the coil	Deflection in galvanometer but in opposite direction
Magnet is held stationary at same position (away from the coil)	No deflection in galvanometer

CONCLUSION: From this experiment Faraday concluded that whenever there is relative motion between conductor and a magnetic field, the flux linkage with a coil changes and this change in flux induces a voltage across a coil.

Michael Faraday formulated two laws on the basis of above experiments. These laws are called Faraday’s laws of electromagnetic induction.

Faraday’s Laws

Faraday’s First Law

Any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil. This emf induced is called induced emf and if the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current.
Method to change magnetic field:
1. by moving a magnet toward or away from the coil
2. by moving the coil into or out of the magnetic field.
3. by changing area of a coil placed in the magnetic field
4. by rotating the coil relative to the magnet.

Faraday’s Second Law

It states that the magnitude of emf induced in the coil is equal to the rate of change of flux linkages with the coil. The flux linkages of the coil is the product of number of turns in the coil and flux associated with the coil.

Faraday Law Formula

Faraday’s law

Consider a magnet approaching towards a coil. Here we consider two instants at time T₁ and time T₂.
Flux linkage with the coil at time, T₁ = NΦ₁ Wb
Flux linkage with the coil at time, T₂ = NΦ₂ wb
Change in flux linkage = N(Φ₂ – Φ₁)
Let this change in flux linkage be, Φ = Φ₂ – Φ₁
So, the Change in flux linkage = NΦ
Now the rate of change of flux linkage = NΦ / t
Take derivative on right hand side we will get
The rate of change of flux linkage = NdΦ/dt
But according to Faraday’s law of electromagnetic induction the rate of change of flux linkage is equal to induced emf.




Considering Lenz’s Law





Where flux Φ in Wb = B.A
B = magnetic field strength
A = area of the coil

HOW TO INCREASE EMF INDUCED IN A COIL

• By increasing the number of turns in the coil i.e N- From the formulae derived above it is easily seen that if number of turns of coil is increased, the induced emf is also increased.
• By increasing magnetic field strength i.e B surrounding the coil- Mathematically if magnetic field increases, flux increases and if flux increases emf induced will also increased Theoretically if the coil is passed through a stronger magnetic field, there will be more lines of force for coil to cut and hence there will be more emf induced.
• By increasing the speed of the relative motion between the coil and the magnet. – If the relative speed between the coil and magnet is increased from its previous value, the coil will cut the lines of flux at a faster rate so more induced emf would be produced.

Applications of Faraday Law

Faraday law is one of the most basic and important law of electromagnetism . This law finds its application in most of electrical machines, industries and medical field etc.

• Electrical Transformers
It is a static ac device which is used to either step up or step down voltage or current. It is used in generating station, transmission and distribution system. The transformer works on Faraday’s law.

• Electrical Generators
The basic working principle of electrical generator is Faraday’s law of mutual induction .Electric generator is used to convert mechanical energy into electrical energy.

• Induction Cookers
The Induction cooker, is a most fastest way of cooking. It also works on principle of mutual induction. When current flows through the coil of copper wire placed below a cooking container, it produces a changing magnetic field. This alternating or changing magnetic field induces an emf and hence the current in the conductive container and we know that flow of current always produces heat in it.

• Electromagnetic Flow Meters
It is used to measure velocity of blood and certain fluids. When a magnetic field is applied to electrically insulating pipe in which conducting fluids are flowing then according to Faraday’s law an electromotive force is induced in it. This induced emf is proportional to velocity of fluid flowing .

• Form the bases of Electromagnetic Theory
Faraday’s idea of lines of force is used in well known Maxwell’s equations. According to Faraday’s law change in magnetic field gives rise to change in electric field and the converse of this is used in Maxwell’s equations.

• Musical Instruments
It is also used in musical instruments like electric guitar, electric violin etc.

Kirchhoff Current and Voltage Laws

There are some simple relationship between currents and voltages of different branches of an electrical circuit. These relationship are determined by some basic laws which are known as Kirchhoff Laws or more specifically Kirchhoff Current and Voltage laws. These laws are very helpful in determining the equivalent resistance or impedance (in case of AC) of a complex network and the currents flowing in the various branches of the network. These laws are first derived by Guatov Robert Kirchhoff and hence these laws are also referred as Kirchhoff Laws.

Kirchhoff Current Law

In an electrical circuit the electric current flows rationally as electrical quantity. As the flow of current is considered as flow of quantity, at any point in the circuit the total current enters is exactly equal to the total current leaves the point. The point may be considered any where in the circuit.
Suppose the point is on the conductor through which the current is flowing, then the same current crosses the point which can alternatively said that the current enters at the point and same will leave the point. As we said the point may be any where on the circuit, so it can also be a junction point in the circuit. So total quantity of current enters at the junction point must be exactly equal to total quantity of current leave the junction. This is very basic thing about flowing of electric current and fortunately Kirchhoff Current law says the same. The law is also known as Kirchhoff First Law and this law stated that at any junction point in the electrical circuit, the summation of all the branch currents is zero. If we consider all the currents enter in the junction are considered as positive current then convention of all the branch currents leaving the junction are negative. Now if we add all these positive and negative signed currents obviously we will get result of zero.
The mathematical form of Kirchhoff Current Law is as follows,
We have a junction where n number of beaches meet together.

Let’s I₁, I₂, I₃, …………………. I_m are the current of branches 1, 2, 3, ……m and
I_{m + 1}, I_{m + 2}, I_{m + 3}, …………………. I_n are the current of branches m + 1, m + 2, m + 3, ……n respectively.


The currents in branches 1, 2, 3 ….m are entering to the junction
whereas currents in branches m + 1, m + 2, m + 3 ….n are leaving from the junction.

So the currents in the branches 1, 2, 3 ….m may be considered as positive as per general convention
and similarly the currents in the branches m + 1, m + 2, m + 3 ….n may be considered as negative.


Hence all the branch currents in respect of the said junction are

+ I₁, + I₂, + I₃,…………….+ I_m, − I_{m + 1}, − I_{m + 2}, − I_{m + 3}, ……………… and − I_n.


Now, the summation of all currents at the junction is
I₁ + I₂ + I₃ + …………….+ I_m − I_{m + 1} − I_{m + 2} − I_{m + 3}………………− I_n.


This is equal to zero according to Kirchhoff Current Law.
⇒ I₁ + I₂ + I₃ + …………….+ I_m − I_{m + 1} − I_{m + 2} − I_{m + 3}………………− I_n = 0


The mathematical form of Kirchhoff First Law is ∑ I = 0 at any junction of electrical network

Kirchhoff Voltage Law

Kirchhoff Voltage Law

This law deals with the voltage drops at various branches in an electrical circuits. Think about one point on an closed loop in an electrical circuit. If some one goes to any other point on the same loop, he or she will find that the potential at that second point may be different from first point. If he or she continues to go to some different point in the loop, he or she may find some different potential at that new location. If he or she goes on further along that closed loop ultimately he or she reaches the initial point from where the journey was started. That means he or she comes back to the same potential point after crossing through different voltage levels.

It can be alternatively said that net voltage gain and net voltage drops along a closed loop are equal. That is what Kirchhoff Voltage law states. This law is alternatively known as Kirchhoff Second Law.
If we consider a closed loop, conventionally if we consider all the voltage gains along the loop are positive then all the voltage drops along the loop should be considered as negative. The summation of all these voltages in a closed loop is equal to zero. Suppose n numbers of back to back connected elements form a closed loop. Among these circuit element m number elements are voltage source and n – m number of elements drop voltage such as resistors.
The voltages of sources are V₁, V₂, V₃,………………. V_m
and voltage drops across the resistors respectively, V_{m + 1},V_{m + 2}, V_{m + 3},………………… V_n.
As it said that the voltage gain conventionally considered as positive, and voltage drops are considered as negative, the voltages along the closed loop are
+ V₁, + V₂, + V₃,………………. + V_m, − V_{m + 1}, − V_{m + 2}, − V_{m + 3},…………………− V_n.

Now according to Kirchhoff Voltage law the summation of all these voltages results to zero.
That means, V₁ + V₂ + V₃ + ………………. + V_m − V_{m + 1} − V_{m + 2} − V_{m + 3} + …………………− V_n = 0

So accordingly Kirchhoff Second Law, ∑V = 0

Application of Kirchhoff laws to circuits

The current distribution in various branches of a circuit can easily be found out by applying Kirchhoff Current law at different nodes or junction points in the circuit. After that Kirchhoff Voltage law is applied each possible loops in the circuit and generate algebraic equation for every loop. By solving these all equations, one can easily find out different unknown currents, voltages and resistances in the circuits.

Some popular conventions we generally use during applying KVL

1) The resistive drops in a loop due to current flowing in clockwise direction must be taken as positive drops.

2) The resistive drops in a loop due to current flowing in anti-clockwise direction must be taken as negative drops.

3) The battery emf causing current to flow in clockwise direction in a loop is considered as positive.

4) The battery battery emf causing current to flow in anti-clockwise direction is referred as negative.

The smallest unit of loop within which no other closed loop exists is called mesh. All electrical closed network either consists of single closed loop or a numbers of closed loop within them. Thus it can be easily said that every closed electrical network is mesh network. If any electrical network consists of only one single closed loop is referred as single mesh network on the other hand if the network has more than one closed circuital loops, the network is referred as multi mesh network.

What is Mesh

Suppose you have a electric source such as a dry battery cell, an LED and two pieces of conducting wire. If you want to make the LED to glow, the positive terminal of the battery must be connected with one lead of LED by means of one conducting wire and in same way the negative terminal of the battery must be connected to other lead of LED via another conducting wire.

If you disconnect any of the points in that closed network the LED will not glow that means current can only flow through the LED as long as the continuity of the circuit exists. The battery then wire then LED then another wire and then again battery form a closed loop and electric current only flows as long as the loop remain closed. This loop is known as an mesh. The network formed is a single mesh network. Again if two LEDs are connected in same manner across the battery, you can see that there would be two closed loops formed as shown in the figure. Every loop is referred as a mesh and the latter network is referred as multi mesh network
The figure shown below has 6 nodes, five branches, three loops and two meshes.
A node is a junction point in a network where tow or more branches meet.
A branch of network is the section which joints two nodes directly without passing through a third node.
A loop in a network is the closed path formed by any number of possible connected branches.
A mesh is a closed loop which contains no other loop within it.

Multi Mesh

Mesh Analysis

In this technique of circuit analysis, we have to write KVL or Kirchhoff Voltage Law for every possible mesh in a mesh network. In these equations there may some known terms and there may be some unknown terms. By solving these equations we can derive the unknown terms. Mesh analysis is one of the simplest and easiest technique of solving network.
KVL ⇒ ∑V = 0 in every closed loop in a circuit.

That means arithmetic sum of total voltage gains and drops in a closed loop in a circuit is zero.
Let’s consider a network having a voltage source (here it is battery) of 6 V across which two series combinations resistors of R₁ = 4 Ω, R₂ = 2 Ω and R₃ = 1 Ω, R₄ = 5 Ω respectively are connected as shown in the figure – 1. Now we will discuss the mesh technique in step by step manner for the example given in the figure – 1 for better understanding the method.

Step – 1

As we have explained earlier that every complete network is mesh network, so for mesh analysis first we have to identify the possible meshes in that network. There are two meshes i.e. mesh -1 formed by R₁, R₂, V and mesh – 2 formed by V, R₃, R₄.

Step – 2

Now choose two mesh currents one for mesh – 1 and say it is I₁ and other is for mesh – 2 and say it is I₂. The direction of these two current may be taken as arbitrary but it is better convention to choice both current in same direction. Here we have chosen both currents I₁ and I₂ are in clockwise direction.

Step – 3

Next step is to identify the polarities of each elements connected in the mesh. The polarities of voltage drops must be positive at upstream end and negative at downstream end of a resistor. Generally we mark + at terminal where current enters in the resistor. The battery polarities should be as orientations given in the diagram

Step – 4

Now for mesh analysis we will apply KVL and generate voltage equation for each mesh in that mesh network.
Here the mesh equations are

1) − I₁.R₁ − I₁.R₂ − V = 0 ……..(i) for mesh – 1

2) + V − I₂.R₃ − I₂.R₄ = 0 ……..(ii) for mesh – 2
After putting the values of R₁, R₂, R₃, R₄ and V in the equations (i) and (ii) we get,

4.I₁ + 2.I₁ + 6 = 0 ⇒ 6.I₁ + 6 = 0 ⇒ I₁ = − 1 A

6 − I₂ − 5.I₂ = 0 ⇒ 6.I₂ = 6 ⇒ I₂ = 1 A
The value of current I₁ becomes negative which implies that the actual direction of current in the circuit was opposite of our assumption of mesh current for mesh – 1. As the value of current I₂ is positive that means the direction of actual current and assumed mesh current match.

Nature of Electricity and Concept of Electricity

Electricity is most common form of energy. Electricity is used for various applications such as for lighting, transportation, cooking, communication, production of various goods in factories and many more.
None of us know exactly what electricity is. 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 whose molecules are made of similar atoms is known as element. The matter whose molecules consist of dissimilar atoms is called compound. The concept of electricity can be achieved form 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.
The electrons have negative charge of − 1.602 X 10 ^{− 19} Coulomb
and the proton in the nucleus has positive charge of + 1.602 X 10 ^{− 19} Coulomb.
Because of the opposite charge there is some attraction force between nucleus and orbital electrons. Electrons have relatively negligible mass compared to the mass of nucleus. The mass of each proton and neutrons is 1840 times of the mass of an electron. As the modulus value of each electrons and each proton are same, the number of electrons is equal to the number protons in a electrically neutral atom.
An atom becomes positively charged ion when it loses electrons and similarly an atom becomes negative ion when it gains electrons.

Structure of Atom

Atoms may have loosely bonded electrons in its outer most orbit. These electrons require vary small amount of energy to detach themselves from there 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 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 proton 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 conductor, the excess electrons of negative body starts flowing towards the positive body to compensate the lack of electrons in that positive body.

Hopping 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, aluminum, zinc etc. The movement of these free electrons can easily be directed to a particular direction if 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 electric current. Actually electrons flow from lower potential ( − Ve ) to higher potential ( + Ve ) but general conventional direction of current is considered as higher potential point to lower potential point so the conventional direction of current is just opposite of the direction of flow of electrons.
In non – metallic materials, such as glass, mica, slate, porcelain, the outer most orbit is completed and there is almost no chance of loosing electrons from its outer most shell. Hence there is hardly any free electrons present in this type of material. Hence these materials can not 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 conductor while an electrical potential difference applied across it but not to flow through insulator even high potential difference in applied across them.