Sunday, 19 May 2013

Electrical Power Factor | Calculation & Power Factor Improvement


Electrical Power Factor | Calculation & Power Factor Improvement



In general power is the capacity to do work. In electrical domain, electrical power is the amount of electrical energy that can be transferred to some other form (heat, light etc) per unit time. Mathematically it is the product of voltage drop across the element and current flowing through it.
Considering first the DC circuits, having only DC voltage sources, the inductors and capacitors behave as short circuit and open circuit respectively in steady state. Hence the entire circuit behaves as resistive circuit and the entire electrical power is dissipated in the form of heat. Here the voltage and current are in same phase and the total electrical power is given by
Electrical Power = Voltage across the element* Current through the element.

Its unit is Watt = Joule/sec.
Now coming to AC circuits, here both inductor and capacitor offer certain amount of impedance given by XL = 2*π*f*L and XC = 1/(2*π*f*C). The inductor stores electrical energy in the form of magnetic energy and capacitor stores electrical energy in the form of electrostatic energy. Neither of them dissipates it. Further there is a phase shift of 90-°between voltage and current. Hence when we consider the entire circuit consisting of resistor, inductor and capacitor, there exists some phase difference between the source voltage and current. The cosine of this phase difference is called electrical power factor.
This factor (0 < cosφ < 1 ) represents the fraction of total power that is used to do the useful work.
The other fraction of electrical power is stored in the form of magnetic energy or electrostatic energy in inductor and capacitor respectively.
The total power in this case is

Total Electrical Power = Voltage across the element*Current through the element

This is called Apparent power and its unit is VA (Volt Amp) and denoted by ‘S’
A fraction of this total electrical power which actually does our useful work is called as active power. It is denoted as ‘P’

P = Active power = Total Electrical Power * cosφ

Its unit is watt.
The other fraction of power is called reactive power. This does no useful work, but it is required for the active work to be done. It is denoted by ‘Q’ and mathematically is given by

Q = Reactive power = Total Electrical Power*sinφ

Its unit is Var. (Volt amp reactive)

This reactive power oscillates between source and load every twice in every cycle
To help understand this better all these power are represented in the form of triangle.
power triangle
Power Factor Triangle
Mathematically S2 = P2 + Q2 and Electrical Power Factor is Active power / Apparent power.

Power Factor Improvement

The term power factor comes into picture in AC circuits only. Mathematically it is cosine of the phase difference between source voltage and current. It refers to the fraction of total power (apparent power) which is utilized to do the useful work called active power.

cosφ = Active power / Apparent power.

Need for power factor improvement

• Real power is given by P = V*I* cosφ. To transfer a given amount of power at certain voltage, the electrical current is inversely proportional to cosφ. Hence higher the pf lower will be the current flowing. A small current flow requires less cross sectional area of conductor and thus it saves conductor and money.
• From above relation we saw having poor power factor increases the current flowing in conductor and thus copper loss increases. Further large voltage drop occurs in alternator, electrical transformer and transmission & distribution lines which gives very poor voltage regulation.
• Further the KVA rating of machines is also reduced by having higher power factor as

KVA = KW / cosφ, hence the size and cost of machine also reduced.
Hence electrical power factor should be maintained close to unity.

Methods of power factor improvement

• Capacitors: Improving power factor means reducing the phase difference between voltage and current. Since majority of loads are of inductive nature, they require some amount of reactive power for them to function. This reactive power is provided by the capacitor or bank of capacitors installed parallel to the load. They act as a source of local reactive power and thus less reactive power flows through the line. Basically they reduces the phase difference between the voltage and current.
• Synchronous condenser: They are 3 phase synchronous motor with no load attached to its shaft. The synchronous motor has the characteristics of operating under any power factor leading, lagging or unity depending upon the excitation. For inductive loads, synchronous condenser is connected towards load side and is overexcited. This makes it behave like a capacitor. It draws the lagging current from the supply or supplies the reactive power.
• Phase advancer: This is an ac exciter mainly used to improve pf of induction motor. They are mounted on shaft of the motor and is connected in the rotor circuit of the motor. It improves the power factor by providing the exciting ampere turns to produce required flux at slip frequency. Further if ampere turns are increased, it can be made to operate at leading power factor.

Power factor calculation

In power factor calculation, we measure the source voltage and current drawn using a voltmeter and ammeter respectively. A wattmeter is used to get the active power.

Now we know P = V*I*cosφ watt

From this cosφ = P/ (V*I) or Watt meter reading /(voltmeter reading * ammeter reading). Hence we can get the electrical power factor.

Now we can calculate the reactive power Q= V*I* sinφ VAR

This reactive power can now be supplied from the capacitor installed in parallel with load in local.

Value of capacitor is calculated as per following formula:

Q = V2 /Xc ⇒ C = Q/(2*π*f*V2) farad
IMPORTANT: In power factor improvement, the reactive power requirement by the load does not change. It is just that it is supplied by some device in local. Thus reducing the burden on source to provide the required reactive power.

Heating Effect of Electric Current

Heating Effect of Electric Current



From Newton’s law of motion we know that there is a reaction for every action. Production of current flow or generation of power at power plants both require huge work to be done. But as work is done there will be reaction of that work too. During electricity generation water power ( potential ), thermal power, mechanical power, are converted into electrical power. Since we cannot use electric power directly we need to convert it into another usable power too like heat, light, or mechanical power etc. When current flows through a wire some loss occurs and this loss is almost inevitable, the more the resistance of wire, the more the loss. This loss due to the electrical resistance of wire is mainly responsible for the heating effect of electric current.
As some power is converted into heat energy, this phenomenon can be described by Joules law, which states that H = i2.r.t, where H is the generated heat in calories, i is the current that is flowing through the wire and it is measured in amperes, r is the resistance of the wire in ohm(Ω) an and t is the duration of current flowing in seconds. If we know the time of current flowing, resistance of wire, amount of current flow, we can easily find out the generated heat of the circuit. This heat can be utilized in various ways.

Applications

We saw that the more the electrical resistance of the wire the more the generated heat in the circuit but to know more accurately about the heating effect of current we should know it in the atomic level. As the flow of electric current is nothing but flow of electrons there will always be resistance from the fixed atoms of the wire. The fixed atoms of the wire resist the flow electrons and as a result there are collisions and as the kinetic energy converts into heat energy we see that the wire is getting hot
Now the generated heat can be viewed from many points of angles. Sometimes it is only seen as loss and is tried to be minimized. Various steps are taken to minimize heat dissipation from the conductor. But many positive application of this heating effect we can see in our daily life. Electric iron, the whole idea or working principle depends upon the heating effect of electric current. High resistant wire is used as the main coil in the electric iron when current flows through the coil, the coil gets heated and the iron works. But what about over heating of electric iron ? This problem can be overcome by using bimetallic conductors. Metal plates made of two different metals are used in the circuit. As expansion co-efficient of heat is different for two metals so due to heating effect one metal’s expansion is different from the other metal as a result the plate is bend and after reaching or certain temperature the contact of the circuit is broken and current flow through the coil is stopped and the electric iron too is not heated anymore.

Same mechanism is used in electric heater the only difference is that there is no bimetallic plate or circuit breaker involved.
Another application of heating effect of current is seen in electric bulbs. The wire which is used inside the bulb gets illuminated and emits light after reaching certain temperature. The metal used in bulb mainly made tungsten.
Finally and perhaps the most important application of heating effect of electric current is in electrical fuses, which are used in almost everywhere. From huge industries to domestic level, everywhere electric fuse is must. Fuse is made of such metals which has certain melting point. They are okay for normal current but when over current flows through the circuit the generated heat in the fuse wire is enough to melt the metal portion of the fuse wire and break the circuit. In this way the costly equipment are protected as huge current flow, can damage the equipments permanently.
From Newton’s law of motion we know that there is a reaction for every action. Production of current flow or generation of power at power plants both require huge work to be done. But as work is done there will be reaction of that work too. During electricity generation water power ( potential ), thermal power, mechanical power, are converted into electrical power. Since we cannot use electric power directly we need to convert it into another usable power too like heat, light, or mechanical power etc. When current flows through a wire some loss occurs and this loss is almost inevitable, the more the resistance of wire, the more the loss. This loss due to the electrical resistance of wire is mainly responsible for the heating effect of electric current.
As some power is converted into heat energy, this phenomenon can be described by Joules law, which states that H = i2.r.t, where H is the generated heat in calories, i is the current that is flowing through the wire and it is measured in amperes, r is the resistance of the wire in ohm(Ω) an and t is the duration of current flowing in seconds. If we know the time of current flowing, resistance of wire, amount of current flow, we can easily find out the generated heat of the circuit. This heat can be utilized in various ways.

Applications

We saw that the more the electrical resistance of the wire the more the generated heat in the circuit but to know more accurately about the heating effect of current we should know it in the atomic level. As the flow of electric current is nothing but flow of electrons there will always be resistance from the fixed atoms of the wire. The fixed atoms of the wire resist the flow electrons and as a result there are collisions and as the kinetic energy converts into heat energy we see that the wire is getting hot
Now the generated heat can be viewed from many points of angles. Sometimes it is only seen as loss and is tried to be minimized. Various steps are taken to minimize heat dissipation from the conductor. But many positive application of this heating effect we can see in our daily life. Electric iron, the whole idea or working principle depends upon the heating effect of electric current. High resistant wire is used as the main coil in the electric iron when current flows through the coil, the coil gets heated and the iron works. But what about over heating of electric iron ? This problem can be overcome by using bimetallic conductors. Metal plates made of two different metals are used in the circuit. As expansion co-efficient of heat is different for two metals so due to heating effect one metal’s expansion is different from the other metal as a result the plate is bend and after reaching or certain temperature the contact of the circuit is broken and current flow through the coil is stopped and the electric iron too is not heated anymore.

Same mechanism is used in electric heater the only difference is that there is no bimetallic plate or circuit breaker involved.
Another application of heating effect of current is seen in electric bulbs. The wire which is used inside the bulb gets illuminated and emits light after reaching certain temperature. The metal used in bulb mainly made tungsten.
Finally and perhaps the most important application of heating effect of electric current is in electrical fuses, which are used in almost everywhere. From huge industries to domestic level, everywhere electric fuse is must. Fuse is made of such metals which has certain melting point. They are okay for normal current but when over current flows through the circuit the generated heat in the fuse wire is enough to melt the metal portion of the fuse wire and break the circuit. In this way the costly equipment are protected as huge current flow, can damage the equipments permanently.

Miniature Circuit Breaker or MCB


Miniature Circuit Breaker or MCB



Nowadays we use more commonly Miniature Circuit Breaker or MCB in low voltage electrical network instead of fuse.
The MCB has some advantages compared to fuse.

1. It automatically switches off the electrical circuit during abnormal condition of the network means in over load condition as well as faulty condition. The fuse does not sense but Miniature Circuit Breaker does it in more reliable way. MCB is much more sensitive to over current than fuse.

2. Another advantage is, as the switch operating knob comes at its off position during tripping, the faulty zone of the electrical circuit can easily be identified. But in case of fuse, fuse wire should be checked by opening fuse grip or cutout from fuse base, for confirming the blow of fuse wire.

3. Quick restoration of supply can not be possible in case of fuse as because fuses have to be rewirable or replaced for restoring the supply. But in the case of MCB, quick restoration is possible by just switching on operation.

4. Handling MCB is more electrically safe than fuse.

Because of to many advantages of MCB over fuse units, in modern low voltage electrical network, Miniature Circuit Breaker is mostly used instead of backdated fuse unit.
Only one disadvantage of MCB over fuse is that this system is more costlier than fuse unit system.
mcb

Miniature Circuit Breaker

Miniature Circuit Breaker Working Principle

There are two arrangement of operation of miniature circuit breaker. One due to thermal effect of over current and other due to electromagnetic effect of over current. The thermal operation of miniature circuit breaker is achieved with a bimetallic strip whenever continuous over current flows through MCB, the bimetallic strip is heated and deflects by bending. This deflection of bimetallic strip releases mechanical latch. As this mechanical latch is attached with operating mechanism, it causes to open the miniature circuit breaker contacts. But during short circuit condition, sudden rising of electric current, causes electromechanical displacement of plunger associated with tripping coil or solenoid of MCB. The plunger strikes the trip lever causing immediate release of latch mechanism consequently open the circuit breaker contacts. This was a simple explanation of miniature circuit breaker working principle.

Miniature Circuit Breaker Construction

Miniature circuit breaker construction is very simple, robust and maintenance free. Generally an MCB is not repaired or maintained, it just replaced by new one when required. A miniature circuit breaker has normally three main constructional parts. These are:

Frame of Miniature Circuit Breaker

The Frame of Miniature Circuit Breaker is a molded case. This is a rigid, strong, insulated housing in which the other components are mounted.

Operating Mechanism of Miniature Circuit Breaker

The Operating Mechanism of Miniature Circuit Breaker provides the means of manual opening and closing operation of miniature circuit breaker. It has three-positions “ON,” “OFF,” and “TRIPPED”. The external switching latch can be in the “TRIPPED” position, if the MCB is tripped due to over-current. When manually switch off the MCB, the switching latch will be in “OFF” position. In close condition of MCB, the switch is positioned at “ON”. By observing the positions of the switching latch one can determine the condition of MCB whether it is closed, tripped or manually switched off.

Trip Unit of Miniature Circuit Breaker

The Trip Unit is the main part, responsible for proper working of miniature circuit breaker. Two main types of trip mechanism are provided in MCB. A bimetal provides protection against over load current and an electromagnet provides protection against short-circuit current.

miniature circuit breaker working principle

There are three mechanisms provided in a single miniature circuit breaker to make it switched off. If we carefully observe the picture beside, we will find there are mainly one bi – metallic strip, one trip coil and one hand operated on – off lever. Electric current carrying path of a miniature circuit breaker shown in the picture is like follows. First left hand side power terminal – then bimetallic strip – then current coil or trip coil – then moving contact – then fixed contact and – lastly right had side power terminal. All are arranged in series.

miniature circuit breaker
Miniature Circuit Breaker

If circuit is overloaded for long time, the bi – metallic strip becomes over heated and deformed. This deformation of bi metallic strip causes, displacement of latch point. The moving contact of the MCB is so arranged by means of spring pressure, with this latch point, that a little displacement of latch causes, release of spring and makes the moving contact to move for opening the MCB. The current coil or trip coil is placed such a manner, that during short circuit fault the mmf of that coil causes its plunger to hit the same latch point and make the latch to be displaced. Hence the MCB will open in same manner. Again when operating lever of the miniature circuit breaker is operated by hand, that means when we make the MCB at off position manually, the same latch point is displaced as a result moving contact separated from fixed contact in same manner. So, whatever may be the operating mechanism, that means, may be due to deformation of bi – metallic strip , due to increased mmf of trip coil or may due to manual operation, actually the same latch point is displaced and same deformed spring is released, which ultimately responsible for movement of the moving contact. When the the moving contact separated from fixed contact, there may be a high chance of arc. This arc then goes up through the arc runner and enters into arc splitters and is finally quenched. When we switch on an MCB, we actually reset the displaced operating latch to its previous on position and make the MCB ready for another switch off or trip operation.

Electrical Fuse HRC Fuse High Rupturing Capacity

 

Electrical Fuse HRC Fuse High Rupturing Capacity


 

What is electrical fuse ?

In normal working condition of electrical network, the electric current flows through the network is within the rated limit. If fault occurs in the network mainly phase to phase short circuit fault or phase to ground fault, the network current crosses the rated limits. This high electric current may have very high thermal effect which will cause a permanent damage to the valuable equipments connected in the electrical network. So this high fault current should be interrupted as fast as possible. This is what an electrical fuse does. A fuse is a part of the circuit which consists of conductor which melts easily and breaks the connection when electric current exceeds the predetermined value.
An electrical fuse is a weakest part of an electrical circuit which breaks when more than predetermined current flows through it.

Fuse wire

The function of fuse wire is to carry the normal current without excessive heating but more than normal current when pass through fuse wire, it rapidly heats up and melts.

Materials used for fuse wires

The materials used for fuse wires are mainly tin, lead, zic, silver, antimony, copper, aluminum etc.

Fuse wire rating

The melting point and specific resistance of different metals used for fuse wire

Metal Melting point Specific Resistance
Aluminium 240oF 2.86 μ Ω – cm
Copper 2000oF 1.72 μ Ω – cm
Lead 624oF 21.0 μ Ω – cm
Silver 1830oF 1.64 μ Ω – cm
Tin 463oF 11.3 μ Ω – cm
Zinc 787oF 6.1 μ Ω – cm

Some important terms need for fuse.

1. Fuse it is already defined earlier.

2. Fuse wire, it is also defined earlier

3. Minimum fusing current: It is minimum value of current due to which fuse melts.

4. Current rating of fuse: It is maximum value of current due to which fuse does not get melt.

5. Fusing factor: This is the ratio of minimum fusing current and current rating of fuse.

Therefore, fusing factor = Minimum fusing current / current rating of fuse.

The value of fusing factor is always more than 1.

6. Prospective Current in fuse: Before melting, the fuse element has to carry the short circuit current through it.The prospective current is defined as the value of current which would flow through the fuse immediately after a short circuit occurs in the network.


7. Melting time of fuse or pre arcing time of fuse: This is the time taken by an fuse wire to be broken by melting. It is counted from the instant, the over current starts to flow through fuse, to the instant when fuse wire is just broken by melting.


8. Arcing time of fuse: After breaking of fuse wire there will be an arcing between both melted tips of the wire which will be extinguished at the current zero. The time accounted from the instant of arc initiated to the instant of arc being extinguished is known as arcing time of fuse.


9. Operating time of fuse: When ever over rated current starts to flow through a fuse wire, it takes a time to be melted and disconnected, and just after that the arcing stars between the melted tips of the fuse wire, which is finally extinguished. The operating time of fuse is the time gap between the instant when the over rated current just starts to flow through the fuse and the instant when the arc in fuse finally extinguished. That means operating time of fuse = melting time + arcing time of fuse.

Current Carrying Capacity of fuse wire

Current carrying capacity of a fuse wire depends upon numbers of factors like, what material used for it, what are the dimension of it, i.e. diameter and length, size and shape of terminals used to connect it, and the surrounding.

Fuse Law

Fuse law determines the cuyrrent carrying capacity of a fuse wire. The law can be established in the following way. At steady state condition that is when fuse carry normal current without increasing its temperature to the melting limit. That means at this steady state condition, heat generated due to current through fuse wire is equal to heat dissipated from it.
Heat generated = I2.R

Where R is the resistance of the fuse wire

Where ρ is the resistivity, l is the length and a is the cross sectional area of fuse wire

Where d is the diameter of fuse wire

Where K1 is a constant
Heat lost ∝ surface area of fuse wire ∝ πd.l

Where K2 is a constant
Now, equating (i) & (ii), we get,




This is known as fuse law
Metal value of K when d is measured in mm
Aluminium 59
Copper 80
Iron 24.6
Lead 10.8

Rewirable or Kit kat fuse unit

rewirable or kit kat fuse unit
This is most commonly used fuse in our day to day life. This fuse has mainly two parts. The unit in which the incoming and outgoing line or phase wire connected permanently is known as fuse base. The removable parts which hold a the fuse wire and fits into the base, is known as fuse carrier. The fuse carrier is also known as cutout.

cartridge fuse

In cartridge fuse the fuse wire is enclosed in a transparent glass tube or bulb, the whole unit is sealed off. In case the fuse blows, it is to be replaced by new one as the cartridge fuse can not be rewired due to its sealing.

Lead – tin Alloy Fuse Wire or Eutectic Alloy Fuse Wire

For small value of current interruption lead – tin alloy fuse wire has been used in past. The most preferred lead – tin alloy for fuse wire containing 37% lead and 63% tin. This alloy fuse wire is also known as known as Eutectic Alloy Fuse Wire. This type of alloy has some specific characteristics due to which this is preferred as fuse wire.
1. It has the high brinnel hardness and has less tendency to spread over.

2. The alloy metal is quite homogeneous.

3. If the fusing characteristics of eutectic alloy and other composition of alloys is studied there is only one arrest point
in eutectic alloy as compared to two other types of alloys.

Approximate fusing currents of lead – tin alloy fuse wire in air

Diameter of
wire in inch
Fusing Current
in A
Maximum safe
Current in A
0.02 3 2
0.022 3.5 2.3
0.024 4 2.6
0.028 5 3.3
0.032 6 4.1
0.036 7 4.8
0.048 10 7
0.064 16 11
NB : – The minimum length of the fuse wire used must be 2.5 to 3.5 inches. The values in the above table are true only when the fuse wire does not touches the fuse grip body because when the fuse wire comes in contact with porcelain or other the value of fusing current increases as the heat dissipation rate from the current carrying fuse wire, is increased. Hence precaution should always be taken during rewiring a fuse wire on a fuse grip so that it should not touch the fuse grip body.

HRC Fuse or High Rupturing Capacity Fuse

hrc fuse cartridge fuse
HRC fuse or High Rupturing Capacity Fuse. In that type of fuse, the fuse wire or element can carry short circuit heavy current for a known time period. During this time if the fault is removed, then it does not blow off otherwise it blows off or melts.

The enclosure of HRC fuse is either of glass or some other chemical compound. This enclosure is fully air tight to avoid the effect of atmosphere on the fuse materials. The ceramic enclosure having metal end cap at both heads, to which fusible silver wire is welded. The space within the enclosure, surrounding the fuse wire or fuse element is completely packed with a filling powder. This type of fuse is reliable and has inverse time characteristic, that means if the fault current is high then rupture time is less and if fault current is not so high then rupture time is long.

Operation of HRC fuse

When the over rated current flows through the fuse element of High Rupturing Capacity Fuse the element is melted and vapourized. The filling powder is of such a quantity that the chemical reaction between the silver vapour and the filling powder forms a high resistance substance which very much help in quenching the arc.

Kirchhoff Current Law and Kirchhoff Voltage Law


Kirchhoff Current Law and Kirchhoff Voltage Law


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.
kirchhoff current law
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, …………………. Im are the current of branches 1, 2, 3, ……m and
Im + 1, Im + 2, Im + 3, …………………. In 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,…………….+ Im, − Im + 1, − Im + 2, − Im + 3, ……………… and − In.


Now, the summation of all currents at the junction is
I1 + I2 + I3 + …………….+ Im − Im + 1 − Im + 2 − Im + 3………………− In.


This is equal to zero according to Kirchhoff Current Law.
⇒ I1 + I2 + I3 + …………….+ Im − Im + 1 − Im + 2 − Im + 3………………− In = 0


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

Video presentation of Kirchhoff Current Law – basic theory

Kirchhoff Voltage Law

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,………………. Vm
and voltage drops across the resistors respectively, Vm + 1,
Vm + 2, Vm + 3,………………… Vn.
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,………………. + Vm, − Vm + 1, − Vm + 2, − Vm + 3,…………………− Vn.
Now according to Kirchhoff Voltage law the summation of all these voltages results to zero.
That means, V1 + V2 + V3 + ………………. + Vm − Vm + 1 − Vm + 2 − Vm + 3 + …………………− Vn = 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.

Video presentation of Kirchhoff Voltage Law – basic theory


Nature of Electricity


Nature 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
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.
movement of free electrons
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.