What is VFD?

VFD stands for Variable Frequency Drive. VFD is used to speed control of AC induction motors and protect the motors. A VFD can also control the speed of motor during start and stop cycle, as well as throughout the run cycle. VFD is also known as VVVFD. The meaning of VVVFD is Variable Voltage Variable Frequency Drive. It means with change in frequency voltage can also be changed and vice versa. 

Working of VFD

The working of VFD is very simple. An AC supply given to the VFD which is first converted into DC supply then it is converted into AC supply again at desired frequency and voltage. Changed magnitude of frequency and voltage used to control of speed of AC induction motors. For better understanding, we write a relation between speed and frequency which are given below

N= (120×f)/P

NS = Synchronous speed in r.p.m

f = frequency of power supplied or input power or supply frequency

P = No. of Poles

In above relation we can see, with change of frequency of input power the speed of the induction motor is changed. Simply we can say that the speed of the induction motor is directly proportional to the supply frequency.  
variable frequency drive VFD

Rectifier Converts ac into dc. SCRs are used in rectifier. In three phase rectifier six SCRs are used. Control Unit control the supply frequency and voltage. inverter converts dc into ac.

Advantages of VFD

VFD have many advantages. some of advantages are given below:-

  • VF drive save energy.
  • It improves the power factor of the machines.
  • It gives smooth starting to the induction motors.
  • It reduces the power when not required.
  • We can change the direction of induction motor very easily.
  • It provides controlled starting and stopping. 
  • It provides protection to the induction motors against short circuit, overload, earth fault etc.

Disadvantages of VFD

  • The initial cost of VFD is very high
  • Skilled workers are required to operate it.

Applications of VFD

  • It is used in industrial application such for the control of speed of motors.




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Why transformers and alternators rated in KVA, not in KW?

Usually we have seen that transformers and generators are rated in KVA instead of KW. We Know that KVA is a product of voltage and current and KW is a product of voltage, current and power factor. For better understanding of this topic first you have to know there are three types of loads Resistive, Inductive and Capacitive. At the of designing of transformer and alternator designer don’t know the nature of load whether it is resistive, inductive or capacitive. There is a term power factor cosΦ that multiplied with KVA and make it KW. 

Simply power factor cosΦ is defined as the cosine of the angle between voltage and current. Larger the angle between voltage and current, greater current drawn by the machine which results in losses are increased. 

From the above explanation, we have seen with change in current copper losses are changed. Copper losses are directly proportional to the square of current. Second quantity is voltage, voltage causes iron losses in the machine.

We have concluded it Copper losses ( I²R)depends on Current which passing through transformer winding while Iron Losses or Core Losses depends on Voltage. So the Cu Losses depend on the rating current of the load so the load type will determine the power factor P.F ,Thats why the rating of Transformers and alternators in kVA,Not in kW.

Energy transfer device such as transformer and energy generated device such as alternator are rated in KVA. Motors are rated in KW

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Torque Equation For DC Motor

Torque Equation for DC Motor

Torque is a rotational force that helps for rotating the armature of DC motor. Torque is produced by electromagnetic effect. In simple words we can say that, when a conductor carrying current placed in a magnetic field or flux a mechanical force experienced by the conductors and conductor moves in a particular direction. In this article we will drive torque equation for dc motor.

Torque is measured by the product of force F and radius r.

T = F × r

Let us suppose that the DC machine working as a motor

                                                       P = number of poles

                                                     Φ = Flux per pole in Weber (Wb)

                                                     B = Flux density in Tesla or Wb/m2

                                                      r = radius of armature in meters

                                                      l = length of the conductor in meters

                                                      i = current flowing through the conductor

Now we will calculate force on each conductor

                                                     F = Bil newtons

Torque due to one conductor

T = F ×r Newton-meter (Nm)

In above equation, we have find torque due to one conductor. But if the number conductors are more than one then the above equation is multiplied by Z. Z denotes the total number armature conductors.

Now total armature torque developed is

T = Z Fr Newton-meter (Nm)

If i is the current in each conductor then total armature conductor is Ia and number of parallel paths are A, then

  Conclusion:- From the above torque equation for dc motor, we arrived at a conclusion, which are discussed below:-

The torque developed is directly proportional to the flux per pole. If the flux is increased torque is also increased.

The torque developed is directly proportional to the number of armature conductor.

Torque depends on number of poles.

The torque depends on armature current or current flowing through the armature conductor.

Torque is inversely proportional to the number of parallel path.


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Lead Acid Battery

Lead Acid Battery

There are two types current namely ac and dc. We know that, DC current can be stored. The electrical energy in dc nature store in the form of chemical energy. The device that stores electrical energy in chemical energy is called “electric cell“. Electric cell has small storage capacity. So cells are connected in series or parallel combination to increase storage capacity. After combination of cells are called batteries. There are many batteries are available but in this topic we will discuss about  Construction,  working and applications of lead acid battery.  Lead acid battery is most commonly used battery as a storage device.

Construction of Lead Acid Battery

This battery has different parts. These parts are explained below.


It is the outer body of the lead acid battery. It is made of hard rubber material so it can bear mechanical stress and strain. The material selected for construction of container should be such that which do not react with chemical. It is sealed at top to avoid spilling of the electrolyte. Some space  left at bottom of the battery so that sediments that drops from the plates collected here in order to protect the short circuit between active material.


An antimonial lead alloy covered with active material is used for manufacture of plates of lead acid battery. The positive plate is made from lead peroxide and negative plate is made from spongy lead. To increase the capacity of a battery we use large number of plates. The number of positive and negative plates are sandwiched.


Separators are thin sheets with small holes placed  between the positive and negative plates for preventing internal short circuit.


Dilute sulphuric acid is used as an electrolyte in lead acid battery. The plates are completely immerse in an electrolyte. Electrolyte is the medium through which the current produces by chemical changes.

Vent Caps or Filler Caps

The function of these caps to prevent escape electrolyte but allow the free exit of the gas during charging It can easily removed for adding water and to insert the nozzle of hydrometer for checking specific gravity of electrolyte. These are made of rubber.

Inter-cell connector

Inter-cell Connector are used to connect the cells together.

Working Principle of Lead Acid battery

There are two plates immersed in dilute sulphuric acid. The positive plate is of lead peroxide chocolate brown in color and negative plate is of spongy lead. when the load is connected across two terminals of the cell, the current start flowing due to chemical action between plates and electrolytes.

lead acid battery


When cell discharge it delivers current to the load, the molecules are dissociated into hydrogen ions and sulphate  ions. During discharging action, hydrogen ions moves towards anode and sulphate ions move towards cathode. At discharging time specific gravity of the battery decreases.


For charging, the cell is connected to the dc source. When cell is recharged, the hydrogen ions moves towards cathode and sulphate ions moves toward anode to the lead acid battery.

Applications of Lead Acid Battery

It is used in automobiles for starting and lightning.

Lead Acid batteries are used in substations and generating stations for operation of protective relays.

It is used with inverter circuit as a storage device.

It is used in telephone exchanges.

It is used in railway system for storing electrical energy.



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Superposition Theorem

Superposition Theorem

This theorem is useful for those circuits that contain two or more than two sources. This theorem is applicable only when network or circuit contains with linear elements. The sources of emf connected only in parallel not in series. According to this theorem the current flowing through any section is the algebraic sum of all the currents which should flow in that section when each source of emf acts alone and all other sources are replaced by their internal resistances. In this article we will solve this theorem step by step and applications of superposition theorem.

Explanation of superposition theorem step by step

Consider a circuit which contains two emf source V1 and V2 and resistive elements R1, R2 and R3. You can see in figure 1.

superposition theorem

Step 1

Take only one source V1 and replace the other source V2 by its internal resistance. If internal resistance is not given then it is taken as zero.

Note- If the circuit contains current source, we will delete the source from the circuit. In other words, we can say that the branch that contains current source which acts as a open circuit.

superposition theorem when one source is removed

Arrow shows the direction of flow of current. Now determine the flow flowing through in various section of the circuit. The current is denoted by I1, I2  and I3.

Step 2.

when other source is removed

Now take other emf’s source V2 and replace the source V1 resistance. Determine the current flowing in various section of the circuit. The current is denoted b I1” , I2” and I3”.
To determine the resultant current just odd the currents obtained in steps 1 and step 2. If the current obtained in step 1 and step 2 in same direction just add, on the other hand if the currents flowing through the circuit in opposite direction the it subtract them. In above explanation, currents flowing through resistance R1 and R2 is in opposite direction and in this case currents obtained by step 1 and step 2 are subtracted where as current flowing through resistance R3 is added.

As per superposition theorem

I1 = I1’ – I1

I2 = I2’ – I2

I3 = I3’ + I3

Applications of superposition theorem

This theorem is applied for those circuits or networks that contains two or more than two current or voltage sources.

Limitations of Superposition Theorem

This theorem is applicable only for circuits or networks that contains only linear elements.

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Insulating Materials

Insulating Materials

Insulating materials are the materials that is able to insulate. It prevent the current flows through them. The materials that posses insulating properties is called an insulator. In this article, we will study about classification, Properties, applications of insulating materials.

Classification of insulating Materials

Insulating Materials are divided into three types

  • Solid insulating materials
  • Liquid insulating materials
  • Gaseous insulating materials

Solid Insulating Materials

Solid insulating materials are used to protect the electrical cables and wires.  A layer solid insulating materials deposits on the conductors used in cables or wires. Solid insulating materials are also used to make switch board sheets, switches etc.

Different Types of Solid Insulating Materials

  • Fibrous materials

Examples of Fibrous Materials

wood, paper and card board, insulating textiles etc.

  • Impregnated fibrous materials
  • Non resinous materials

Examples of Non resinous materials

asphalts, bitumens, waxes etc.

  • Ceramics

Examples of Ceramics

porcelain, steatite, titanate, etc.

  • Natural and synthetic rubbers

Examples of Natural and synthetic rubbers

natural rubber, hard rubber, butyl rubber, neoprene, hypalon, silicon rubber etc.

  • Mica

Liquid Insulating Materials

Liquid insulating materials are used in circuit breakers and capacitors. Oil is the example of liquid insulating materials.

Different types of liquid insulating materials

  • Oils
  • Varnishes

Gaseous Insulating Materials

Some gases are also good insulators. These gases are used in circuits breakers and many other devices.

Examples of Gaseous Insulating Materials

Carbon dioxide (CO2), Dry air, nitrogen, etc.

Properties of Insulating Materials

An good insulating materials should have following properties:-

  • Insulating materials should have high resistivity in the order of mega ohm so that, no current flows through it.
  • Insulating materials should have low thermal conductivity.
  • Insulating materials should be chemically inert.
  • Insulating materials should have high dielectric strength at the specified temperature
  • Insulating materials should be such that it does not affected by moisture.

Applications of Insulating Materials

  • Insulator are used transmission line towers.
  • Insulating materials coating is used over the cables and wires.
  • Insulating materials used in all hand held electrical tools to prevent their user from electrical shock hazard.



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Introduction to Electrical Machines

Electrical Machines 

Electrical Machines are the machines that required electrical energy for their operation. These machines may be ac or dc (means what kind of supply requires for their operation). The ac machines are two types static and rotating machines. On the other hand dc machines are only rotating one. In this article we will study about the different kind of machines.

AC Machines

First of all we will talk about the AC Machines. AC Machines are two types static and rotating.

Transformers falls into the category of static machine it is used in generating station for raising the voltage level, used in substation for lowering the voltage to a suitable level. it plays an  important role in electrical engineering.

Three Phase Induction Machines are rotating machines, the application of these machines found in industries. these machines are cheap in cost and robust in construction. These motors are singly excited motors. Induction motor are two types squirrel cage induction motor and slip ring or wound rotor induction motor.

Synchronous Machines  are divided into two types synchronous motors and synchronous generators or alternators. Synchronous  motors are used to improve the power factor and synchronous generators are installed at power generating station  to generate electrical energy. Synchronous machines are divided into two types salient pole and non-salient pole type.

Single Phase Induction Machines are used for domestic purposes. In mixer grinder, fans etc. single phase induction motors are used.

DC Machines

These machine are doubly excited machines. DC machines are divided into two types DC Motor and DC Generator.

DC Motors are of three types:-

DC Shunt Motors are used where constant speed is required for all load. The characteristics of these motors are similar to three phase induction motors.

DC Series motors are used in traction system. These motors have starting torque. These motors have poor speed regulation. DC series motors can not run at no-load and with belted load.

DC Compound Motors


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Graph Theory

Graph Theory

When all the elements in a circuit or network are replaced by lines with dots, such configuration is called graph of the network. The all elements such as capacitor, inductor or resistor must satisfy Kirchhoff’s laws. Based on these laws, we can form a number of equations in graph theory.

Terminology Used in Graph Theory

1.     Node

A node is a point where branch is connected.


In following example we will find number of nodes.

Example 1.

graph theory node

In above diagrams, there are three nodes

Example 2

graph theory example of node

In above diagram, there are two number of nodes.

2.   Branch  

A branch is a line segment connected between two pair of nodes.

Number of branches in a network = n – 1


graph theory example of branch

In above figure, there are four numbers of branches.

3.     Tree

A tree is a connected sub-graph of a network which includes all the nodes but no closed path. The graph of a network may have a number of trees.

4.     Co-Tree

The certain branches are removed to form tree, this removed branches are called links. The set of all links of a given tree is called the co-tree of the graph.

5.     Twigs

The branches of the tree are called, its twigs. The number of twigs on a tree is always one less than the number of nodes.

Twigs = nodes – 1

6.     Planar and Non-Planar Graphs

Planar graph are drawn on a plane surface where no two branches cross each other. Whereas, non-planar graph are those graph that can not be drawn on a plane surface without a crossover.

What is incidence matrix?

Incidence matrix shows which branch is incident to which node.

graph theory example of incident matrix

Arrows indicated in the branches of a graph result in an oriented or a directed graph. These arrows shows the flow of current or voltage rise in the network.

graph theory example of incident matrix with matrix

Properties of incidence matrix [Ai]

i)                   Algebraic sum of the column entries of an incidence matrix is zero.

ii)                 Determinant of the incidence matrix of a closed loop is zero.

iii)               The rank of a complete incidence matrix of a graph is n-1.


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Power Transformer and Distribution Transformer

Power Transformer and Distribution Transformer

Transformer plays an important role in the area of electrical engineering. Transformer is used either for raising or lowering the voltage of ac supply. It is used at electrical energy generating station where basically it raise the voltage level of an ac supply and it is also used at substations where it is used to lowering the voltage at suitable level. In power engineering it occupies a very important place.In this article, we will study about power transformer and distribution transformer. The power transformer are located at power generating stations whereas the distribution transformers are installed in the localities of the city.


The power transformers are installed at the sending and receiving end of the high voltage transmission lines whereas the distribution transformers are installed at the near to the load centre to provide utilization at the consumers premises. Distribution transformers are basically pole mounted.


Power transformers are usually operated at full load or nearly full load in simple words we can say that the power transformer gives high efficiency at full load or nearly full load. On the other hand distribution transformers are operates at light load during major part of the day.


The rating of a power transformer is very high in the orders of MVA and power transformer generally rated above 100MVA. The rating of distribution transformer is smaller and distribution transformer are generally less than 100MVA.


The insulation required in case power transformer is more in comparison to the distribution transformer because the power transformer generally operates at very high voltage in order of 400KVA, 220KVA, 132KVA etc.


The power transformer is basically larger in size as comparatively distribution transformer.

Copper Losses and Iron Losses

The power transformers are operated at nearly full load so iron losses are less so the power transformer are designed to have low copper losses. However, the load on the distribution transformer vary time to time so these transformer designed to have low iron losses.


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Transformer on No-Load

Transformer on No-Load

Transformer on No-Load transformer, there is no iron losses and copper losses. The ideal transformer is not practically possible. In case actual transformer these losses are present. When an actual transformer put on load, there is iron loss in the core and copper loss in the windings. When secondary of the transformer is kept open and primary winding is connected to alternating source, the transformer is called transformer on no-load.

When primary is connected to source and transformer is on no load, the transformer draws some current which is not wholly reactive. The primary input current under no load conditions has to supply iron losses in the core and copper losses in the windings (both primary and secondary).


When transformer is connected to source. It draws no load current IO at voltage VI. The current lags the voltage by angle φO which is less than 900. No load current IO has two components. One component is called Active or Working Component and second component is called Reactive or Magnetizing Component.

transformer on no-load

Active or Working component IW is in phase with input voltage V1. Active component supplies the iron loss and small quantity of copper loss. This component is also known as wattfull component or iron loss component.

phasor diagram of transformer on no load

IW = IO Cos φO

Reactive or Magnetizing component is in quadrature with VI. The Function of reactive component is to sustain the alternating flux in the core. This component is also known as wattless component because it does not consume energy.

      Im = IO Sin φO           


  1. The no-load primary current IO is very small in value as compared to the full load primary current. It value may be 2 or 3% of the full load primary current.
  2. The value of input primary current IO is very small. Hence, copper loss is negligibly small. It means input power is equal to the iron loss in the transformer.

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