﻿﻿﻿﻿ October 2017 – APSEEE

## 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.

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.

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

Container

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.

Plates

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

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

Electrolyte

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.

Discharging

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.

Charging

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.

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.

## 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.

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.

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.

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.

## 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.

## 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