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Monday, 28 November 2011 13:54

TYPES OF MATRICES

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Column Matrix

typesofmatrices1

A matrix is said to be a column matrix if it has only one column.  In general, a = [aij] m x 1 is a column matrix of order m x 1
                      
For example:     typesofmatrices2
                               
Order of A is 3 x 1 and that of B is 4 x 1

Row Matrix

A matrix is said to be a row matrix if it has only one row.  In general,           B = [bij] 1 x n is a row matrix of order 1 x n

For example: A = [2  0  5  -3]        B = [1/2  0   √3     6    7]
Here order of A is 1 x 4 and that of B is 1 x 5

Square Matrix

A matrix whose numbers of columns are equal to number of rows is said to be a square matrix.  Thus an m x n matrix is said to be a square matrix if m = n and is known as a square matrix of order ‘n’.
                                
For example:   typesofmatrices3 
                                                                  
Hence A is of order 3 and B is of order 2.

Diagonal Matrix

A square matrix B = [bij]mxm is said to be a diagonal matrix if all its non diagonal elements are zero.
                                                         
For example: typesofmatrices4
                                     

Hence the orders of A, B and C are 1,2 and 3 respectively

Scalar Matrix

A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal.
That is bij = 0, when i ≠ j
           bij = k, when i = j, for some constant k
                                                                  
For example: typesofmatrices5
Hence the order of A, B and C are 1, 2 and 3 respectively.

Identity Matrix

A square matrix in which elements in the diagonal are all 1 and rest all are zero is called and identity matrix.  In other words, the square matrix A =

typesofmatrices6

Zero Matrix


A matrix is said to be a zero matrix if all its entries are zero.  Another name for zero matrix is null matrix.  It is denoted by 0.
                                       
For example:    typesofmatrices7
The orders of the above matrices are 1 x 1, 2 x 2 and 2 x 3 respectively.

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Tuesday, 30 August 2011 09:50

Electric motor

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Introduction to electric motors

An electric motor is all about magnets and magnetism.  An electric motor uses magnets to create motion. You know the law of magnets: opposite poles attract and like poles repel.  So if you have two bar magnets with their ends marked "north" and "south," then the north end of one magnet will attract the south end of the other. On the other hand, the north end of one magnet will repel the north end of the other.  Inside an electric motor, these attracting and repelling forces create rotational motion.

elect_motor_1


What is an electric motor?

An electric motor is an electromechanical device that converts electrical energy to mechanical energy. This mechanical energy is used, for example, to rotate a pump impeller, fan or blower, drive a compressor, lift materials etc. Electric motors are sometimes called the “work horses” of industry; it is estimated that motors use about 70% of the total electrical load in industry.



Components of electric motors

If you take apart a small electric motor, you will find that it contains the following: two small permanent magnets inside casing, two brushes held in housing, and an electromagnet that is made by winding wire around pieces of shaped metal (laminations) on a steel shaft, known as an armature or rotor. The rotor will almost always have three poles or more, and there are two good reasons this:
1.    Having three or more poles causes the motor to have better dynamics (movement). In a two-pole motor, if the electromagnet is at the balance point, which is perfectly horizontal between the two poles of the field magnet when the motor starts, you can imagine the armature getting "stuck" there. That never happens in a three-pole motor, which can start turning from any starting position.
2.    Each time the commutator hits the point where it flips the field in a two-pole motor, the commutator temporarily shorts out the battery (i.e., it directly connects the positive and negative terminals). This shorting wastes energy and needlessly drains the battery. A three-pole motor solves this problem.  In fact, an efficient motor’s timing switches on the armature when the magnetic repulsion is strongest.
An electric motor can have any number of poles, depending on the size of the motor and its specific application. Motors come in different shapes and sizes to fit almost anywhere.



Types of Electric Motors


 elect_motor_2

 

How does an electric motor work?elect_motor_3

The general working mechanism is the same for all electric motors (see first figure above):
a)    An electric current in a magnetic field will experience a force.
b)    If the wire that carries current is bent into a loop, then the two sides of the loop, which are at right angle to the magnetic field, will be forced in opposite directions.
c)    The pair of forces creates a turning torque to rotate the coil.
d)    Practical motors have several loops on an armature to provide a more uniform torque. The magnetic field is produced by electromagnet arrangement called the field coils.





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Monday, 29 August 2011 08:52

AC and DC current

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Introduction to AC and DC Current

ac1AC means “Alternating Current” and DC means “Direct Current.” AC and DC are also used when referring to voltages and electrical signals, which are not currents. DC is electricity flowing in a constant direction, and/or possessing a voltage with constant polarity.

DC is the kind of electricity that a battery with definite positive and negative terminals makes, or the kind of charge that is generated by rubbing certain types of materials against each other. Certain sources of electricity (most notably, rotary electro-mechanical generators) naturally produce voltages that alternate in polarity, reversing positive and negative over time. Either as a voltage switching polarity or as a current switching direction back and forth, this "kind" of electricity is known as Alternating Current (AC).

What is Alternating Current (AC)


ac2Alternating Current (AC) flows one way, then the other way, continually reversing direction. An AC voltage is continually changing between positive (+) and negative (-). The rate of changing direction is called the frequency of the AC and it is measured in hertz (Hz), which is the number of forwards-backwards cycles per second. An AC supply is suitable for powering some devices such as lamps and heaters but almost all electronic circuits require a steady DC supply.

 
This shape portraying AC from a power supply is called a sine wave. Alternating current is the most common form used in the transmission of electricity from power plants to homes and businesses. It is convenient because the voltage can be changed easily with transformers. High voltage is good for long-distance transmission of electricity because it means less current has to flow to achieve the same amount of power, and power is lost in the resistance of wires in proportion to the square of the current. Alternating current is generated at the power station by rotating a coil of wire inside a big magnet. The energy needed to make the coil turn is provided by burning fuels such as coal, oil, natural gas, or by harnessing air, water, or nuclear power to do it. Faraday's law of induction relates the change in the voltage around the coil of wire to the rate of change of the amount of magnetic flux through the wire. If the wire turns around in circles, the voltage will be positive, then negative, then postitive again. Because the voltage swings back and forth between positive and negative values, at some times it crosses zero.

What is Direct Current (DC)


Direct Current (DC) always flows in the same direction, but it may increase and decrease. DC voltage is always positive (or always negative), but may increase and decrease. Electronic circuits normally require a steady DC supply which is constant at one value or a smooth DC supply which has a small variation called ripple.
Cells, batteries, and regulated power supplies provide steady DC which is ideal for electronic circuits.

Power supplies contain a transformer which converts the mains AC supply to a safe low voltage AC. The AC is then converted to DC by a bridge rectifier. However, the output is varying DC which is unsuitable for electronic circuits.

Direct current is very useful in powering small things such as flashlights and radios and toys. Batteries are the most common source of direct current -- the voltage of a battery is constant. Things that need lots of power in the form of direct current, like computers, have power supplies inside which transform alternating current from the wall plug to direct current. This way, they don’t run out of batteries.
 

Steady DC

from a battery or regulated power supply, this is ideal for electronic circuits.
ac3 

Smooth DC

from a smoothed power supply, this is suitable for some electronics

ac4

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Wednesday, 29 June 2011 06:38

A Seral Community

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The ecosystem moves towards the climax community. A seral community is an intermediate stage in an ecosystem.  Before attaining the climax community sometimes more than one seral stage can also evolve.


Depending on the substratum and climate, a seral community can be classified into water community, rock community, sand community, dry area community & saline body ommunity. This can be termed biologically as Hydrosere, Lithosere, Psammosere, Xerosere, and Halosere respectively.

 

 

Hydrosere

It is a plant succession occurs in a freshwater lake. If the water dried up it becomes the woodland. Because of this change the land types will succeed each other.


 seral-2

           Mute Swan  - Hydrosere Community


The Loch a' Mhuilin lake is located in the Isle of Arran, Scotland. The lake exhibits characteristic features of a hydrosere, the succession from a fresh water surface with small pioneer plant species to a sub-climax vegetation of alder and willow.  Because of clearing grazing land by human activities and by red deer and rabbits, the climax vegetation of oak and Thomas beech woodland has not been achieved.


seral-3
Loch a' Mhuilin Lake

 

 

Lithosphere

It is a plant succession that begins life on a newly exposed rock surface.  Once the Laki and Katla fissures erupted, the lava fields of Eldgjá in Iceland began to form a lithosere.

 

 

Psammosere

An ecological succession began life on newly exposed coastal sand. Example: sand dune systems

 

 

Xerosere

It is limited by water availability with xerarch succession of ecological communities originated in extremely dry situation. Example:  sand deserts, sand dunes etc.

 

 

Halosere

The succession occurs in a saline environment. Example: salt marsh

 

Note: A xerosere may include lithoseres and psammoseres

 

 

Climax Community

It is a biological community of plants and animals through the process of ecological succession

 

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Wednesday, 11 May 2011 09:30

What are Genes?

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Gene – The Hereditory Material

bio_gen_a1_3Gene is a nucleic acid segment which contains the genetic information necessary to produce a protein. Genes have a long strand of DNA with a promoter. This promoter controls the gene activity and a coding sequence.







bio_gen_a1The gene coding determines what the gene produces. The informations present in the genes pass on to next generation. The organelle mitochondria self-replicate and they are not coded for by the organism's DNA.

 
Genes and its Bases
The genes are having 4 nucleotide bases  and hence named as polynucletides. Each nucleotide made up of a base group, a sugar and one ore phosphate groups.

 

  1. Adenine(A)
  2. Thymine (T)
  3. Guanine (G)
  4. Cytosine (C).


    bio_gen_a1

    •    The bases Adenine(A) and Guanine(G) are Purines

    •    Thymine (T) and Cytosine (C) are Pyrimidines.

 

 

Base Pairs
The sugar group is the backbone of DNA. The phosphate group links one nucleotide to another. The nitrogenous bases holds each other with the help of complimentary bases. Adenine is complimentary to Thymine while Guanine is complimentary to Cytosine. A forms 2 hydrogen bonds with T while G forms 3 hydrogen bonds with C.

 

bio_gen_a1_1


So the  G≡C bond is more stable than an A=T bond.

Definition of Gene
The gene is a "A locatable region of genomic sequence, corresponding to a unit of inheritance, which is associated with regulatory regions, transcribed regions, and or other functional sequence regions"
Gene may refer to an allele:
•    A gene is the basic instruction, a sequence of nucleic acid
•    An allele is one variant of that gene.
The genetic changes can be observed in the single letter of the genetic code and this change is termed as ‘ a single nucleotide polymorphism’.

 

The expression of genes
The gene expressions encoded in DNA. It begins by the transcription process into RNA. RNA contains the nitrogenous base – uracil in place of thymine of DNA. RNA molecules are  single stranded and thus they are less stable than DNA.

 

bio_gen_a1_2Genetic Code
Genes that encode proteins are composed of codons. The codons are the series of three-nucleotide sequences. For example AUG,  AGG etc.This is the gene lanugauge and it is alomost same for all organisms.

 
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Friday, 09 January 2009 12:00

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