Learn definition of sec

Introduction :
Learn definition of Sec is defined as the function which is used to calculate the ratio of sides of the triangle. It is also known as inverse of cos function. Sec is a one kind of trigonometric functions. Sec of an angle is the ratio of hypotenuse and the length of the adjacent side. In other words, the learn definition of Sec is the reciprocal of cos.

In a right angle triangle,

                  Sec(A)=hypotenuse       
                              adjacent side        
               Here A is a angle, Sec (A) = 1/ (cos A)        

Learn definition of sec:

Learn properties of sec angle:
Learn definition of sect is intervallic and repeats itself every 2 radians. An essential property is sec(0)=1. Few other main properties are

By the definition of sec,
           sec x               = 1/cos x
           sec( x + 2 )   = sec (x) sec ( /2)    = ∞ (infinity)
           sec(-x)            = sec(x)
           sec(x)             = i sec h(ix)

Learn important calculus relations of sec:
             d/dx sec(x) = sec(x) tan(x)    (differentiation)
            ∫ sec(x) dx   = ln sec(x) + tan(x) = ln ( /4 + /2)  (integral)

Learn series expansion of the function of sec:
           sec(x)  = 1 + x²/2 + 5x⁴/24 + 61z⁶/ 720 + ..... + (-1)ⁿ E_2n/(2n)! X_2n + ......
Here the E's are the Euler numbers of secant.

Learn domain of sec:
          Every numbers are real except /2 + k , k is an integer.

Learn range of sec:
           (-∞ , -1] U [1 , +∞)

Learn Period of sec:
                 2 π

Learn y intercepts of sec:
           y = 1

Learn of sec symmetry:
           sec(-x) = sec (x).   Because sec (x) is an even function and graph is symmetric.

Learn of sec intervals of increase/decrease:
From 0 to 2, sec (x) is increasing on (0 to /2) U ( /2  to  ) and decreasing on ( to 3 /2) U (3 /2 to 2 ).

Learn vertical asymptotes of sec:
           Vertical asymptote = /2 + k π , where k is an integer.

Learn co function for sec : 
           sec x  = cosec (90^o - x).

Practice problem for learn definition of sec:

Practice problems using learn of secant function:
1. Find the function value of sec 45^o.

Solution:
         Use the Sec's co task identity to solve the problem.
By the definition of sec,
        function for sec is  sec x   = cosec (90^o - x)
                                         sec 30^o= cosec (90^o – 30^o )
                                                      = cosec (60^o)
                                          sec 30^o = 0.866
         The solution of sec of 30^o is 0.866.

2. Find the angle of a right triangle where hypotenuse = 2, length of the adjacent side = 1 using secant function?

  Given:
         In a right angle triangle length of the hypotenuse = 2, length of the adjacent side = 1

  Solution:         
By the definition of sec,
           Sec x  =  hypotenuse/adjacent side
                      = 2 / 1
                   x = sec^-1 (2)
                   x = 60^o 
The secant angle of triangle is 60 degrees.

Electricity sources

Introduction :

Electricity is the main branch of physics, which deals with the motion of the charges. The device which produce electricity or which can convert one form of energy into another form is called the sources of electricity.The sources of elecricity can be had from nuclear plant,  fossil fuels like coal, natural gas etc. Even the solar radiation can be used to obtain electricity.Here we discuss the sources of electricity.

About Electricity sources

Electricity is the very important form of energy, which we use, in our daily life. Now these days we even do not imagine the life in the absence of electricity. The sources of electricity are cells, which are very common and very convenient in use. There are two types of the cells one are called the primary cells and t0he other are called the secondary cells. The primary cells are those, which cannot be recharged, and the secondary cells are recharged several times up to some limit. Voltaic cell is the most important type of the source of electricity.

It is the simplest form of the electrochemical cell. It consists of a glass vessel containing dil. sulphuric acid. Copper and the zinc rod are dipped in the dil. Sulphuric acid. These copper and zinc rods are called the electrodes. When the bulb of a torch is connected across the electrodes through a conducting wire, it glows that means the electricity is produced due to some chemical reaction. When sulphuric acid dissolved in water, it decomposes into ions as shown in the reaction given below

H2SO4       `->`         2H+ + SO4 2-

Zinc atoms from zinc plate begin to dissolve slowly in H2SO4 in form of Zn2+. Each zinc atom dissolved in H2SO4 from the Zn plates leaves two electrons on the Zn plate. This zinc plate becomes negatively charged.

Zn (in solution)        `->`        Zn 2+   + 2e- (on Zn plate)

The potential acquired by the Zn plate is – 0.62 Volt. When Zn ions enter the solution from the Zn plate, an equal number of H+ leaves the solution and deposit on the copper plate. The hydrogen ions get electrons from the copper plate to become neutral hydrogen atoms.

H+ + e -    `->`            H

A pair of hydrogen atom combines to form the hydrogen molecule and the bubbles of the hydrogen gas are formed. Copper plate becomes positively charged and the potential is 0.46 Volt. So the potential difference of the voltaic cell is 0.46 – (-0.62) = 1.08 Volts.

Conclusion of the electricity sources

Thus, we observed that the same potential difference is developed across the plates of the cell. That means there are some free charges, which are in motion. As we connect a resistance in the path of the free charges, it will move and the electricity is produced so that the current flows through the bulb and it will glow.

How does electricity works

Introduction:

The basic electrical circuits consists of the following ;

The Source which generates power such as a generator,

the load which utilizes the power,

and two wires to carry the electrons act as conductor from the power source and back to power source.This is how the electricity will works.

                                        how does electricity works

Measure of electricity or power is Watts and Kilowatts.

Watts = (Volts X Amps).

Electron: In order to understand electrons, we need to have a understanding of the atom. Atom consists of  a nucleus(having protons and neutrons)  and electrons revolving around it in circular orbits.

How does electricity works

Current: Movement of charge carriers (electrons) from one place to another place is called as current.

One amp is defined as one coulomb of charge carriers passed through a cross section of conductor per unit time.That is  6.28 x 10^18 electrons per second.

Voltage: It is the electrical force that gives the energy to free electrons to move from one atom to another. Just as water needs some pressure to force it through a pipe, electrical current needs some force to make electron flow. "Volts" is the unit of measurement of "electrical pressure" that causes current flow. Voltage is also called as potential difference between two points along a conductor.

Load: Load is the one which consumes the generated energy

 The power source generates the voltage which force the electrons to flow through the conductors when load is connected and it is a closed loop. The load utilizes the power to convert electrical energy to some other form.

Importance of electricity:

Electricity is  life blood that flows in our society. Our survival based on electricity. Electricity generates in several forms. Electricity most basic generated form is lightning. Portable devices like torches,mobiles use batteries which is a form of static electricity.Sun is also one of the major source of electricity if we convert the radiated light energy to electricity with the help of photocells.

The very fundamentals of electricity starts with electrons. Electron flow depends upon the type of material . Some materials do not allow electrons to move through it freely from one atom to another, those type of materials called as Insulators. Some materials allow free flow of electrons those are good conductors of electricity called as conductors. The movement of electrons referred as current.

Electrons can freely move in conductors then why we need voltage ?

 Conductors having the movement of electrons in a random direction in order to make the the electrons to flow in a particular direction we need to impart energy for the electrons that energy is called as Voltage. We can compare this two terms with a dam having potential head as voltage and the stream of water flow can be compared with electron flow. The more the potential head in the dam the larger will be the flow of water.

A battery works in the similar way it is having two terminals, a positive terminal and a negative terminal. The source, whether may be generator or battery, will push the electrons to the negative terminus. The rate at which it pushes the electrons is the voltage. The equipment, electronics appliances you that will consume electricity  is called the load. The electrons will leave the negative side of the power source, energize the equipment, and flow to the positive side of the power source.

Resistance: It is the force that resists the flow of electrons.. The units of resistance Ohms..

OHM’S LAW:Ohm’s law  state that voltage  (V) in a circuit is directly proportional to the , current or amps are (I) .

 V=IR.

In  a light bulb. The thin wire inside  the bulb is called filament. When power is applied to the bulb, the tungsten filament resists the flow of electrons. We can calculate that resistance by Making Resistance as subject of formula, r=V/I. So a 60 Watt light bulb’s resistance would be 240 Ohms.

There are basically two types of electrical currents,
    Direct current (DC)

   Alternating current (AC).

Direct current :Here the magnitude of the current is constant through out the wave form .Example battery  produces the DC current that flows in one direction only that is moving directly from the negative terminal to the positive terminal of the battery.

Alternating current: The magnitude of the current continuously varies with time.Example of AC power sources Generator.The magnitude is varying with time so frequency comes into picture. Frequency can be defined as the number of cycles produced in a given unit of time.This is called Hertz (Hz) or Cycle.

How does electricity works

Advantages:

The advantage of alternating current is that from  power  generating stations send millions of volts from their power plants through small conductors to transformers that will step down to required voltages in the distribution end.

Fcc unit cell

Introduction to unit cell
A regular three dimensional arrangement of points in space is called a crystal lattice. A unit cell is the smallest of a crystal lattice which, when repeated in different directions generates the entire lattice

Face centered cubic unit cell

A face centered cubic unit cell contains atoms at all the corners and at the centre of all the faces of the cube. Each atom located at the face centre is shared between two adjacent unit cells and only half of each atom belongs to a unit cell. Thus, in a face centered cubic unit cell:

1. 8 corners atoms × 1/8 atoms per unit cell=1 atom
2. 6 face centered atoms × 1/2 atoms per cell=3 atoms

Therefore, total no. of atoms per unit cell = 4 atoms

Packing efficiency of fcc unit cell

Packing efficiency is the percentage of total space filled by the particles. Let us calculate the packing efficiency of fcc unit cell. Let the unit cell edge be ‘a’  and face diagonal be ‘b’.
We know that b=√2a
If r is the radius of the sphere, we find
    b = 4r =√2a or a = 2√2r
we know that each unit cell in fcc structure, has effectively 4 spheres. Total volume of four spheres is equal to 4×(4/3)πr³ and the volume of the cube is a³ or (2√2r)³.
Therefore,
Packing efficiency of fcc unit cell
=volume of 4 spheres ×100/volume of unit cell  %
=4×(4/3)πr³×100/(2√2r)³
=74%

Density of unit cell

Volume of unit cell = a³
Mass of the unit cell =number of atoms in unit cell×mass of each atom
=z × m
Where z is the number of atoms in unit cell and m is the mass of single atom.
Mass of an atom present in a unit cell:
    m = M/N_a   (M is molar mass)
therefore, density of the unit cell =mass/volume
         =z×m/a³ = z×M/a³×N_a
     d   =    zM/a³N_a

Summay

The number of atoms in a fcc unit cell is four and these are present at all corners as well as at the centre of all faces of the cube

Make a fuel cell

Introduction :
A Fuel Cell is a device that converts the energy of the chemical reaction between a fuel and an oxidant into electricity and heat.  It is easy to make a fuel cell working, by using an anode, cathode, catalysts and most often an electrolyte.  Fuels and oxidants are also necessary to make a fuel cell.  Fuel cells are combined into groups to obtain a usable voltage and power output, called stacks. Fuel cells generate electricity electrochemically, rather than mechanically, so they are more efficient over a wider load factor and can cut greenhouse gases by over 50 percent.  Fuel cells are very much different from batteries. Fuel cells consume reactant from an external source, which must be replenished.  Fuel cells produce electricity with an efficiency of about 70 % compared to thermal plants whose efficiency is about 40%.

How to make a fuel cell

We can make a fuel cell (Hydrogen Fuel Cell) in our kitchen in just 10 minutes, and demonstrate how hydrogen and oxygen combines to give clean electricity.
To make a fuel cell, we would need:

• One foot of platinum coated nickel wire along with small piece of wood or Popsicle stick.  
• A 9 volt battery clip and a 9 Volt battery.
• A little transparent sticky tape.
• One glass full of water.
• Volt meter device.

Hydrogen-oxygen Fuel cell

One of the most successful fuel cells uses the reaction of hydrogen as fuel and oxygen as oxidant to form water (Hydrogen oxygen fuel cell).  The cell was used for providing electrical power in the Apollo space programme.  The water vapors produced during the reaction were condensed and added to the drinking water supply for the astronauts.  In the cell, hydrogen and oxygen are bubbled through porous carbon electrodes into concentrated aqueous solutions of sodium hydroxide.  Catalysts like finely divided platinum or palladium metal are incorporated into the electrodes for increasing the rate of electrode reactions.

Catalysis plays a very important role in Hydrogen oxygen fuel cells, separating the electrons and protons of the reactant fuel (at the anode), and forcing the electrons to travel though a circuit, generating electrical power.  At the cathode, another catalytic process takes the electrons back, combining them with the protons, which have traveled across the electrolyte and the oxidant to form waste products like carbon dioxide and water.
The electrode reactions of Hydrogen oxygen fuel cell are given below:
Cathode reaction:     O₂ (g) + 2H₂O (l) + 4e⁺    4OH^–(aq)
Anode reactions:       2H₂ (g) + 4OH^–(aq)  4H₂O (l) + 4e^–
Overall reactions:     2H₂ (g) + O₂ (g)   2 H₂O (l)
The cell can run continuously as long as the reactants are supplied.

Alcohol fuel cell

Introduction

A fuel cell is an electrochemical device which converts the chemical energy of compounds into electrical energy via electrochemical reactions. Unlike a conventional battery, a fuel cell is not an energy-storing apparatus but reactants are continuously replenished into the cell separately during the operation. A Hydrogen rich compound or pure hydrogen is used as a fuel, while oxygen from the air or pure oxygen commonly serves as oxidant. The benefits obtained using a fuel cell for energy production are high efficiency and low emissions of harmfull effluents.

Alcohol fuel cell

In an alcohol fuel cell, as the name indicates alcohol is used as a fuel to produce electricity.  The cell in which Methanol is directly used as fuel is named as Direct Methanol Fuel cell. The technology behind Direct Methanol Fuel Cells (DMFC), a particular example for alcohol fuel cell.  It is still in the early stages of development, but it has been successfully demonstrated powering mobile phones and laptop computers—potential target end uses in future years.

In the early 1990s, DMFCs were not appreciated because of their low efficiency and power density, as well as other problems. Improvements in catalysts and other recent developments have increased power density to 20-fold and it is expected that the efficiency may eventually reach 40%.

DMFC is very similar to the PEMFC in that the electrolyte is a polymer and the charge carrier is the hydrogen ion (proton). However, in a DMFC, the liquid methanol (CH₃OH) is oxidized in the presence of water at the anode generating CO₂, hydrogen ions and the electrons that travel through the external circuit as the electric output of the fuel cell. The hydrogen ions travel through the electrolyte and react with oxygen from the air or pure oxygen, used as oxidant and the electrons from the external circuit to form water at the anode completing the circuit.

Cell reactions

Reaction at the Anode:      CH₃OH + H₂O => CO₂ + 6H+ + 6e^-
Reaction at the Cathode:   3/2 O₂ + 6 H⁺ + 6e^- => 3 H₂O
Overall Cell Reaction:       CH₃OH + 3/2 O₂ => CO₂ + 2 H₂O

These cells have been tested to work in a temperature range from about 50ºC-120ºC. This low operating temperature and advantage of no requirement for a fuel reformer make the DMFC an excellent candidate for very small to mid-sized applications, such as cellular phones and other consumer products, up to automobile power plants.

One of the drawbacks of this alcohol fuel cell is that the low-temperature oxidation of methanol to hydrogen ions and carbon dioxide requires a more active catalyst, which typically means a larger quantity of expensive platinum catalyst is required than in conventional PEMFCs.

One other demerit of driving the development of alcohol fuel cells is the fact that methanol is toxic. Therefore, some companies have been developing the advantageous Direct Ethanol Fuel Cell (DEFC). The performance of the DEFC is currently only about half that of the DMFC, but this gap is expected to narrow within very short time.

Diagram of atom structure

Introduction :
Atom is defined as the very small particle. The atoms are having many chemical properties of the elements. The atoms structure are having the nucleus at its center. The electrons are also present in the atom. The electron is always surrounds the nucleus part. The particles like protons and neutrons are also present in the atom.

Various particles present in the diagram of an atom structure

The atom diagram structure consists of three types of particles. They are defined below the following,
1. Protons
2. Neutrons
3. Electrons

Explanation for the various particles for the diagram of atom structure

The diagram of Structure of an Atom is shown below,
                 

Protons:
The protons present in the atom are having a positive charge. The positive charge is equal to the negative charge present in the electrons. The number of particles present in the atoms is used for the representation of the atomic number. Protons are 1836 times greater than the electrons. The proton structure is discovered by the scientist named Ernest Rutherford.

• The mass of the proton is given by 938 MeV/c² = 1.67 x 10^-27 kg.
• The charge of the3 proton is given by 1.602 x 10^-19 Coulombs.
• The diameter of the proton is given by 1.65 x 10^-15 m.

Electron:
The electrons are having the negative charges. The electrons cannot able to split into the further particles. The electrons move freely in the diagram of an atom. The electron forms the electron clouds.

• The mass of an electron present in the atom is given by 9.2095 x 10^-31 kg.
• The charge of an electron present in the atom is given by -1.602177 x 10^-19 C.
• The electron rest energy present in the atom is given by 0.511 MeV.
• The spin of an electron present in the atom is given by + `(1)/(2)` or -`(1)/(2)`

Neutron:
The charge of the neutron present in the atom is having neutral charge. The neutrons present in the atom are used to represent the isotope of the element.

• The mass of the neutron is given by 1.67492729 × 10⁻²⁷ kg.
• The charge of the neutron is given by 0.  
• The spin of the neutron is given by `(1)/(2)`