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Showing posts with label Basic electrical. Show all posts
Showing posts with label Basic electrical. Show all posts

Sunday, December 22, 2019

December 22, 2019

RMS or Root Mean Square Value of AC Signal

RMS or Root Mean Square Value of AC Signal


Why rms values are used in AC system?
What does an average and rms value mean?
Why all the ratings of AC systems are in rms not in average value?
What is the difference between rms and average value?
These are the questions which come in our minds every time when we are dealing with AC circuits.
Suppose, we have a simple DC circuit (figure – 1) and we want to replicate it in an AC circuit. We got every thing same, except supply voltage which is now to be an AC supply voltage. Now, the question is what should be the value of AC supply voltage so that our circuit works exactly same as that of DC.
Let us put same value of AC supply voltage (AC Vpeak = 10 volt) which is in our DC circuit. By doing that we can see (figure 3) for a half cycle how the AC voltage signal is not covering up the whole area (blue area) of constant DC voltage, which means our AC signal can not supply the same amount of power as our DC supply.

Which means we must increase the AC voltage to cover the same area and see if it is supplying the same amount of power or not.
We found that (figure 4) by increasing the peak voltage Vpeak up to (Ï€/2) times of DC supply voltage we can actually cover the whole area of DC in AC. When the AC voltage signal completely represents the DC voltage signal then that value of DC signal is called the average value of AC signal.
Now our AC voltage should supply the same amount of power. But when we switched-on the supply surprisingly, we found that AC voltage is supplying more power than the DC. Because an average value of AC supplies same amount of charges but not the same amount of power. So, to get same amount of power from our AC supply we must decrease our AC supply voltage.
We found that by decreasing the peak voltage Vpeak up to √2 times DC voltage we get same amount of power flowing in both the circuits. When the AC voltage signal supply same amount of power as in DC then that value of DC voltage is called root mean square or rms value of AC.
We are always concerned about how much power is flowing through our circuits irrespective of how much electrons are needed to supply that power and that is the reason why we always use the rms value of AC supply instead of average value everywhere in AC system.
Conclusion
Average value of an AC current represent the equal amount of charges in DC current.

RMS value of an AC current represent the equal amount of power in DC current

AC current takes less amount of charges to supply the same amount of DC power.






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December 22, 2019

Electron volt or eV

Electron volt or eV

The concept of electron volt is very simple. Let us start from very basic. We know the unit of power is watt.
W = VI, where V is the voltage and I is the current.
Now as I is current, it is nothing but rate of charge transfer. Therefore, instantaneous impression of power would be
Where, q(t) is the amount of charge transferred in time t.
Now energy is expressed as

Where, q is the charge in Coulomb crosses a voltage V volts.
From the expression of energy we can write the energy required or work to be done for crossing an electric field of total voltage V by a charge Q coulomb is QV coulomb – volt or joules. Now we know the charge of an electron is – 1.6 × 10-19 coulomb and consider it has crossed an electric field of total voltage 1 V. Then the total work to be done is charge of electron × 1 V.
This amount of energy is considered as a micro unit of energy called electron-volt.

Definition of Electron – volt

One electron – volt is the unit of energy in joules which equals to the amount of work to be done for bringing one electron against an electric field of potential difference 1 volt.
This is very tiny or micro unit of energy mainly used for different calculation in atomic and electronic levels. The concept of energy levels in the materials is dealt with this micro unit of energy that is electron volt. Not only the energy of electrons, this unit is also used for all types of energy like thermal, light etc.
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December 22, 2019

Cyclotron Basic Construction and Working Principle

Cyclotron Basic Construction and Working Principle


Before understanding the basic working principle of Cyclotron it is necessary to understand force on a moving charged particle in a magnetic field and also motion of the charged particle in the magnetic field.

Force on a Moving Charged Particle in a Magnetic Field

When a current carrying conductors of length L metre with current I ampere placed perpendicularly in a magnetic field of flux density B Weber per metre square, then the force rather to say magnetic force acting on the conductor would be
Now, let us consider there are total N number of mobile free electrons in the conductor lie in length L metre causing the current I ampere
Where, e is the electric charge of one electron and it is 1.6 × 10-19 coulomb.
Now from equation (1) and (2) we get
Here, N number of electrons causing current I ampere, and consider that they travel length L metre in time t, therefore drift velocity of the electrons would be
From equation (3) and (4), we get
It is the force acting on N number of electrons in the magnetic field hence force on a single electron in that magnetic field can be

Motion of Charged Particle in a Magnetic Field


When a charged particle moves in a magnetic field, there would be extreme two conditions. The particle moves either along the direction of the magnetic field or it moves perpendicular to the magnetic field.
When the particle moves along the axis of the direction of magnetic field, magnetic force acting on it,

Hence there will be no force acting on the particle, hence no change in the velocity of particle and hence it moves in straight line with constant speed.
Now if the charged particle moves perpendicular to the magnetic field then there will be no change in the speed of the particle. This is because the force acting on the particle is perpendicular to the motion of the particle hence the force will not do any work on the particle so there will be no change in the speed of the particle.
But this force acting on the particle perpendicular to its motion and the direction of the motion of the particle will change continuously. As a result the particle will move in a in the field in a circular path of a constant radius with constant speed.
If the radius of the circular motion is R metre then
Now,

Hence radius of the motion depends upon the velocity of the motion.
Angular speed and time period are constant.

Basics Principle of Cyclotron

This concept of motion of charged particle in a magnetic field was successfully employed in an apparatus called cyclotron. Conceptually this device is very simple but it has huge uses in the field of engineering, physics and medicine. This is a charged particle accelerating device. The motion of the charged particle under perpendicular magnetic field is solely applied in the apparatus named cyclotron.

Construction of Cyclotron

This device basically has three main constructional parts
  1. Large sized electromagnet to create uniform magnetic field in between its two face-to-face placed magnetic opposite poles.
2. Two low height hollow half cylinders made of high conductive metals. These components of cyclotron are called Dees.
3. A high-frequency alternating high voltage source.

Constructional Details


The Dees are placed face to face in between the electromagnetic poles. The dees are so placed, that the straight edge will be face-to-face with small gap between them. Also the magnetic flux of the electromagnet cut these Dees exact perpendicularly. Now these two Dees are connected to two terminals of an alternating voltage source so that if one Dees is in the positive potential than other will be in exact opposite negative potential at same time. As the source is alternating the potential of the Dees are altered according to the frequency of the source. Now if a charged particle is thrown from a point near to the centre of one Dees with certain velocity V1. As the movement of the particle now perpendicular to the externally applied magnetic field, there will be no change of velocity but the charged particle will follow a circular path of radius
Where, m gram is the mass and q coulomb is the charge of the thrown particle and B Weber/metre2 is the flux density of externally applied perpendicular magnetic field.
After travelling Ï€ radians or 180o with radius R1 the charged particle comes to the edge of the Dee. Now the time period and frequency of the applied voltage source is so adjusted with the time period of circular motion that is
That the polarity of the other Dee becomes opposite that of the charged of the particle. Hence due to attraction of the Dee ahead the moving particle and also due to repulsion of the Dee in which the particle is now situated, the particle gets extra kinetic energy.
Where ν1 is the velocity of the particle at previous Dee and ν2 is the velocity of the particle in next Dee. Now the particle will move with this greater velocity with radius R2 metre.
Again due to constant perpendicular magnetic field the particle travels another half cycle with this new radius R2 metre and comes to the edge of present Dee. When it comes to this edge, the ahead Dee again becomes in opposite polarity of the behind and the particle crosses the gap between Dees with gain of kinetic energy qV and hence again there is gain of velocity and radius of the circularly travelling charged particle. In this way the charged particle follows a spiral path of motion with continually increasing velocity. Therefore the charged particle gets sufficiently high required velocity before leaving the cyclotron gun head.

The frequency of voltage source say f.

Here, 2Ï€ is constant, m, q and B are known hence T can be calculated and hence frequency of the voltage source would be

Application of Cyclotron

There are mainly two types of application of cyclotron. One is in lavatory of different physics experiments when highly accelerated photons are required. Also highly accelerated photons are used to irradiate tissues.





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December 22, 2019

What is Electrical Energy Definition Formula Unit of Electrical Energy

What is Electrical Energy Definition Formula Unit of Electrical Energy


What is Electrical Energy?

Before explaining what electrical energy is, let us try to review the potential difference between two points in an electric field.

Suppose potential difference between point A and point B in an electric is v volts.
As per the definition of potential difference we can say, if one positive unit electrical charge that is a body containing one-coulomb positive charge travels from point A to point B, it will do v joules work.
Now instead of one-coulomb charge if q coulomb charge moves from point A to B, it will do vq joules work.


If the time taken by the q coulomb charge to travel from point A to B is t second, then we can write the rate of work done as
Again, we define the work done per second as power. In that case, the term

wouldbe electrical power. In differential form, we can write, electrical power
Watt is the unit of power.

Now, if we place a conductor in between A and B, and through which the quantity of electric charge q coulomb is passing. The charge passing through a cross-section of the conductor per unit time (second) is 
It is nothing but the electric current i, through the conductor.

Now, we can write,
If this current flows through the conductor for a time t, we can say the total work done by the charge is
We define this as electrical energy. So, we can say,

Electrical Energy Definition

Electrical energy is the work done by electric charge. If current i ampere flows through a conductors or through any other conductive element of potential difference v volts across it, for time t second, the electric energy is,

Electrical Energy Formula

The expression of Electrical energy isThe electrical energy is


Unit of Electrical Energy

Basically, we find the unit of electrical energy is joule. This equals to one watt X one second. Commercially, we also use other units of electrical energy, such as watt-hours, kilo watt hours, megawatt hours etc.

Watt Hours

If one watt power is being consumed for 1 hour time, the energy consumed is one watt-hour.

BOT Unit or Board of Trade Unit or Kwh

The practical, as well as a commercial unit of electrical energy, is kilowatt hour. The fundamental commercial unit is watt-hour and one kilowatt hour implies 1000 watt hours. The electrical supply companies take electric energy charges from their consumer per kilowatt hour unit basis. This kilowatt hour is board of trade unit that is BOT unit.
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December 22, 2019

Ionization Energy

Ionization Energy

The ability of an element to give away its outermost electrons to form positive ions is manifested in the amount of energy supplied to its atoms sufficiently enough to take away the electrons out of them. This energy is known as Ionisation Energy. Simply speaking, the Ionisation Energy is the energy supplied to an isolated atom or molecule to knockout its most loosely bound valence shell electron to form a positive ion. Its unit is electron-volt eV  or kJ/mol and is measured in an electric discharge tube in which a fast-moving electron collides with a gaseous element to eject one of its electrons. The lesser Ionisation Energy (IE), the better the ability to form cations.


This can be explained with the Bohr Model of an atom , in that it considers a hydrogen-like atom in which an electron revolves around a positively charged nucleus due to the columbic force of attraction and the electron can only have fixed or quantized energy levels. The energy of a Bohr model electron is quantized and given as below :

Where, Z is the atomic number and n is the principal quantum number where n is an integer. For a hydrogen atom, Ionisation energy is 13.6eV.
The Ionisation Energy (eV) is the energy required to take the electron from n = 1 (ground state or most stable state) to infinity. Hence taking 0 (eV) reference at infinity, the Ionisation Energy can be written as :
The concept of Ionisation Energy supports the evidence of Bohr model of atom that the electron can revolve around the nucleus in a fixed or discrete energy levels or shells represented by the principal quantum number ‘n’. As the first electron goes away from the vicinity of the positive nucleus, then greater energy is required to remove the next loosely bound electron as the electrostatic force of attraction increases, i.e., the second Ionisation Energy is greater than the first one.
For example, the first ionization energy of Sodium (Na) is given as :
And its second Ionisation Energy is
Hence, IE2 > IE1 (eV). This is also true if there are K number of ionisations, then IE1 < IE2 < IE3……….< IEk
Metals have low Ionisation Energy. Low Ionisation Energy implies better conductivity of the element. For example, the conductivity of Silver (Ag, atomic number Z = 47) is 6.30 × 107 s/m and its Ionisation Energy is 7.575 eV and for Copper (Cu, Z = 29) is 5.76 × 107 s/m and its Ionisation Energy is 7.726 eV. In conductors the low Ionisation Energy causes the electrons to move throughout the positively charged lattice, forming an electron cloud.

Factors Affecting Ionisation Energy

In the periodic table, the general trend is that the Ionisation Energy increases from left to right and decreases from top to bottom. So the factors affecting ionization energy can be summarised below:
  • Size of the Atom: The Ionisation Energy decreases with the size of the atom because as the atomic radius increases the columbic force of attraction between the nucleus and outermost electron decreases and vice-versa.
  • Shielding Effect: The presence of inner shell electrons shield or weaken the columbic force of attraction between the nucleus and the valence shell electrons. Hence ionization energy decreases. The number of inner electrons means more shielding. However, in the case of gold, the Ionisation Energy is greater than silver even if the size of gold is more than silver. This is due to the weak shielding offered by the inner d and f orbitals in case of gold.
  • Nuclear Charge: The more the nuclear charge, the more it will be difficult to ionize the atom due to more attraction force between nucleus and electrons.
  • Electronic Configuration: The more stable the electronic configuration of the atom, the more difficult is to withdraw an electron hence more Ionisation Energy.
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