E.M.F Equation of The Transformer and Voltage Transformer Ratio

Transformer

In a transformer,
Source of alternating current is applied to the primary winding. Due to this, the current in the primary winding (called as magnetizing current) produces alternating flux in the core of transformer. This alternating flux gets linked with the secondary winding, and because of the phenomenon of mutual induction an emf gets induced in the secondary winding. Magnitude of this induced emf can be found by using the following EMF equation of the transformer.

EMF equation of the Transformer:

Let,
N₁ = Number of turns in primary winding
N₂ = Number of turns in secondary winding
Φ_m = Maximum flux in the core (in Wb) = (B_m x A)
f = frequency of the AC supply (in Hz)

As, shown in the fig., the flux rises sinusoidally to its maximum value Φ_m from 0. It reaches to the maximum value in one quarter of the cycle i.e in T/4 sec (where, T is time period of the sin wave of the supply = 1/f).
Therefore,
average rate of change of flux = ^Φ_m /_(T/4)    = ^Φ_m /_(1/4f)
Therefore,
average rate of change of flux = 4f Φ_m       ....... (Wb/s).
Now,
Induced emf per turn = rate of change of flux per turn

Therefore, average emf per turn = 4f Φ_m   ..........(Volts).
Now, we know,  Form factor = RMS value / average value
Therefore, RMS value of emf per turn = Form factor X average emf per turn.

As, the flux Φ varies sinusoidally, form factor of a sine wave is as shown in figure.
Therefore, RMS value of emf per turn =  1.11 x 4f Φ_m = 4.44f Φ_m.

RMS value of induced emf in whole primary winding (E₁) = RMS value of emf per turn X Number of turns in primary winding

          E₁ = 4.44f N₁ Φ_m          ............................. eq (1)

Similarly, RMS induced emf in secondary winding (E₂) can be given as

          E₂ = 4.44f N₂ Φ_m.          ............................ eq (2)

from the above equations 1 and 2,

This is called the EMF Equation of Transformer, which shows, emf  and number of turns is same for both primary and secondary winding.

For an ideal transformer on no load, E₁ = V₁ and E₂ = V₂

_{where, V1 = supply voltage of primary winding
            V2 = terminal voltage of secondary winding} 

Voltage Transformation Ratio (K):

From above Equation,

Where, K = constant
This constant K is known as voltage transformation ratio.

• If N₂ > N₁, i.e. K > 1, then the transformer is called step-up transformer.
• If N₂ < N₁, i.e. K < 1, then the transformer is called step-up transformer.

 

 

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Coulomb’s Law-Explanation Statement Formulas Principle Limitations

Coulomb’s Law-Explanation Statement Formulas Principle Limitations

Charles Augustin de Coulomb

Coulomb's law, or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. The law was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. It is analogous to Isaac Newton's inverse-square law of universal gravitation. Coulomb's law can be used to derive Gauss's law, and reverse can be possible. The law has been tested heavily, and all observations have upheld the law's principle.

Coulomb's law statement:

1st law: 

The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive ; if they have different sign, the force between them is attractive

2nd law:

The magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distance between them

 

 FORMULAS OF COULOMBS LAW:

According to the Coulomb’s 2nd law,

Where,

   1. ‘F’ is the repulsion or attraction force between two charged bodies.
   2. ‘Q1’ and ‘Q2’ are the electrical charged of the bodies.
   3. ‘d’ is distance between the two charged particles.
   4. ‘k’ is a constant that depends on the medium in which charged bodies are presented. In S.I.          system, as well as M.K.S.A. system k=1/4πε. Hence, the above equation becomes.

The value of ε₀ = 8.854 X 10^-12 C²/Nm²

Hence, Coulomb’s law can be written for medium as,

Then, in air or vacuum ε_r = 1. Hence, Coulomb’s Law can be written for air medium as,

 The value of εr would change depends on the medium. The expression for relative permittivity ε_r is as follows,

PRINCIPLE OF COULOMBS LAW:

if we have two charged bodies one is positively charged and one is negatively charged, then they will attract each other if they are kept at a certain distance from each other. Now if we increase the charge of one body keeping other unchanged, the attraction force is obviously increased. Similarly if we increase the charge of second body keeping first one unchanged, the attraction force between them is again increased. Hence, force between the charge bodies is proportional to the charge of either bodies or both.

Now, by keeping their charge fixed at Q₁ and Q₂ if you bring them nearer to each other the force between them increases and if you take them away from each other the force acting between them decreases. If the distance between the two charge bodies is d, it can be proved that the force acting on them is inversely proportional to d² .

 This development of force is not same for all mediums. As we discussed in the above formulas, εr would change for various medium. So, depends on the medium, creation of force can be varied.

LIMITATIONS OF COULOMB'S LAW:

1. Coulomb’s Law is valid, if the average number of solvent molecules between the two interesting charge particles should be large.
2. Coulomb’s Law is valid, if the point charges are at rest.
3. It is difficult to apply the Coulomb’s Law when the charges are in arbitrary shape. Hence, we cannot determine the value of distance‘d’ between the charges when they are in arbitrary shape.

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Lemon Battery - a simple elctrical project for school college students

Lemon Battery

The lemon battery is a simple type of electrical battery that is commonly made for school science projects because it illustrates a battery's main components. Typically, a piece of zinc metal and a piece of copper metal are inserted into a lemon. Everyday objects such as galvanized nails and copper pennies can be used for the zinc and for the copper. A single lemon is usually studied using an electrical meter. Several lemons can be wired together to form a more powerful battery that will power a light-emitting diode, a buzzer, or a digital clock.

The lemon battery is similar to the first electrical battery invented in 1800 by Alessandro Volta in Italy. Volta used brine (salt water) instead of lemon juice. The lemon battery is described in some textbooks in order to illustrate the chemical reactions that occur in batteries. The zinc and copper are called the electrodes of the battery, and the juice inside the lemon is called the electrolyte. There are many variations of the lemon battery that use different fruits (or liquids) as electrolytes and metals other than zinc and copper as electrodes.

This article contains instructions for making a lemon battery and using it to power a light-emitting diode. If you want to know more about the science and history of the lemon battery, you can get started  Wikipedia.

Materials and equipment required:

• Light emitting diode. These look like plastic pieces with 2 wires stuck into them. They are usually just called LEDs, which comes from the first letters of the three words Light Emitting Diode. When the right battery is hooked up, the LED will glow. A red one is good for the lemon battery experiment; there is another section of this article that discusses how to find an LED. While LEDs are a good choice for this experiment, some other ideas are given below in the section "Alternative devices".
• Lemons. You'll need 3 or 4. Any citrus fruit, like limes, grapefruits, or oranges, or even a potato will work.
• Zinc electrodes. You'll need 3 or 4. Most likely you'll use a piece of metal that's been coated with zinc. This is what the word "galvanized" means. A galvanized metal washer that's about one inch (2 – 3 cm) in diameter will work well. Galvanized roofing nails, galvanized screws and bolts, and even paper clips can also work. If you can find some zinc sheet, and some shears or tough scissors to cut it, that will work very well. Be careful if you do this; the edges of sheared metal sheets are sharp. If you can, file the edges to make them less sharp.
• Copper electrodes. You'll need 3 or 4. Copper or copper-coated pennies work well. You may find some good copper fittings in the plumbing section of a hardware store. Again, if you can find some copper sheet, and some shears or scissors to cut it, that will work. Again, be careful about sharp edges.
• Leads. You'll need 5 or 6. The easiest thing is to get hold of a packet of insulated lead wires with "alligator clips" on each end.
• Multimeter (optional). If you know how to use an electrical multimeter, it can be helpful in getting your battery to work.

Making a single lemon cell

Make the first lemon cell. Your battery is going to have at least 3 lemon cells, but each cell is made the same way.

1. Clean your electrodes carefully. Your goal is to get any dirt or grease off of them, and also to scrub away the thin "oxide" coatings on them. It should work fine if you clean them in the same way that you'd clean a pan in the kitchen to make it clean and shiny. Scrubbing with steel wool or with an abrasive sponge will work fine; if you are using a galvanized electrode, be careful not to rub off the zinc coating completely.
2. Stick one zinc electrode into the lemon (or other fruit). You may need to use a small knife to cut a slit into the lemon. You want the electrode to go into the lemon as deeply as possible, but you'll need a little bit of the electrode to stick out of the fruit so you can attach a lead wire to it. Wiggle the electrode around a little to smash the membranes inside the fruit.
3. Next, stick the copper electrode into the same lemon. You want this electrode to be close to the zinc electrode, but it must not touch the zinc inside the lemon. If they do touch, your cell will not work. As for the zinc electrode, you want to stick the copper electrode into the fruit as far as you can, and you want to wiggle it a bit to make sure the membranes near the electrode are broken.(Optional) If you are using a multimeter, you can do the following tests to make sure your lemon cell is working.
4. Hook up two alligator clips from your leads to the two electrodes. Connect the two clips to the leads of the multimeter.
5. Measure the voltage from your lemon cell. It should read about 0.9 - 1.0 volts.
6. Measure the current from your cell. You should read a few tenths of a milliampere. Some multimeters are not sensitive enough to measure currents less than one milliampere, in which case you'll just see 0.0 as the reading.

Making the lemon battery

When several lemon cells are wired together, the collection is called a battery. We usually call a single lemon cell a battery also. Most batteries that you may purchase to use in toys and electronics have just one cell inside.

1. You need to make 3 lemon cells. If you're using a multimeter, make sure that each cell generates the correct voltage and the correct current.
2. Using two lead wires, connect the three cells together. Connect the zinc electrode on the first cell to the copper electrode on the second. Connect the zinc electrode on the second cell to the copper electrode on the third lemon. This is called a "series" connection; the three cells make up the lemon battery.

Connecting the LED

Connect a lead wire from the copper electrode of the first lemon cell to the longer lead wire from the LED. Connect a lead wire from the zinc electrode of the third cell to the shorter wire of the LED. You may need to gently pull the lead wires that come from the LED apart; the alligator clips on the ends of the two lead wires that connect your battery to the LED must not touch each other.
The LED will glow now enjoy your diy project.

Any questions please leave a comment below:

 

 

 

 

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