TRANSFORMER

TRANSFORMER
THE DEVICE WHICH IS USED TO CHANGE THE VOLTAGE.
                                       OR
  A transformer is a power converter that transfers AC electrical energy through inductive coupling between circuits of the transformer's windings. A varying current in the primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic flux through the secondary winding. This varying magnetic flux induces a varying electromotive force (EMF), or "voltage", in the secondary winding. This effect is called inductive coupling.
If a load is connected to the secondary winding, current will flow in this winding, and electrical energy will be transferred from the primary circuit through the transformer to the load. Transformers may be used for AC-to-AC conversion of a single power frequency, or for conversion of signal power over a wide range of frequencies, such as audio or radio frequencies.
In an ideal transformer, the induced voltage in the secondary winding (V_s) is in proportion to the primary voltage (V_p) and is given by the ratio of the number of turns in the secondary (N_s) to the number of turns in the primary (N_p) as follows:

By appropriate selection of the ratio of turns, a transformer thus enables an alternating current (AC) voltage to be "stepped up" by making N_s greater than N_p, or "stepped down" by making N_s less than N_p. The windings are coils wound around a ferromagnetic core, air-core transformers being a notable exception.
Transformers range in size from a thumbnail-sized coupling transformer hidden inside a stage microphone to huge units weighing hundreds of tons used in power stations, or to interconnect portions of power grids. All operate on the same basic principles, although the range of designs is wide. While new technologies have eliminated the need for transformers in some electronic circuits, transformers are still found in nearly all electronic devices designed for household ("mains") voltage. Transformers are essential for high-voltage electric power transmission, which makes long-distance transmission economically practical.

OHM'S LAW

^{ohm's law}
 Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.
The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly more complex equation than the one above (see History section below) to explain his experimental results.

Capacitor

CAPACITOR
the instrument which is used  to store the charges.
 A capacitor (originally known as condenser) is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric (insulator); . Capacitors are widely used as parts of electrical circuits in many common electrical devices.
When there is a potential difference (voltage) across the conductors, a static electric field develops across the dielectric, causing positive charge to collect on one plate and negative charge on the other plate. Energy is stored in the electrostatic field. An ideal capacitor is characterized by a single constant value, capacitance, measured in farads. This is the ratio of the electric charge on each conductor to the potential difference.it is used in any things like mobiles,toys and also there are many capacitor used in  motherboard of computer.
Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass, in filter networks, for smoothing the output of power supplies, in the resonant circuits that tune radios to particular frequencies, in electric power transmission systems for stabilizing voltage and power flow, and .

COLOUMB'S LAW

The law

Coulomb's law states that the magnitude of the Electrostatics 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 distances between 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.
The scalar and vector forms of the mathematical equation are

and

,   respectively.

An electric field

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.

The magnitude of the electric field force, E, is invertible from Coulomb's law. Since E = F ⁄ Q it follows from the Coulomb's law that the magnitude of the electric field E created by a single point charge q at a certain distance r is given by:this law is used very much in the world for many things.it can not be challenge.

.

An electric field is a vector field which associates to each point of the space the Coulomb force that will experience a test unity charge. Given the electric field, the strength and direction of a force F on a quantity charge q in an electric field E is determined by the electric field. For a positive charge, the direction of the electric field points along lines directed radially away from the location of the point charge, while the direction is towards for a negative charge.

COLOUMB'S LAW

HERE IS THE COLOUMB'S LAW
Coulomb's law or Coulomb's inverse-square law is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. This law states that "The force of attraction or repulsion between two point charges is directly proportional to the product of magnitude of each charge and inversely proportional to the square of distance between them".^[1][2] Coulomb's law has been tested heavily and all observations are consistent with the law.
 
In 1785, the French physicist Charles Augustin de Coulomb published his first three reports of electricity and magnetism where he stated his law and this publication was essential to the development of the theory of electromagnetism.He used a torsion balance to study the repulsion and attraction forces of charged particles and determined that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

as their are many scientist passed and are alive have shown their laws and their theories in every field.columb has also maked columbs law which has been accepted uptil now and can not be challenged.In 1769, Scottish physicist John Robison announced that according to his measurements, the force of repulsion between two spheres with charges of the same sign varied as x^-2.06.

Defects of a lens

the defects of lens are following

Spherical Aberration

• Light impinging on different areas of the spherical surface of the lens will not meet at precisely the same spot. The rays striking the lens farthest from the center will focus slightly closer to the lens than rays than strike the lens near its center.

Chromatic Aberration

• Chromatic aberration results from the fact that a lens refracts or bends some colors of light more sharply than others. A lens bends violet light rays more sharply than green, and red suffers even less refraction. As a result, the lens tends to separate white light into its component colors, and a colorful halo results.

Comatic Aberration

• Comatic aberration occurs when light rays from a distance impinge upon a lens at an angle rather than perpendicular to the plane of its disc. .

LENS FORMULA

 

Derivation of Lens Formula (Convex Lens)

Let AB represent an object placed at right angles to the principal axis at a distance greater than the focal length f of the convex lens. The image A¹B¹ is formed beyond 2F₂ and is real and inverted.
OA = Object distance = u
OA¹ = Image distance = v
OF₂ = Focal length = f
OAB and OA¹B¹ are similar


But we know that OC = AB
the above equation can be written as


From equation (1) and (2), we get



Dividing equation (3) throughout by uvf