ELECTRICAL CONDUCTIVITY

                                   ELECTRICAL CONDUCTIVITY

Electrical conductivity is a basic property of material. Due to this property one material can conduct electricity. Some materials are good conductor of electricity that means electrical current can pass through them very easily; again some materials do not allow electrical current to flow through them. The material through which current easily, called good conductor of electricity in other words, the electrical conductivity of these materials is high. On the other hand the materials do not allow the electrical current to flow through them are called insulators. There are some materials whose electrical conductivity is not as high as conductor and also not as poor as insulator, they have an intermediate conductivity and these type of materials are known as semiconductors.

In an atom, electrons revolve in the orbits around the nucleus. The electrons are revolving in different orbits. Some orbits are closer to the nucleus some are away from the nucleus. The electrons closer to the nucleus posses lower energy than those farther from nucleus. This phenomenon can be compared to a mass m, which possessing increasing potential energy as its distance above the earth is increased. If a mass is lifted from earth surface, its potential energy increases with increase in height of lifting. Similarly in atom, if the distance between electrons and nucleus increases, the potential energy of the electrons is increased. Thus it can be said that the position occupied by an electron in an atom signifies a certain energy level of that electron.

Again due to opposite charges in electron and nucleus, there will be an attraction force between them. Naturally this attraction force becomes weaker as the distance between nucleus and electrons increase. Hence the electrons min the outer most orbit of an atom experiences least attraction force. So the outermost atom can easily be detached from the parent atom.

Let’s explain the details with band theory

When a number of atoms are brought together, the electrons of one atom experience forces of other atoms. This effect is most pronounced in outer most orbits. Due to this force, the energy levels, which were sharply defined in an isolated atom, are now broadened into energy bands. Due to this phenomenon generally two bands result, namely valance band and conduction band.

Valance Band

The outermost orbital of an atom, where electrons are so tightly bounded that, they can not be removed as free electron

Conduction Band

This is the highest energy level or orbital in outer most shell, in which electrons are free enough to move.

Band Gap

There is one energy gap separates these two bands, - the valance band and conduction band. This gap is called forbidden energy gap.

Electrical Conductivity of Metal

In metals, the atoms are so tightly packed that electrons of one atom experience sufficiently significant force of other closed atoms. That result, the valance band and conduction band in metals come very closer to each other may even overlap. Consequently, by receiving very small amount of energy from external heat or electrical energy source, the electrons readily ascend to higher levels in the metal. Such electrons are known as free electrons. These free electrons are responsible for current flows through a metal. When external electric source is connected to a piece of metal, these free electrons starts flowing towards higher potential terminal of the source, causing current to flow in the metal. So metal is good electrical conductor. In metal density of free electrons in conduction band is much higher than other materials, hence metal is referred as very electrical conductor. In other words electrical conductivity of metal is very good.

Electrical Conductivity of Semiconductor

In semiconductor the valance band and conduction band are separated by a forbidden gap of sufficient width. At low temperature, no electron possesses sufficient energy to occupy the conduction band and thus no movement of charge is possible. But at room temperature it is possible for some electrons to give sufficient energy and make the transitions in conduction band. The density of electrons in conduction band at room temperature is not as high as in metals, thus can not conduct electrical current as good as metal. The electrical conductivity of semiconductor is not as high as metal but also not as poor as insulator. That is why, this type of material is called semiconductor.

Electrical Conductivity of Insulator

Practically electrical conductivity of insulator is nil. The atoms in the insulator molecules are electrically stable enough. The outer most shell of these atoms are completely filled with electrons. In such material where forbidden gap is very large and as a result the energy required by the electron to cross over to the conduction band is practically large. Insulators do not conduct electricity easily. That means the electrical conductivity of insulator is very poor.

PIYUSH PUSHKAR

ELECTROMOTIVE FORCE

Electromotive force

Also called EMF, (denoted  and measured in volts), refers to voltage generated by a battery or by the magnetic force according to Faraday's Law, which states that a time varying magnetic field will induce an electric current.
Electromotive "force" is not considered a force, as force is measured in newtons, but a potential, or energy per unit of charge, measured in volts. Formally, EMF is classified as the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals By separating positive and negative charges, electric potential difference is produced, generating an electric field. The created electrical potential difference drives current flow if a circuit is attached to the source of emf. When current flows, however, the voltage across the terminals of the source of emf is no longer the open-circuit value, due to voltage drops inside the device due to its internal resistance.
Devices that can provide emf include electrochemical cells, thermoelectric devices, solar cells, electrical generators, transformers, and even Van de Graaff generators. In nature, emf is generated whenever magnetic field fluctuations occur through a surface. An example for this is the varying Earth magnetic field during a geomagnetic storm, acting on anything on the surface of the planet, like an extended electrical grid.
In the case of a battery, charge separation that gives rise to a voltage difference is accomplished by chemical reactions at the electrodes a voltaic cell can be thought of as having a "charge pump" of atomic dimensions at each electrode.
A source of emf can be thought of as a kind of charge pump that acts to move positive charge from a point of low potential through its interior to a point of high potential. … By chemical, mechanical or other means, the source of emf performs work dWon that charge to move it to the high potential terminal. The emf ℰ of the source is defined as the work dW done per charge dq: ℰ= dW/dq.

We have refrained from using the term 'electromotive force' or 'e.m.f.' for short; for there is no consistency between different authors in the meaning of the term. … To some authors it is synonymous with 'voltage.' To others it means the open-circuit voltage of a battery. To a third group of authors it means the open-circuit voltage of any two-terminal device. This use is met most often in connection with Thevenin's theorem in circuit theory. To a fourth group it means the work accounted for by agencies other than differences of the (not measurable) Galvani potentials. Such authors equate the current–resistance product of a circuit branch to the sum of voltage plus e.m.f. A fifth group extends this use to field theory. The authors of this group equate the product of current density and resistivity to the sum of electric-field strength plus an e.m.f. gradient. A sixth group applies the term to electromagnetic induction. These authors define e.m.f. as the spatial line integral of the electric-field strength taken over a complete loop. To them the term 'counter e.m.f.' means something.


PIYUSH PUSHKAR

Theory of VOLTAGE/POTENTIAL DIFFERENCE

Voltage Theory

Let us consider two parallel plates, which are connected to a battery. The upper plate is connected with positive terminal of a battery hence this plate is positively charged and lower plate is connected with negative terminal of the battery and hence this, lower plate is negatively charged.

These plates produce an electric field between them which is proportional to surface charge density of both plates. Let's the surface charge density of the upper plate is σ. Then surface charge density of lower plate will be - σ. The electric field produced by only positive plate is surface charge density divided by twice of permeability of the space between the plates i.e.

σ

2εo.

Similarly electric field produced by only negative plate is

−	σ
	2εo.

Hence resultant electric field between the plates is

σ	− (	− σ	) =	σ
2εo		2εo		εo

Let us now assume a positively charged particle enters into that electric field. If the particle has a charge of q Coulomb, then electrostatic force applied on that particle will be

F_e = q.E
Where E is the electric field vector and it is constant for an uniform electric field.

Now acceleration of the particle,

Fe	=	q	.E
m		m

Where m is the mass of the particle.

Hence velocity of the particle at any instant t can be written as,

v(t) = vo + ∫(	q	).E.dt
	m

Where v_o is the initial velocity of the particle at entrance into uniform electric field.

v(t) = vo +	q	.E.t
	m

So, position of the particle at any instant t can be written as,

	∫
p(t) = po +		v(t).dt

Where p_o is the initial position of the particle at entrance into uniform electric field

p(t) = po + ∫{vo + (	q	).E.t}.dt
	m

p(t) = po + vo.t +	q	.E.t2
	2m

This is a function of parabola hence it can be predicted from the function that the motion of charged particle in an uniform electric field is projectile motion in parabolic path.

Electrical Potential Difference and Definition of Voltage

We can use electric field vector to characterize electric field in a space. By observing the movement of charge particles inside an electric field one can predict the exact characteristics of that field. If field is strong enough the deflection of charged particle in parabolic path will be more sharp and if the field is weak, deflection is less. But it is not the practical way of measuring the intensity of an electric field. Another physical quantity is there which is much easier to measure and also used to characterize an electric field and this quantity is known as electric potential difference.

Electrical potential V(t) of a position in the electrical field is such that, electric potential energy required to place a particle of charge q at that position would be the product of charge of the particle q and the potential of that position V(t). That is potential energy U(t) = q.V(t).

The SI unit of electrical potential is Volt after name of Italian physicist Alessandro Volta (1745 - 1827).

Voltmeter is used to measure the potential difference between two points.

There is a misconception about potential and voltage. Many of us think that both are same. But voltage is not exactly potential it is the measure of electric potential difference of tow points.

Electrical Potential and Electrical Field vector

Electrical Potential and Electrical Field vector both characterize the same thing that is space of electrical field. Since both electric potential and electrical field vector describe an electric field, they are related.

dV = - E.ds where dV is the potential difference between tow points separated by a distance ds and electrical field vector is E.

Definition of potential difference or voltage

After going through the above portion of voltage theory we can now establish a definition of potential difference, definition of voltage in few words. Which says " Voltage is the difference in electric potential energy per unit charge between two points. Voltage is the work to be done, upon an unit charge to move between two points , against a static electric field. A voltage which is a measure of electric potential difference is the cause of current to flow in a closed circuit."

PIYUSH PUSHKAR