Electric Current and Theory of Electricity

Electric Current and Theory of Electricity

While a potential difference is applied across a conductor, electrical charge flows through it and electrical current is the measure of the quantity of the electrical charge transferred through the conductor per unit time.

Electric Current Theory

Before understanding electric current theory we should gather knowledge of atomic structure. An atom consists of central nucleus having positively charged protons surrounded by negatively charged electrons in motion. Total number of positively charged protons is equal to negatively charged electrons in an atom. Hence net charge of an atom is zero which means an atom as a whole is electrically neutral.
Each electron has negative charge of − 1.602 X 10 ^{− 19} Coulombs
Each proton has positive charge of + 1.602 X 10 ^{− 19} Coulombs
Let’s have a discussion on theory of electricity. Flow of electrons in a substance causes the current. The electrons revolve around the nucleus in various orbits. hence due to centripetal force, the electrons have a tendency to detach from the parent atom. But the attraction force between negative electrons and positive nucleus keep them bounded in the atomic orbit. The centripetal force increases with increase in distance of the electrons from the nucleus and attraction force between electrons and nucleus decreases with increase in distance of electrons from nucleus. Moreover the electrons in outer orbit also experience a repulsion force from other electrons in inner cells. That is why electrons in outer most orbit are most loosely bonded with nucleus.

Animated Atom

In some specific substances these outermost electrons are so loosely bonded that a very small force is sufficient to detach them from their parent atom. Atoms are electrically neutral as because the number of electrons and protons are equal in them. But due to short of electrons, these atoms become positively charged. After detaching from parent atoms these electrons move in the substance’s body freely in random manner. In general, the outermost electrons in a metal atom is very loosely bonded hence free electrons are hugely available in metal, which makes the metal a good conductor of electric current.

Structure of Atom

That loosely bonded electron comes out from an atom and moves here and there in the metal body. Again if any free electron finds any atom nearby where there is short of electron then the free electron may enter into that vacant shell of this atom again after sometime if any collision takes place between this electron with other free electron, it leaves this shell and again starts moving in random manner until it gets another vacant shell. As the electron or negative charge carrier moves freely here and there in a substance body and makes an atom positively charged and neutral alternatively in random manner, we can assume that positive charge carrier moves in same relative random motion. This random movement may be directed to some particular direction if external force is applied on the electrons and directed random motion of electrons causes electric current. The actual phenomenon is explained below.

Drift Velocity

Drift velocity is associated with random velocities of free charge carriers in a substance.

Definition of drift velocity

The average velocity V_d(r) of charge carriers over a differential velocity of given location r is called the drift velocity at this location

Explanation of drift velocity

For drift velocity we have to consider a relatively small space inside which we have to examine what is the average velocity of all randomly moving particles inside that space. For calculating drift velocity at one particular location when in a space, we consider the particle movement at that location in the space and movements of other particles surround it. The average of velocities of the considered particle and those particles surrounded it in a particular direction will be the drift velocity of that location. Drift velocity of free electrons is greatly associated with current theory in a substance.

Current Density

We can derive mathematical expression for electric current from current density. Think about the movements of charge carriers in a conductor. They have the same kind of random velocities as we explained in last paragraph. So the drift velocity at any location in a conductor can be calculated. If we consider a unit volume of space in the conductor where concentration of charge carriers is ′n′ number of similar charge carriers and ′q′ is the charge of each similar charge carrier, the rate of charge transferring to a particular direction through the surface, (particular to the direction of drift velocity) of the said space is nothing but product of ′n′, ′q′ and the drift velocity V_d of that location to the said direction. The rate of charge transferring through a surface, particular to the direction of drift velocity is known as current density of that location to the said direction.

Let us again assume a small surface area of the space is dA. If the current density of the space is J, then obviously current passing through this small surface, is J.dA. Therefore, total current through an area A is,

Explanation of electric current as a phenomenon

Current is associated with charge carried by charged particles. Electrical current means the charge flows to one end from other by means of charged particles. The phenomenon of transferring charge from one place to another is referred as electric current.

Electric Current

It can be assumed that a beam of positively charged holes moving from one side to another. If that beam of holes moving from left to right, the current would be assumed, directed from left to right. As the holes are associated with atoms generally they can not move. Then what we mean by movement of positive holes ? Actually negatively charged free electrons move from right to left, which is assumed as if positive holes are moving in opposite direction of electrons movement that is from left to right. According to the general agreement the direction of current is chosen to coincide with the direction in which positive charge carriers or holes move even the actual movable carriers of charge are electrons and they move in opposite direction. So direction of conventional current flow is in opposite of electrons movement.
So it can be concluded like this, if potential difference is applied across a conductor, then due to electrical field, free electrons in the conductor start moving toward positive or higher potential end of the conductor. The direction of the electric current is considered to be flowing from higher potential end to lower, as the relative motion of static positive charges is assumed to be in that direction.

Explanation of current as a physical quantity

Let us consider a conductor and assume one surface across the cross – section of the conductor. By definition, electrical current is the rate of transferring electric charge through this surface in respect of time or alternatively, current across a surface is defined as the rate at which charge is transferred through this surface. Therefore, current

So, whenever we will think about current, we should always keep in mind the surface of cross – section of the conductor and current is nothing but , the amount of charge is transferred through this surface for unit time.
If 1 Coulomb of charge is transferred through any surface in 1 second, then current would be

André-Marie Ampère

Therefore the unit of electrical current is Coulomb/second which is known as ′Ampere′ after the name of André-Marie Ampère (20 January 1775 – 10 June 1836), a French physicist and mathematician. This was all about basic theory of electricity