# Electric Current and Theory of Electricity

## Definition of Electric Current

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 flowing through the conductor per unit time.

Let's explain in little bit detail the definition of electric current.

The general concept of electric current is very simple. Whenever a potential difference is applied across the substance, electrons inside the substance start flowing according to the electric field caused by the applied potential difference. Actually, an electric field appears inside the substance due to which the negatively charged free electrons experience an attraction toward higher potential terminal or relatively positive terminal of the substance. As a result the electrons start drifting from lower potential terminal to higher potential terminal. Flow of electrons means transfer of charge from one point to other in the substance. Electric current is nothing but measure of rate of this transferring charge. So it is measured as transferred charge per unit time. Mathematically it can be represented as
$Current\;I\;=\frac{\Delta Q}{\Delta t}$

## Unit of Electric Current

As in the definition of electric current we have already told, that this is nothing but transferring charge per unit time in other view it can be seen as amount of charge crossing the perpendicular cross section of a conductor per unit time. So due to application of potential difference, if δQ Coulomb charge crosses a particular cross section of any conductor at Δt second then,
$Current\;I\;=\frac{\Delta Q\; coulomb}{\Delta t\; second}$
Hence, unit of electric current is Coulomb per Second and it is named as Ampere. After name of famous French mathematician Andre-Marie Ampere.

SI unit of electric current is Ampere and it abbreviated as A or Amp. In CGS system its unit is biot and abbreviated as Bi. 1 Bi = 10 A.

## Electric Current Formula

The most simple formula of electric current can be determined by Ohm's law. As per this low,
$Current\;\propto\;voltage\;\Rightarrow\;voltage\;=\;RI\Rightarrow\;I\;=\;\frac{V}{R}$

Where, V is voltage and R is electrical resistance.

Again, single phase active power P = VIcosθ where cosθ is power factor of the system. From that we get,
$I\;=\;\frac{P}{Vcos\theta}$

Similarly for reactive power Q,
$I\;=\;\frac{Q}{Vsin\theta}$

And for apparent power S
$I\;=\;\frac{S}{V}$

Similarly, for three phase power active power
$P\; =\;\sqrt{3}VIcos\theta\;\Rightarrow\;I\;=\;\frac{P}{\sqrt{3}Vcos\theta}$.

For three phase reactive and apparent power the current will be
$I\;=\;\frac{Q}{\sqrt{3}Vsin\theta}\;and\;I\;=\;\frac{S}{\sqrt{3}V}\;respectively$

Electric current formula can also be expressed in terms of power and resistance only.
$Power\;P\; =\; I^2R\;\Rightarrow\;I\;=\;\sqrt{\frac{P}{R}}$

## 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.

Animated Atom

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.

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. Not only a metal, every conducting substance in this universe consists of some free electrons inside it. These free electrons move with a random manner at room temperature.

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 Vd(r) of charge carriers over a differential velocity of given location r is called the drift velocity at this location
$V_d\;=\;\frac{1}{N}\sum V$

#### 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 Vd 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

### Types of Current

There are only two types of electrical current, direct current and alternating current. We abbreviate them as DC and AC respectively. Concept of DC was developed before AC. But AC becomes most popular means of generating, transmitting and distributing of electric power. The direction of flow of direct current is unidirectional means this electric current does not alter its direction during flowing. Most common example of DC in our daily life is the current we get from all kind of battery system. All the house hold products, operated by battery, utilize DC as their source. One of the most important use of DC is in relay and control system of electrical power system. Actually in all the circuit breakers, DC is only means of electrical ON / OFF and TRIP / CLOSE operation. Another important use of DC is, excitation of field magnetic system of all kinds of DC rotating machine, synchronous rotating machines.

Most popular form of electrical current is alternating current or AC. As the current produced by battery system, is always DC, the current produced form rotating generator, is AC. Even in DC generators, the fundamental current produced is alternating current but by means of commutator system, it is converted to DC. In case of AC generators, the produced alternating current at armature is directly taken. Alternating current periodically alters its direction of flow and forms a particular alternating waveform. The most commonly among them is sinusoidal wave form but in some special case these waveform can also be triangular type or square type. AC does have some advantages over DC for generating, transmitting and distributing and that is why the current we get from our electric supply companies, is normally alternating current.