In modern Electron Theory there are three form of matter solid, liquid and gas. Composed of very small particles , those are called molecules. A molecules made with atoms. An atom consists of electron, neutron and proton. The central part is called nucleus and around the nucleus the electron revolve in different path those are call orbit.

The size of nucleus is smaller than compared to atom. The nucleus contains protons and neutrons.   The proton is a positively charged particle having mass of 1837 times that of an electron.  A neutron has the same mass as proton but no charge. Clearly ,the nucleus of an atom bears a positive charge and an electron is a negatively charged particle having negative charge equal to the positive charge on a proton.

The above discussion shows that matter is electrical in nature i.e.it contain particles of electricity viz protons and electrons. Whether a given body exhibits or not depends upon the relative number of these particles of electricity.

  • When the number of protons is equal to the number of electrons in a body, the resultant charge is zero and the body will be electrically neutral. Thus the paper of book is electrically neutral because it has the same number of protons and electrons.
  • If from a neutral body, some electrons are removed, there occurs a deficit of electrons in the body , the body attains a positive charge. Hence a positively charged body has deficit of electrons from the normal due share
  • A negatively charged body has an excess of electrons from the normal due share.


Unit of Charge

The charge on an electron is so small that it is not convenient to select it as the unit of charge .Coulomb is used as the unit of charge for practice.
$$ 1 \text{ Coulomb} = { \text {Charge on} 625 * 10^{16} \text {electron}}.$$
So, We say that a body a positive charge of 1 Columbo (IC) ,it means that it has a deficit of 625x10^16 electrons from the normal due share.

Free Electron

From the Modern Electron theory we know that in atom electrons are moves around the nucleus in individual orbits. The electrons in last orbit are known as Valence Electrons. In metal conductor link copper and silver, the valence electrons are weakly attached to their nuclei that they can easily detach. Such type of Electrons are called Free Electrons.


Electric Current

The flow of free electrons in a definite direction is called electric current. When electric pressure or voltage is applied, the free electrons being negatively charged start moving toward positive end. This directed flow of electrons is called electric current 


Measurement of Current

The flow of charge in a definite direction is called electric current. It is measured by the time rate of flow of charge through the conductor. If q is the charge flowing through any cross-section of the conductor in time t, then

$$  Electric Current , I= {q \over t}.$$ 

Instantaneous Current - if the rate of flow of charge varies with time, then current at any time is given by,  $$ i= {dq \over dt}.$$ 

Where dq is the small charge passing through any cross-section of the conductor in time dt. The SI unit of electric current is ampere. If q = 1C and t= 1s then I = 1/1 = 1 Ampere

So, it means One coulomb of charge flows in one second through the wire.

If n electrons are passing through any cross-section of the wire in time t, then

$$  I= {q \over t}= {ne \over t} $$  

\[where \ e = {-b -1.6 X 10^{-19} }.\]



Electric Potential

The electric potential at a point is the electric potential energy/unit charge
A charged body has electric potential energy. When a body is charged, work is done in charging the body. This work done is stored in the body in the form of electric potential energy. The Charged body has the capacity to do work by moving other charges either by attraction or repulsion 
Electric Potential is defined as,

The SI unit of energy or work is J and the charge is C. So that the SI Unit of electric potential is  J/C which is referred as  V.


Potential Difference

The difference in the potentials of two charged bodies is called potential difference. If we consider two body A and B having potentials of +5V and +3 V respectively as shown. Each Coulomb of charge on body A has an energy of 5 joules while each coulomb of chare on body B has energy of 3 joules. Clearly, the body A is at higher potential than body B.
If the two bodies are joined through a conductor then electron will flow from body B to body A. When the two bodies attain the same potential, the flow of current stops. Therefore, we arrive at a very important conclusion that current will flow in a circuit if potential difference exists. No potential difference, no current flow. It may be noted that potential difference is sometimes called voltage.


E.M.F and Potential Difference

This is a distinct difference between e.m.f and potential difference. The e.m.f of a device battery, is a measure of the energy the battery gives to each coulomb of charge. Thus if a battery supplies 4 joules of energy pre coulomb, we say that it has an e.m.f of 4 volts. The energy given to each coulomb in a battery is due to the chemical action.
The potential difference between two points, A and B is a measure of the energy used by one coulomb in moving from A to B. Thus if potential difference between points A and B is 2 V. It means that each coulomb will give up an energy of 2 joules in moving from A to B.


Drift Velocity of Free Electrons

When Potential difference is applied across the ends of a metallic wire, the free electrons start drifting towards the positive terminal of the source. The average velocity with which free electrons get drifted in a metallic conductor under the influence of potential difference is called drift velocity of free electron.

Relation Between Current and Drift Velocity


Resistance

The opposition offered by a substance to the flow of electric current is called its resistance. Since current is the flow of free electrons, resistance is the opposition offered by the substance to the flow of free electrons. This opposition occurs because atoms and molecules of the substance obstruct the flow of theses electrons. Certain substances offer very little opposition to the flow of electric current and are called conductors. On the other hand, those substances which offer high opposition to the flow of electric current 
The practical unit of resistance is ohm and represented by the symbol ohm. 
It can be define as ,
A wire is said to have a resistance of 1 ohm if a potential difference of 1 volt across its ends cause 1 ampere to flow through it.


Calculating Resistance 

The resistance R of a material of length l and area of cross section A is given by
R= row l/A
Where row is called resistivity or specific resistance of the material. Its value depends upon the nature of the material and temperature.


Resistance or Specific Resistance

R = rho l/A
If l=1 m; A = am2 then R = rho
Hence specific resistance of a material is the resistance offered by 1 m length of wire material having area of cross section of 1 m2.
The SI unit of resistivity is ohm-m. Different materials have different resistivity. For example, the resistivity of copper is 1.7 x 10^-8 ohm m. It means that if you take a copper wire 1 m long and having an area of X section of 1 m2, then resistance of this piece of copper wire will be 1.7 x 10^-8 ohm

Conductance 

The reciprocal of resistance of a conductor is called its conductance(G). If a conductor has a resistance R, Then its conductance G is given by 
G =1 /R
A circuit with high conductance has low resistance , and a circuit with low conductance has high resistance. The SI unit of conductance is Siemen. It is denoted by the symbol S. Suppose a wire has a resistance of 0.5 ohm. Then its conductance will be
G = 1/R = 1/0.5 = 2S


Conductivity

The reciprocal of resistivity of a conductor is called its conductivity. It is denoted by the symbol σ . If a conductor has resistivity row, then its conductivity is given by;


$$  sigma = {1 \over p} $$ 
$$  σ = {1 \over 𝜌} $$ 
$$  G = {1 \over R} ={A \over 𝜌l} $$ 
$$ Now, G = {σ \over l} $$ 
So, SI unit of conductivity is Siemen per meter $$   {Sm^-1} $$  

Carbon Resistors

A component whose function in a circuit is to provide a specified value of resistance is called a resistor. The most commonly used resistors in electrical and electronic circuits are the carbon resistors. A carbon resistor is made from powdered carbon mixed with a binding material and baked into a small tube with a wire attached to each end. These small sized resistors are manufactured in values from a fraction of an ohm to several million ohms. Note that the power rating of a carbon resistor depends upon the physical size of the resistor. A larger resistor is able to throw off more heat than a smaller one. 

Color code for carbon resistors. Since a carbon resistor is physically quite small, it is more convenient to use a color code indicating the resistance value than to imprint the numerical value on the case. In this scheme, there are generally four color band A, B , C and D.
Temperature Effect on Resistance

In different experiment, it has been established that, with temperature the resistance of a conductor(Metallic) increases linearly with proportional to the rise of the temperature. 




If we imagine a metallic conductor having resistance R0 and 0 degree Celsius Temperature and R1 at t1 degree Celsius, Then in the increase of in resistance (i.e. R1 - R0)

1. It will directly proportional to the primary resistance (i.e R1 - R0 ∝ R0)

2. It directly proportional to rise in temperature (i.e  R1 - R0 ∝ t1)

3. is depends upon the nature of the material .

Integrating the first two we get, 

    R1 - R0 ∝ R0 t1

    or, R1- R0 = ∝0 R0 t1


Ohmic and Non-Ohmic Conductors

There are two types of conductors 1. Ohmic Conductor

2. Non-Ohmic Conductor

1. Ohmic Conductors: Those conductors which obey ohm's law (I proportional to V) are called ohmic conductors e.g. metals The V-I graph for such  a conductor is a straight line passing through the origin. (i) shows V-I graph for two ohmic conductors namely 1Kohm and 2Ohm resistors. The 1-Kohm resistor conductors 5mA at 5V. 10mA at 10V. The 2 KΩ resistor conducts 2.5mA at 5 V and 5mA at 10V.



Ohm's Law

The relationship between voltage across and current through a conductor was first discovered by German scientist George Simon Ohm. This relationship is called Ohm's law and may be stated as under:

The current flowing through a conductor is directly proportional to the potential difference across its terminals provided the physical conditions(temperature, strain) do not change . or, V/I = Constant = R

Where R is a constant of proportional and is called resistance of the conductor.

If a graph is drawn between supplied potential difference and current flowing through the conductor, it will be a straight line passing through the origin. 


Electric Power

The Power of an electric appliance is the rate as which electrical energy is converted into other forms of energy. For example a 60W bulb converts 60J of electrical energy into heat and light each second.

Thus referring to Fig as the charge 1 moves from the point A to B, it losses electric potential energy qV. 

In other word  qV joules of electrical energy is converted into heat in t seconds.

$$ \text{ Electric Power, P} = {q V\over t } = {(It)V \over t} \text { J/s or watts}.$$
$$ \text{ Electric Power, P} = {VI } \text {watts}.$$
$$ \text{ Electric Power, P} =  { I^2R } \text {watts}.$$
$$ \text{ Electric Power, P} = { V^2 \over R }  \text {watts}.$$
Any of the three formulas can be used for calculation of electric power, depending upon the problem in hand.
 $$ \text{ Unit of Electric Power, P} = \text { V I} \text {watts}.$$
The SI unit of potential difference is 1 V and that of current is 1 A so that SI unit of power = 1 V x 1 A = 1 VA or 1 watt (1w)
The bigger units of electric power are kilowatt (kW) and megawatt (MW)
$$ \text{ 1 kW } = \text {1000 W ;} = {1 MW} = {10^3 kW} = {10^6 W} $$

Electrical Energy

The loss of electrical potential energy in maintaining current in a circuit is called electrical energy consumed in the circuit. 


In the above , as the charge q = (I t) moves from point A to B, it loses electric potential energy = q V = V I t joules. This loss of electric potential energy is converted into heat. 

We say that electrical energy consumed in t seconds in VIt joules.

$$ \text{ Electric Energy Consumed, W} = \text { V I t} = {I^2 R t} = {V^2 \over R} \text {t joules}.$$


Use of power and Energy Formulas

It already been discussed that electric power as wheel as electrical energy consumed can be express by these formulas.

1.

$$ \text{ Electric Power, P} = { I^2R } = {V2 \over R} \text {watts}.$$
$$ \text{ Electrical energy consumed, W} = { I^2Rt } = {V2 \over R} \text {t joules}.$$
The formulas apply only to resistors and to devices where all electrical energy consumed is converted into heat.
2.
$$ \text{ Electric Power, P} = {VI} \text {watts}.$$
$$ \text{ Electrical energy consumed, W} = {VIt} \text {  joules}.$$

Electrical Materials

Materials used in electricity and electronics can be divided into three major types

1. Conductors

2. Semiconductor

3. Insulators

Conductors can conduct current very easily while insulators practically conduct no current. In other word, Conductors have small resistivity and insulators have high value of resistivity. The resistivity of semiconductors lies between conductors and insulators.