Ohm's Law
Microscopic form: As it is clear 
Where s is called the electrical conductivity of the material it depends upon material and temperature. The above equation is microscopic form of ohm's law.
Macroscopic form: The electric field inside the conductor is . If the current in the conductor is i, the current density is .
Ohm's law 
then becomes
[Where r is the resistivity of a material is defined as
]
Further the above equation reduces to
where 
is called the resistance of the given conductor. Important Points
The another form of Ohm's law which is widely used in circuit analysis.
The quantity 
is called conductance
The SI unit of resistance ohm (W), resistivity r is ohm-metre (W-m) and conductivity (s) is (ohm-m)
written as mho/m.
It is due to the collisions of free electrons with the ions or atoms of the conductor while drifting towards the positive end of the conductor.
Resistivity of some electrical material: 
After stretching if length increases by n times then resistance will increase by n2 times i.e. 
Similarly if radius be reduced to 
times then area of cross-section decreases 
times so the resistance becomes n4 times i.e. 
.
After stretching if length of a conductor increases by x% then resistance will increases by 2x %
(valid only if x < 10%)
Factors upon which Resistance Depends
- Resistance is directly proportional to its length, i.e.,
- Resistance is inversely proportional to its area of
cross-section, i.e.,
- Resistance depends upon the nature of the material
- Resistance changes with temperature.
From the first three points (leaving temperature for the time being), we have,
; 
where r (Greek letter `Rho') is a constant of proportionality and is known as resistivity or specific resistance of the conductor. Its value depends upon the nature of the material and temperature.
Resistivity or Specific Resistance: 
Fig.
We have seen above that 
If l = 1 m; A = 1 m2, then 
Hence specific resistance (or resistivity) of a material is the resistance offered by 1 m length of wire of the material having area of X-section of 1m2 , as shown in fig.
For example, the resistivity of copper is
1.7 × 10_8W-m. It means that if you take a copper wire 1 m long and having an area of cross-section of 1m2 , then resistance of this piece of copper wire will be
1.7 × 10_8W
Another definition: If we take a cube of the material of each side 1m, then area of cross-section of each face is 1m2 and length between opposite faces is 1m.
Hence resistivity may be defined as the resistance between the opposite faces of a metre cube of the material.
Unit of Resistivity
We know that 
or 
The SI unit of length is 1m and that of area is 1m2.
The resistivity of substances varies over a wide range. To give an idea to the reader, the following table is :
| Material | Nature | Resistivity (W-m) No. at room temperature |
|---|---|---|
| Copper | Metal | 1.7 × 10- 8 |
| Iron | Metal | 9.68 × 10- 8 |
| Manganin | Alloy | 48 × 10- 8 |
| Nichrome | Alloy | 100 × 10- 8 |
| Pure Silicon | Semiconductor | 2.5 × 103 |
| Pure Germanium | Semiconductor | 0.6 |
| Glass | Insulator | 1010 to 1014 |
| Mica | Insulator | 1011 to 1015 |
The resistivity of metals and alloys is very small. Therefore, these materials are good conductors of electric current. On the other hand, resistivity of insulators is extremely large. As a result, these materials hardly conduct any current. There is also an intermediate class of semiconductors. The resistivity of these substances lies between conductors and insulators.