The resistance of a material depends upon the fallowing four factors, which are called laws of resistance.
1st law of resistance
The resistance of conductor is directly proportional to the length of the conductor. Greater is the length of conductor greater will be the resistance, similarly smaller is the length, and smaller will be the resistance of the conductor.
2nd law of resistance
The resistance of the conductor is inversely proportional to the cross sectional area of the conductor. Greater is the cross sectional area smaller will be the resistance and when smaller is cross sectional area greater will be the resistance
3rd law of resistance
The resistance of the conductor depends upon the nature of the conductor. Two wire having the same gauges, but different material will have different resistance.
4th law of resistance
The resistance of the conductor depends upon the temperature of it. Resistance of metallic conductor increase with increase in temperature of the conductor.
Taking in to consideration 1st three laws and neglecting 4th law for movement, we have
R ∝ L ...........(eq. 1)
R ∝ l / A ...........(eq. 2)
From equation 1 and 2 we get
Where ρ is called rho .it is a constant and is known as resistivity or specific resistance of a material.
Its unit is Ωm.
It is the resistance of opposite faces of a unit cube of a material.
The resistivity of a material is based on the resistance of define volume of that material the letter symbol for resistivity is ϱ (the Greek letter Rho).
Resistivity may also be called specific resistance. Table list the resistivity in ohm-centimetre (Ω.cm). It also lists values in units of circular mil-ohms per foot (cmil-Ω/ft) for the conductor group.
|Resistivity of Selected Electrical Materials|
|Material||ϱ (resistivity) at 20o C|
|Silver||1.65 X 10-6||9.9|
|Copper||1.72 X 10-6||10.37|
|Gold||2.44 X 10-6||14.7|
|Aluminum||2.83 X 10-6||17|
|Tungsten||5.49 X 10-6||33|
|Nickel||7.81 X 10-6||47|
|Iron||1.23 X 10-5||74|
|Constantan||4.90 X 10-5||295|
|Nichrome||9.97 X 10-5||600|
|Carbon||3.49 X 10-3|
|Germanium||4.70 X 101|
|Silicon||6.40 X 104|
Specific resistance can be derived from the following relations of the resistance dependence factors.
Resistance is directly proportional to the length of conductor.
R ∝ L ---------1
Resistance is inversely proportional to the area of conductor.
R ∝ 1/A ----------2
by combining 1 and 2
R ∝ L/A
R = ϱ L/A
Where ϱ (Rho) is constant for the material called its specific resistance or resistivity.
"The Specific resistance of a material is the resistance of a piece of unit length and unit cross-sectional area."
"It is the resistance between opposite faces of unit cube of the material."
Specific resistance is measured in Ohm-inch or Ohm-cm or Micro ohm-inch or Micro ohm-cm.