Resistivity Formula
We know that the large number of free electrons are move randomly in conductor. When a potential difference is applied between two ends at conductor then these electrons starts moving from lower potential and to higher potential end and due to this motion of electron current is posses in conductor or wire. Resistor is component that opposes the flow of current. Resistivity is property of material.
The resistance of conductor is depends on its length (l), area of cross-section (A) and nature of material. The resistance of conductor is directly proportional to the length (L) and inversely proportional to area of cross section.
Mathematically,
R ∝ l —– (1)
And R ∝ 1/A —– (2)
∴ R ∝ l/A —— (3)
R = ρ L/A —- (4)
ρ (Rho) is the constant of proportionality and ρ is called as resistivity of the material.
ρ = RA/L —– (5)
Unit of Resistivity
ρ = Ωm2/m
ρ = Ωm (after cut m2 by m)
Unit of resistance is Ω (ohm)
Unit of area m2 (meter square)
Unit of length is m (metre)
So, the SI unit of resistivity is ohm meter (Ωm). Resistivity is properly of materials and value of resistivity is different for different material.