Resistance Law and Resistivity of Material:
Resistance of any material is directly proportional to the length of material and inversely proportional to its area of cross-section (supposing cylindrical material of length l and cross-section area A).
i.e. R ∝ l
R ∝ 1/ A
∴ R ∝ l/ A
or R =ρ (l /A)
where l = length in metre,
A = area of cross section in metre2, and
ρ = resistivity of material (specific resistance).
It is described as the resistance among the opposite faces of a metre cube of any material.
ρ= R (A /l)
= ohm × (metre2 / metre)
Reciprocal of resistivity is known as conductivity or the specific conductance. It is ment by 'σ' and its unit is Ω/metre.
σ= 1 /ρ
= G .( l /A) mho/metre
Conductors have its conductivity extremely high or in other terms, the resistivity of conductor is extremely small. Insulator has its conductivity extremely low or resistivity very high. Semiconductor has its conductivity lies among that of conductor and insulator.