Experiment shows that the resistance of a metallic conductor is directly proportional to the length of the wire and inversely proportional to the cross sectional area.

i.e, R∝LA∴R=ρLA

Hence, ρ=RAL

Where ρ the constant of the equation called the resistivity, expressed in ohm-meter (Ωm)

Resistivity of a wire is defined as the product of the wire’s resistance and its cross sectional area, divided by the length of that wire. It can also be defined as the resistance of unit length of material of unit cross sectional area. It is the ability of a substance to restrict heat.

If a wire has a diameter d, then

A=πr2=πd24∴R=4ρLπd2andρ=πRd24L

Conductivity on the other hand, is a measurement of the ability of a substance to conduct heat. It is the reciprocal of resistivity and denoted by σ

Hence, σ=1ρσ=LRA=4LπRd2

Example:

A2m resistance wire, area of cross-section 0.50mm^{2}, has a resistance of 2.20Ω. Calculate

(a) the resistivity of the wire.

(b) the length of a wire which, when connected in parallel with the 2m wire will give a resistance of 2.0 Ω.

Solution:

(a) ρ=RALρ=2.2×0.5×10−62ρ=5.5×10−7Ωm

EVALUATION (POST YOUR ANSWERS USING THE QUESTION BOX BELOW FOR EVALUATION AND DISCUSSION):

Define resistivity.

What is the relationship between resistivity and conductivity?