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Question
Find the expression for the resistivity of a material and state the SI unit of resistivity.
Solution
The resistance of a conductor is directly proportional to its length l and inversely proportional to its area of cross-section A.
`R prop l` and `R prop 1/A`
`:. R prop l/A`
`:. R = rho 1/A`
where ρ is the proportionality constant and is called the resistivity of the material of the conductor.
Rearranging the above equation,
`rho = "RA"/l`
This is the expression for resistivity.
The SI unit of resistivity is ohm-meter (Ω.m).
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