Question

Write the relationship between electrical resistance and electrical resistivity for a metallic conductor of a cylindrical shape. Hence derive the SI unit of electrical resistivity.

Answer 1

Resistance of a uniform metallic conductor is directly proportional to its length (I) and inversely proportional to the area of cross-section (A).

i.e., R ∝ l     ...(i)

and `"R" prop l/"A"`

Combining equations. (i) and (ii) we get

`"R" prop l/"A"`

or  R = `rho  l/"A"`

where `rho` (rho) is a constant of proportionality and is called the electrical resistivity of the material of the conductor.

Now, putting the units of R, A and l in the expression.

`rho = (Omega "m"^2)/"m"`

`= Omega - "m"`

Thus, the S.I. unit of resistivity is Ohm - meter (Ω - m).