Which one of the following correctly represents the SI unit of resistivity?

Concept:

The dimensional formula is defined as the expression of the physical quantity in terms of mass, length, time and ampere.

Explanation:

Electrical resistivity (ρ)

It is defined as the resistance of a unit length with a unit area of cross-section of the material of the conductor.

According to ohm’s law,

V = IR,

Where V = Potential difference, I = current and R = Resistance

The resistance of a conductor is proportional to the length of the conductor and inversely proportional to the area of a cross-section of the conductor.

 \(\Rightarrow R = \rho\frac{l}{A}\)

 \(\Rightarrow \rho = \frac{{RA}}{l}\rightarrow \frac{Ω . m^2}{m}\rightarrow Ω m\)

Where ρ = The proportional constant which is actually the property of the material and this is called the resistivity of the material., A =The cross-sectional area, l =The length

So, the unit of the resistivity will Ωm.

So, the correct answer will be option 4.