[Physics] Why is resistivity of conductor inversely proportional to the area of the conductor

electrical-resistanceelectricity

A simple Physics question regarding Ohm's law. The resistivity of the conductor is inversely proportional to the area of the conductor. I would like to have a simple explanation for this.

How does resistivity increase if the area decreases in a conductor?

Best Answer

You mean: The resistance of a conductor is inversely proportional to the area. [Resistivity is a property of the material of which the conductor is made, and is independent of the size or shape of the conductor.]

You can imagine making up a cylindrical conductor from two strands of semicircular cross-section (running lengthways). If each strand has a resistance $R_{semi},$ then the complete conductor will have a resistance $R$ of $\frac{1}{2}R_{semi}$ because the strands are in parallel. [It doesn't matter that the strands are in contact all along and not just at the ends, because no current will flow between them.]

So a wire of twice the cross-sectional area (but the same length and material) has half the resistance.

You can easily extend the argument to show that resistance is inversely proportional to cross-sectional area (for a given length and material).