Question

Suppose the resistance of a wire varies inversely as the area of its cross-section. Write a relation between resistance and area of cross-section.

Answer 1

Resistance: The opposition that a substance provides to the flow of electric current is referred to as resistance.

Second law of resistance: The resistance of the conductor is inversely proportional to the cross-section area of the conductor.

Step 1: Assumptions:

Let $r$ be the radius of the wire.

Then the cross-section area of the wire is $=\pi r^2$

Let $R$is the resistance of the conductor

Step 2: Find the relation:

$R\propto \frac{1}{\pi r^2}$(From $2^{nd}$ law of resistance )

$\Rightarrow R=\frac{\rho }{\pi r^2}$ [ where $\rho$ is some arbitrary constant]

Hence, the relation is $R=\frac{\rho }{\pi r^2}$.