How does the resistance of a wire vary with its area of cross-section?

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Solution

Resistance: Resistance of a wire is directly proportional to the length of the conductor and inversely proportional to the area of the cross-section.
That is, $R \propto \frac{L}{A}$
Introducing a constant of proportionality,
$R = \frac{ρ L}{A}$ (where $ρ$ is the resistivity of the material.)
From the formula, we can observe that the resistance is inversely proportional to the cross-section area.
Hence, the resistance increases as the cross-section area decreases and vice-versa.

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