What happens to the resistance of a wire when its cross-sectional area increases?

When the cross-sectional area of a wire increases, the resistance of the wire decreases. This relationship is grounded in the principles of electrical conductivity and material science.

Resistance is determined by a few key factors, primarily the material's resistivity, the length of the wire, and the cross-sectional area. The formula that relates these factors is given by:

[ R = \frac{\rho \cdot L}{A} ]

Where:

• (R) is the resistance,

• (\rho) is the resistivity of the material,

• (L) is the length of the wire, and

• (A) is the cross-sectional area.

From this equation, it’s clear that as the area (A) increases, the overall resistance (R) decreases, provided the resistivity and length remain constant. This is because a larger cross-sectional area allows more pathways for the electric current to flow, effectively reducing the opposition to that flow, or resistance.

So, in practical terms, a wider wire has a lower resistance than a narrower one made from the same material and of the same length. This principle is crucial for linemen to understand, as selecting the appropriate wire gauge directly impacts electrical efficiency and safety in