What happens to the resistance of a wire if its cross-sectional area is increased?

When the cross-sectional area of a wire is increased, the resistance of that wire decreases. This is due to the relationship defined by Ohm's Law and the principles of electrical conductivity. Specifically, resistance (R) is inversely proportional to the cross-sectional area (A) of the conductor, described by the formula:

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

where:

• ( R ) is the resistance,

• ( \rho ) is the resistivity of the material (a property that depends on the material itself),

• ( L ) is the length of the wire, and

• ( A ) is the cross-sectional area.

As the cross-sectional area increases, the ability of electric current to flow through the wire improves because there is more room for electrons to move. This results in a lower overall resistance.

In contrast, if other factors such as the length or material properties remain constant, the increase in area will lead to a decrease in resistance, enabling more efficient current flow. Understanding this principle is crucial for applications in electrical engineering and in practical scenarios encountered in the field.