The resistance of a conductor is inversely proportional to its cross-sectional area. What happens to the resistance as the cross-sectional area of the conductor decreases?

The relationship between the resistance of a conductor and its cross-sectional area is defined by the formula ( R = \frac{\rho L}{A} ), where ( R ) is the resistance, ( \rho ) is the resistivity of the material, ( L ) is the length of the conductor, and ( A ) is the cross-sectional area. In this context, when the cross-sectional area ( A ) decreases, the denominator of the fraction becomes smaller, which causes the overall value of resistance ( R ) to increase.

This principle is rooted in physics, where a smaller cross-sectional area means that there is less space for the electric current to flow. As a result, more opposition is encountered, resulting in higher resistance. Conversely, a larger cross-sectional area allows for more paths for the current to travel through, leading to a reduction in resistance.

Understanding this concept is crucial for designing electrical systems, as the resistance of conductors directly affects the overall efficiency and performance of electrical circuits.