In relation to the variation of resistance of a conductor, how is the increased resistance value related to the area of the conductor?

The relationship between the resistance of a conductor and its cross-sectional area is that resistance is inversely proportional to the area. This means that as the area of the conductor increases, its resistance decreases.

This concept arises from the formula for resistance, which is given by Ohm's Law and modified for the geometry of the conductor:

[ 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 equation, if the area ( A ) increases while keeping resistivity ( \rho ) and length ( L ) constant, the overall resistance ( R ) decreases. This is because a larger area allows more charge carriers (such as electrons in a wire) to flow through simultaneously, thus reducing the overall resistance experienced by the conductor.