How is the increased value of resistance of a conductor related to the area of the conductor?

The relationship between the resistance of a conductor and its cross-sectional area is based on fundamental principles of electrical conduction. As a conductor's area increases, its resistance decreases. This occurs because a larger area allows more pathways for charge carriers (like electrons) to flow through, effectively reducing the overall resistance offered to the current.

This principle can be quantitatively described using the formula for resistance in a uniform conductor, which is given by:

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

where ( R ) is resistance, ( \rho ) is the resistivity of the material, ( L ) is the length of the conductor, and ( A ) is the cross-sectional area. According to this formula, as the area ( A ) increases, the resistance ( R ) decreases, indicating an inversely proportional relationship.

Therefore, the correct answer pertains to how an increase in the conductor's cross-sectional area results in a decrease in its resistance. This principle is crucial for understanding how to design efficient electrical circuits and select appropriate conductor sizes for specific applications to minimize power loss due to resistance.