What is the effect of halving the cross-sectional area of a conductor?

What is the effect of halving the cross-sectional area of a conductor?

• A. It halves the resistance
• B. It doubles the resistance
• C. It keeps resistance the same
• D. It quadruples the resistance

Answer: (B)

Halving the cross-sectional area of a conductor has a direct impact on the resistance due to the fundamental relationship defined by the formula for resistance. The resistance \( R \) of a conductor is given by the equation: \[ R = \frac{\rho L}{A} \] where \( \rho \) is the resistivity of the material, \( L \) is the length of the conductor, and \( A \) is the cross-sectional area. When the cross-sectional area \( A \) is halved, the formula indicates that the resistance \( R \) will increase because resistance is inversely proportional to the cross-sectional area. Specifically, if the area is halved, the expression becomes: \[ R' = \frac{\rho L}{\frac{A}{2}} = \frac{2\rho L}{A} \] This shows that the new resistance \( R' \) is twice the original resistance \( R \). Therefore, halving the cross-sectional area results in doubling the resistance, confirming that the correct choice reflects this relationship.

Halving the cross-sectional area of a conductor has a direct impact on the resistance due to the fundamental relationship defined by the formula for resistance. The resistance ( R ) of a conductor is given by the equation:

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

where ( \rho ) is the resistivity of the material, ( L ) is the length of the conductor, and ( A ) is the cross-sectional area.

When the cross-sectional area ( A ) is halved, the formula indicates that the resistance ( R ) will increase because resistance is inversely proportional to the cross-sectional area. Specifically, if the area is halved, the expression becomes:

[ R' = \frac{\rho L}{\frac{A}{2}} = \frac{2\rho L}{A} ]

This shows that the new resistance ( R' ) is twice the original resistance ( R ). Therefore, halving the cross-sectional area results in doubling the resistance, confirming that the correct choice reflects this relationship.