What happens to a conductor's resistance when its cross-sectional area doubles?

What happens to a conductor's resistance when its cross-sectional area doubles?

• A. Resistance remains unchanged
• B. Resistance decreases to half its original value
• C. Resistance doubles
• D. Resistance is halved

Answer: (B)

When the cross-sectional area of a conductor doubles, its resistance decreases to half its original value. This relationship can be derived from the formula for resistance, which is given by: \[ R = \frac{\rho L}{A} \] 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. If the cross-sectional area \( A \) doubles, the formula can be rewritten as: \[ R' = \frac{\rho L}{2A} \] This shows that the new resistance \( R' \) is half of the original resistance \( R \). Therefore, if the area increases, the resistance decreases inversely; doubling the area leads to halving the resistance. Thus, the correct conclusion is that the resistance becomes half its original value, confirming that the impact of cross-sectional area on resistance is significant.

When the cross-sectional area of a conductor doubles, its resistance decreases to half its original value. This relationship can be derived from the formula for resistance, which is given by:

[ 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.

If the cross-sectional area ( A ) doubles, the formula can be rewritten as:

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

This shows that the new resistance ( R' ) is half of the original resistance ( R ). Therefore, if the area increases, the resistance decreases inversely; doubling the area leads to halving the resistance. Thus, the correct conclusion is that the resistance becomes half its original value, confirming that the impact of cross-sectional area on resistance is significant.