What happens to resistance if the cross-sectional area is halved?

• A. Resistance remains the same
• B. Resistance doubles
• C. Resistance is halved
• D. Resistance is quartered

Answer: (B)

When considering how resistance behaves in relation to the cross-sectional area of a conductor, it is important to understand the relationship described by the formula for resistance:

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

Where:

• ( R ) is the resistance,

• ( \rho ) is the resistivity of the material,

• ( L ) is the length of the conductor,

• ( A ) is the cross-sectional area.

If the cross-sectional area ( A ) is halved, the resistance ( R ) can be analyzed as follows:

When you halve the area, you effectively make the denominator of the formula smaller. Since resistance is inversely proportional to the area, a decrease in the area leads to an increase in resistance. Specifically, if the area is reduced by half, the resistance doubles. This behavior follows the principle that a narrower conductor (smaller cross-section) presents more opposition to the flow of electric current, resulting in a higher resistance.

In summary, halving the cross-sectional area of a conductor leads to a doubling of its resistance due to the inverse relationship defined in the resistance equation.