How does increasing the cross-sectional area affect resistance?

How does increasing the cross-sectional area affect resistance?

• A. Resistance decreases in proportion to cross-sectional area; R ∝ 1/A.
• B. Resistance remains constant when area changes.
• C. Resistance increases with larger area.
• D. Resistance becomes proportional to area squared.

Answer: (A)

Resistance in a uniform conductor falls as the cross-sectional area grows, because more area means more paths for electrons to travel, reducing the opposition to flow. The relationship is R = ρL/A, so with length and material fixed, increasing A makes R decrease in inverse proportion: R ∝ 1/A. If the area doubles, the resistance roughly halves. The idea that resistance stays the same, increases with area, or grows with area squared doesn’t fit this inverse relationship.

Resistance in a uniform conductor falls as the cross-sectional area grows, because more area means more paths for electrons to travel, reducing the opposition to flow. The relationship is R = ρL/A, so with length and material fixed, increasing A makes R decrease in inverse proportion: R ∝ 1/A. If the area doubles, the resistance roughly halves. The idea that resistance stays the same, increases with area, or grows with area squared doesn’t fit this inverse relationship.