If the cross-sectional area of a conductor is quadrupled while length and temperature remain constant, what happens to the resistance?

• A. Four times its original value
• B. One-fourth its original value
• C. Found by multiplying the original resistance by the percentage increase in cross-sectional area
• D. It remains unchanged

Answer: (B)

The main concept is that resistance is inversely proportional to cross-sectional area when length and temperature are fixed. For a uniform conductor, R = ρL/A. If length and temperature stay the same, and you quadruple the cross-sectional area, A becomes 4A, so the new resistance is R' = ρL/(4A) = (1/4)R. In other words, the resistance becomes one-fourth of its original value.

This happens because adding more conducting paths (a larger area) reduces the opposition to current flow. The other options don’t fit: resistance does not increase with more area, nor is it found by multiplying by the percentage increase in area, and it certainly does not remain unchanged when the area changes.