Which of these will cause the resistance of a conductor to decrease?

Which of these will cause the resistance of a conductor to decrease?

• A. Decrease the length or increase the cross-sectional area
• B. Increase the length
• C. Increase cross-sectional area only
• D. Increase the temperature

Answer: (A)

Resistance in a conductor depends on how long the path is and how much cross-sectional area is available for current to flow. For a uniform material, R is proportional to length and inversely proportional to area: R = ρL/A. So making the wire shorter reduces the path electrons must travel, and making it thicker (increasing cross-sectional area) gives more paths for current, both of which lower resistance. Temperature usually raises resistance for most metals because resistivity increases with heat, so increasing temperature does not decrease resistance. Increasing length increases resistance, so that would not help. Increasing cross-sectional area alone does lower resistance, but the option that captures both ways to reduce R—shortening the length or increasing the area—is the best description of how to decrease resistance.

Resistance in a conductor depends on how long the path is and how much cross-sectional area is available for current to flow. For a uniform material, R is proportional to length and inversely proportional to area: R = ρL/A. So making the wire shorter reduces the path electrons must travel, and making it thicker (increasing cross-sectional area) gives more paths for current, both of which lower resistance.

Temperature usually raises resistance for most metals because resistivity increases with heat, so increasing temperature does not decrease resistance. Increasing length increases resistance, so that would not help. Increasing cross-sectional area alone does lower resistance, but the option that captures both ways to reduce R—shortening the length or increasing the area—is the best description of how to decrease resistance.