If the length of a conductor is halved, what happens to its resistance?

• A. It halves.
• B. It doubles.
• C. It stays the same.
• D. It quadruples.

Answer: (A)

Resistance depends on how far electrons must travel through the material. For a fixed material and cross-sectional area, resistance is proportional to length: R = ρL/A. Halving the length cuts the travel distance in half, so the resistance becomes half: R_new = ρ(L/2)/A = (1/2)ρL/A = R/2. This assumes the cross-sectional area and material are unchanged and temperature is constant. If the length were doubled, the resistance would double; if unchanged, the resistance would stay the same; quadrupling would occur only if the length were increased by a factor of four.