If one wire is twice as long as another wire that is otherwise identical, what is true about their resistances?

If one wire is twice as long as another wire that is otherwise identical, what is true about their resistances?

• A. The longer wire has greater resistance.
• B. The resistance is the same.
• C. The shorter wire has greater resistance.
• D. Resistance depends on thickness.

Answer: (A)

Longer length increases resistance when the material and cross‑section are the same. The resistance formula, R = ρL/A, shows that with the same material (ρ) and the same cross-sectional area (A), doubling the length (L) doubles the resistance. So the longer wire has greater resistance—specifically, it’s twice as large as the shorter one. Since the wires are identical in thickness, changing only length is what changes resistance here. The other statements don’t fit because equal resistance would require equal length and area, and thicker would lower resistance only if that were changing between the two wires.

Longer length increases resistance when the material and cross‑section are the same. The resistance formula, R = ρL/A, shows that with the same material (ρ) and the same cross-sectional area (A), doubling the length (L) doubles the resistance. So the longer wire has greater resistance—specifically, it’s twice as large as the shorter one. Since the wires are identical in thickness, changing only length is what changes resistance here. The other statements don’t fit because equal resistance would require equal length and area, and thicker would lower resistance only if that were changing between the two wires.