If a wire has resistivity ρ, length L, and cross-sectional area A, giving R = ρL/A, what happens to R if the length is doubled while the material and area remain the same?

If a wire has resistivity ρ, length L, and cross-sectional area A, giving R = ρL/A, what happens to R if the length is doubled while the material and area remain the same?

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

Answer: (C)

Resistance in a uniform material increases with length, and R is given by R = ρL/A. with ρ and A fixed, R is directly proportional to L. So if the length is doubled, the resistance becomes double as well. The other possibilities would require changing either the cross-sectional area or the material’s resistivity, which isn’t happening here.

Resistance in a uniform material increases with length, and R is given by R = ρL/A. with ρ and A fixed, R is directly proportional to L. So if the length is doubled, the resistance becomes double as well. The other possibilities would require changing either the cross-sectional area or the material’s resistivity, which isn’t happening here.