Which statement correctly explains why longer wires have higher resistance?

Which statement correctly explains why longer wires have higher resistance?

• A. The longer path increases collisions
• B. The material changes along the length
• C. The longer wire is heavier
• D. Electrons collide with more ions over the longer path

Answer: (D)

Resistance in a metal comes from electrons colliding with the lattice ions and losing energy as heat. In a longer wire, electrons must travel a greater distance, so they encounter more ions along the way. Each collision transfers some electric energy to the lattice, so the total energy lost per unit charge increases with length. That’s why resistance grows with length (and, for a given material, is proportional to L and inversely proportional to cross-sectional area, R = ρL/A). The idea that the longer path means more collisions with ions is the precise reason the resistance is higher. The other ideas—changes in material along the length or the wire simply being heavier—don’t explain the electrical resistance in the same direct way.

Resistance in a metal comes from electrons colliding with the lattice ions and losing energy as heat. In a longer wire, electrons must travel a greater distance, so they encounter more ions along the way. Each collision transfers some electric energy to the lattice, so the total energy lost per unit charge increases with length. That’s why resistance grows with length (and, for a given material, is proportional to L and inversely proportional to cross-sectional area, R = ρL/A). The idea that the longer path means more collisions with ions is the precise reason the resistance is higher. The other ideas—changes in material along the length or the wire simply being heavier—don’t explain the electrical resistance in the same direct way.