Which factors influence the resistance of a wire, according to the formula R = K x L / A?

Which factors influence the resistance of a wire, according to the formula R = K x L / A?

• A. Length Only
• B. Cross-Sectional Area Only
• C. Length and Cross-Sectional Area
• D. Temperature Only

Answer: (C)

The main idea is that resistance in a wire is affected by how long the path is and how wide the path is, with a material constant shaping the overall value. In the given formula R = K × L / A, K represents the material’s resistivity (assumed constant here). Resistance grows as length increases because electrons encounter more collisions along a longer path. It decreases as cross-sectional area increases because a thicker wire provides more pathways for current to flow. To put it another way, if you double the length, resistance doubles. If you double the cross-sectional area, resistance halves. If you double both length and area, the effects can cancel so that R stays the same, since R is proportional to L/A. Temperature isn’t part of this expression because K is treated as a constant. In reality, changing temperature changes resistivity, which would change R, but that effect would be captured by a different version of the formula where K (or ρ) depends on temperature.

The main idea is that resistance in a wire is affected by how long the path is and how wide the path is, with a material constant shaping the overall value. In the given formula R = K × L / A, K represents the material’s resistivity (assumed constant here). Resistance grows as length increases because electrons encounter more collisions along a longer path. It decreases as cross-sectional area increases because a thicker wire provides more pathways for current to flow.

To put it another way, if you double the length, resistance doubles. If you double the cross-sectional area, resistance halves. If you double both length and area, the effects can cancel so that R stays the same, since R is proportional to L/A.

Temperature isn’t part of this expression because K is treated as a constant. In reality, changing temperature changes resistivity, which would change R, but that effect would be captured by a different version of the formula where K (or ρ) depends on temperature.