Resistivity from slope of R-L graph

Steps:

• Resistance R of a wire is given by R = ρ L / A, where ρ is resistivity, L is length, and A is cross-sectional area.
• The graph plots R versus L for a uniform wire, so the gradient G equals the slope ΔR/ΔL.
• From the formula, G = ρ / A.
• Rearrange to solve for ρ: ρ = G × A.

Why A is correct:

• The formula R = ρ L / A rearranges to ρ = (R/L) A, and G is the slope R/L.

Why the others are wrong:

• B. A: Gives only area, ignoring slope and material property ρ.
• C. G: Equals ρ/A, so misses multiplication by A.
• D. G × A²: Introduces extra A factor not in the formula.

Final answer: A