Resistance depends on length, area, and temperature via R = ρ L / A, with ρ increasing with temperature Steps: - Resistance R = ρ L / A; ρ = ρ₀ [1 + α (T - T₀)], so R ∝ (L / A) × [1 + α (T - T₀)]. - For same metal, compare relative values assuming T₀ fixed and α > 0, so higher T increases R. - Compute factors: A has (2L / A) × k(2T) = 2 (L/A) k(2T); B and C have (L / 2A) × k(2T) = 0.5 (L/A) k(2T); D has 0.5 (L/A) k(T). - Since k(2T) > k(T) and 2 k(2T) > 0.5 k(2T) > 0.5 k(T), A is largest. Why A is correct: - It maximizes R by doubling L (increases R), halving effective A (increases R), and doubling T (increases ρ via temperature coefficient α). Why the others are wrong: - B: Smaller L/A ratio (0.5 vs. 2) outweighs same high T, yielding 1/4 of A's R. - C: Identical to B, so same lower resistance. - D: Same small …