Wire resistance formula relates length and radius Steps: - Resistance of a wire is R = ρ L / A, where ρ is resistivity, L is length, and A = π r² is cross-sectional area. - For the first wire: R = ρ L / (π r²). - For the second wire with resistance R/2: R/2 = ρ l / (π r'²). - This simplifies to 1/2 = (l / L) × (r / r')², or l / L = (1/2) (r' / r)². Why D is correct: - For r' = 2r and l = 2L, (r' / r)² = 4, so l / L = (1/2) × 4 = 2, matching the required ratio from the resistance formula. Why the others are wrong: - A: For r' = r/2, l = L/2, (r' / r)² = 1/4, l / L = (1/2) × (1/4) = 1/8 ≠ 1/2. - B: For r' = r/√2, l = L, (r' / r)² = 1/2, l / L = (1/2) × (1/2) = 1/4 ≠ 1. - C: √(r/2) is dimensionally …