Resistance scales with length and inversely with cross-sectional area for same material

Steps:

• Resistance R = ρL/A; ρ is same, so R₂/R₁ = (L₂/L₁) × (A₁/A₂).
• L₂/L₁ = 2.0 m / 0.50 m = 4.
• A₁/A₂ = (1.0 × 10^{-2} m²) / (5.0 × 10^{-3} m²) = 2.
• R₂ = 0.75 Ω × 4 × 2 = 6.0 Ω.

Why D is correct:

• Matches R = ρL/A formula, where ratio gives exactly 6.0 Ω.

Why the others are wrong:

• A: Ignores length increase, underestimates by factor of 20.
• B: Approximates half the scaling, misses full area inverse effect.
• C: Doubles resistance but ignores area ratio properly.

Final answer: D