Resistance formula and constant volume

Steps:

• Resistance R = ρ L / A, where ρ is resistivity (constant), L is length, A is cross-sectional area.
• Volume V = L × A is constant for both wires.
• For wire Y, L_Y = 2 L_X, so A_Y = V / L_Y = (L_X A_X) / (2 L_X) = A_X / 2.
• Thus, R_Y = ρ L_Y / A_Y = ρ (2 L_X) / (A_X / 2) = 4 (ρ L_X / A_X) = 4 R.

Why C is correct:

• Doubling length halves area at constant volume, so R ∝ L/A increases by 2 × 2 = 4, per the resistance formula.

Why the others are wrong:

• A: Ignores dimensional changes; resistance varies with L and A.
• B: Accounts only for doubled length (×2), neglects area halving (another ×2).
• D: Overestimates; no basis for ×8 factor in formula.

Final answer: C