Resistance depends on length and cross-sectional area

Steps:

• Resistance formula: R = ρL/A, where ρ is resistivity (same for copper), L is length, A is area.
• For wire Y: L_Y = 2L_X, A_Y = (1/2)A_X.
• Substitute: R_Y = ρ(2L_X) / ((1/2)A_X) = ρ(2L_X) × (2/A_X) = 4(ρL_X/A_X).
• Thus, R_Y = 4R_X.

Why D is correct:

• Resistance is directly proportional to length and inversely proportional to area (from R = ρL/A), so doubling length multiplies R by 2, halving area multiplies R by 2 again, yielding 4R.

Why the others are wrong:

• A: R/2 would require halving length and doubling area.
• B: R assumes no net change, but length doubles and area halves, increasing resistance.
• C: 2R accounts only for length change, ignoring area effect.

Final answer: D