Resistance increases by (1 / 0.94²)² due to constant volume

Steps:

• New diameter is 94% of original, so new radius ratio is 0.94; new area A' = π(0.94r)² = (0.94)²A ≈ 0.8836A.
• Volume V = LA = L'A' (constant), so new length L' = L(A/A') = L / 0.8836 ≈ 1.131L.
• Resistance R = ρL/A, so R' = ρL'/A' = ρ(1.131L)/(0.8836A).
• Ratio R'/R = (L'/L)(A/A') = 1.131 × 1.131 = (1/0.94²)² ≈ 1.28.

Why D is correct:

• Formula R ∝ L/A and constant volume imply R'/R = (A/A')² = 1/(0.94⁴) ≈ 1.28, matching the stretched wire's increased length and decreased area.

Why the others are wrong:

• A: 1.06R approximates 1/0.94 (ignores area effect on length).
• B: 1.13R approximates 1/0.8836 (only length increase, ignores area in resistance formula).
• C: 1.20R has no direct relation to 0.94 factor (arbitrary miscalculation).

Final answer: D