Resistance depends on length and cross-sectional area

Steps:

• Resistance R = ρL/A, where ρ is resistivity, L is length, A is cross-sectional area.
• For the second wire, length L₂ = 2L₁, so resistance factor from length is ×2.
• Diameter d₂ = 2d₁, so radius r₂ = 2r₁; area A = πr², thus A₂ = π(2r₁)² = 4πr₁² = 4A₁, resistance factor from area is ÷4.
• Total resistance R₂ = R₁ × (L₂/L₁) × (A₁/A₂) = R × 2 × (1/4) = R/2.

Why B is correct:

• Formula R = ρL/A shows resistance doubles with length but quarters with quadrupled area (from doubled diameter), yielding R/2.

Why the others are wrong:

• A ignores area increase, underestimating by factor of 8.
• C assumes equal resistance, neglecting length and area changes.
• D overestimates by only considering length doubling without area effect.

Final answer: B