Resistance depends on length and cross-sectional area via R = ρL/A

Steps:

• Resistance formula is R = ρL/A, where ρ is constant for the same metal.
• First wire: R = ρL/A.
• Second wire: R₂ = ρ(L/2)/(4A).
• Simplify: R₂ = R × (1/2) × (1/4) = R/8.

Why A is correct:

• Formula shows resistance scales with length (halved: factor 1/2) and inversely with area (quadrupled: factor 1/4), yielding total factor 1/8.

Why the others are wrong:

• B. 2R: Assumes length doubled with unchanged area.
• C. R/2: Assumes length halved with unchanged area.
• D. 8R: Assumes length quadrupled with unchanged area.

Final answer: A