Voltage drop across cable resistance Steps:

• Voltage drop in cable = 12 V - 10 V = 2 V.
• Total cable resistance R = drop / current = 2 V / 2.5 A = 0.8 Ω.
• Cable has two wires in series, so R = 2 × (ρ L / A), where ρ = 1.70 × 10^{-8} Ω m, A = 6.00 × 10^{-6} m².
• Solve for L: L = (R × A) / (2 ρ) = (0.8 × 6.00 × 10^{-6}) / (2 × 1.70 × 10^{-8}) = 10.6 m.

Why A is correct:

• Matches the calculated cable length using Ohm's law for the total resistance of two wires carrying current.

Why the others are wrong:

• B ignores one wire's resistance, doubling the length.
• C uses lamp voltage instead of drop, overestimating L.
• D assumes single wire or total circuit resistance, quadrupling L.

Final answer: A