For a wire of circular cross-section, made of the same material and with the same length, how does the resistance change if the diameter is doubled? (Same temperature.)

Answer: B. It becomes 1/4

A wire's resistance is R = ρL/A (ρ: resistivity, L: length, A: cross-sectional area), inversely proportional to area. A circle's area is proportional to the square of its diameter, so doubling the diameter quadruples the area and reduces the resistance to 1/4. For reference, copper's resistivity at 20 °C is about 1.7×10⁻⁸ Ω·m. Heavy-current wiring is made thicker to reduce resistive voltage drop and heating (I²R).

• A. 1/2 assumes resistance is inversely proportional to diameter.
• B. Correct. The area becomes four times larger, so the resistance becomes 1/4.
• C. Doubling reverses the relationship between area and resistance.