With a 9.0 V potential difference across a nichrome wire of diameter 0.60 mm and length 65 cm, what is the current in the wire?

• A. 1.0 A
• B. 2.0 A
• C. 2.6 A
• D. 3.0 A

Answer: (C)

Current in a wire comes from Ohm’s law I = V/R, and the resistance of a uniform wire is R = ρL/A, where ρ is the resistivity. The cross-sectional area from the diameter is A = πd^2/4. With d = 0.60 mm = 6.0×10^-4 m, A = π(6.0×10^-4)^2/4 ≈ 2.83×10^-7 m^2. The length is L = 0.65 m. Using nichrome’s resistivity ρ ≈ 1.5×10^-6 Ω·m, the resistance is R = (1.5×10^-6 × 0.65) / (2.83×10^-7) ≈ 3.45 Ω. Then the current is I = 9.0 V / 3.45 Ω ≈ 2.61 A, about 2.6 A. If a smaller resistivity were used, the current would be larger; with a typical lower value like 1.1×10^-6, you’d get a current around 3–4 A, which would not match the given answer.