Question

12-gauge copper wire has a radius of 1.03×10−3 m. (a) What is the resistance of 11.5 m of this wire at 20°C? (b) How much current will pass through the wire if a potential difference of 9.00 V is applied across it?

A) is not 0.058 ohm or 0.059 ohm. I have no idea.

b) 155A

Answer 1

Use R = ρL/A, where ρ is the resistivity of copper (at 20 °C); L is the length of the wire; A is the cross-sectional area of the wire.

(a) Here, ρ = 1.68 × 10ˉ⁸ Ω·m; L = 11.5 m; A = πr² = π(1.03 × 10ˉ³ m)² = π(1.0609 × 10ˉ⁶) m², so

R = (1.68 × 10ˉ⁸ Ω·m)(11.5 m) / (π(1.0609 × 10ˉ⁶) m²) = 5.80 × 10ˉ² Ω (to 3 significant figures).

The answer is correct, the problem must be with sig. Figures. Try 0.06 ohm as an answer.

(b) I = E/R = (9.00 V)/(5.80 × 10ˉ² Ω) = 155 A.