What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be 6.0 Ω? The resistivity of this metal is 1.68 × 10^-8Ω ∙ m.

Question

Quizplus · Accepted Answer

The resistance R of a wire is given by R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. Solving for A gives A = ρL/R. Substituting the given values, A = (1.68 × 10^-8 Ω∙m)(120 m) / 6.0 Ω = 3.36 × 10^-7 m². The area of a circle is A = π(d/2)², so d = 2√(A/π). Substituting A = 3.36 × 10^-7 m² gives d ≈ 0.65 mm.

What Must Be the Diameter of a Cylindrical 120-M Long