What is the resistance of 1.0 m of a solid cylindrical metal cable having a diameter of 0.40 inches and a resistivity of 1.68 × 10^-8 Ω ∙ m? A)0.00012 Ω B)0.00021 Ω C)0.0012 Ω D)0.0021 Ω

Question

Quizplus · Accepted Answer

The resistance R of a cylindrical conductor is given by the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. First, convert the diameter from inches to meters (0.40 inches = 0.01016 meters). The radius is half of the diameter, so r = 0.00508 meters. The cross-sectional area A = πr² = π(0.00508)². Then, calculate the resistance: R = (1.68 × 10⁻⁸ Ω ∙ m)(1.0 m) / (π(0.00508 m)²) ≈ 0.00021 Ω.

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