If a mile of 24-gauge copper wire has a resistance of 0.14 kΩ and the resistivity of copper is 1.7 × 10−8 Ω ⋅ m, what is the diameter of the wire? (1 mile = 1.6 km)
A)0.40 mm
B)0.50 mm
C)0.63 mm
D)0.80 mm
E)0.25 mm

Question

Quizplus · Accepted Answer

First, convert 1 mile to meters: 1 mile = 1.6 km = 1600 m
Then, use the formula for the resistance of a wire: R = (ρL)/A, where R is resistance, ρ is resistivity, L is length, and A is cross-sectional area (diameter squared).
We can rearrange this formula to solve for A: A = (ρL)/R
Plugging in the given values: A = [(1.7 x 10^-8 Ω m)(1600 m)]/0.14 kΩ = 0.194 mm^2
Solving for diameter (remember that A = π/4 x d^2): d = sqrt((4A)/(π)) = sqrt((4 x 0.194)/(π)) = 0.495 mm, which rounds to 0.50 mm. Therefore, the answer is B.

If a Mile of 24-Gauge Copper Wire Has a Resistance