Most telephone cables are made of copper wire of either 24 or 26 gauge.If the resistance of 24-gauge wire is 137 $\Omega$/mile and the resistance of 26-gauge wire is 220 $\Omega$/mile,what is the ratio of the diameter of 24-gauge wire to that of 26-gauge wire?
A)1.6
B)1.3
C)0.62
D)0.79
E)0.88

Question

Quizplus · Accepted Answer

The resistance of a wire is proportional to its length and inversely proportional to its cross-sectional area. The diameter of 24-gauge wire is larger than that of 26-gauge wire. Let the ratio of their diameters be x. Then, the cross-sectional area of the 24-gauge wire is (x/2)^2 times that of the 26-gauge wire. Therefore, the resistance of the 24-gauge wire is (x/2)^2 times that of the 26-gauge wire. Equating this to the given values, we get (x/2)^2 = 137/220. Solving for x, we get x = sqrt((137/220)*4) = 1.3. Therefore, the ratio of the diameter of 24-gauge wire to that of 26-gauge wire is 1.3.

Most Telephone Cables Are Made of Copper Wire of Either Ω\OmegaΩ

Most Telephone Cables Are Made of Copper Wire of Either $\Omega$