Use the fact that the resistance of a wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area.
A 10-foot piece of copper wire produces a resistance of 0.2 ohm.Use the constant of proportionality k = 0.000833 to find the diameter of the wire.

(Round the answer up to three decimal places. )

A)0.23 ft
B)0.58 ft
C)0.38 ft
D)0.48 ft
E)0.73 ft

Question

Use the fact that the resistance of a wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. ​
A 10-foot piece of copper wire produces a resistance of 0.2 ohm.Use the constant of proportionality k = 0.000833 to find the diameter of the wire.
​
(Round the answer up to three decimal places. )
​
A)0.23 ft
B)0.58 ft
C)0.38 ft
D)0.48 ft
E)0.73 ft

Quizplus · Accepted Answer

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. This means that the resistance of a wire is equal to a constant multiplied by the length of the wire divided by the cross-sectional area of the wire. The constant of proportionality is different for different materials. For copper, the constant of proportionality is 0.000833.We are given that a 10-foot piece of copper wire produces a resistance of 0.2 ohm. We can use this information to find the diameter of the wire.Let's call the diameter of the wire d. The cross-sectional area of the wire is equal to pi * (d/2)^2 = pi * d^2 / 4.The resistance of the wire is equal to 0.000833 * 10 / (pi * d^2 / 4) = 0.000833 * 40 / (pi * d^2) = 0.0104 / (pi * d^2).We are given that the resistance of the wire is 0.2 ohm. So, we can set up the following equation:0.0104 / (pi * d^2) = 0.2Solving for d, we get:d = sqrt(0.0104 / (pi * 0.2)) = 0.230 ftTherefore, the diameter of the wire is 0.230 ft, which is rounded up to three decimal places as 0.230 ft.

Use the Fact That the Resistance of a Wire Carrying