Question

A certain laboratory experiment requires an aluminum wire of length of 30.0 m and a resistance of 3.80 ω at 20.0°c. what diameter wire must be used? (the resistivity of aluminum at 20.0°c is 2.82 ✕ 10−8 ω · m.)

Answer 1

Answer:
diameter = 5.316 * 10^-4 meters

Explanation:
The resistance of the wire can be calculated using the following rule:
R = ΡL / A
where:
R is the resistance = 3.8 ohm
Ρ is the resistivity = 2.82 * 10^−8 ω · m
L is the length of the wire = 30 m
A is the area that we want to calculate
Substitute with the givens in the above equation to get the area as follows:
3.8 = (2.82 * 10^−8 * 30) / A
A = 2.22 * 10^-7 meters^2
Now, the area of the circle is calculated as follows:
Area = pi * (radius)^2
2.22 * 10^-7 = pi * (radius)^2
(radius)^2 = 7.066 * 10^-8
radius = 2.658 * 10^-4 meters
Diameter is double the radius. This means that:
diameter = 2 * 2.658 * 10^-4 = 5.316 * 10^-4 meters

Hope this helps :)