Final answer:
The resistance of the 20.0-meter piece of 12-gauge copper wire is approximately 0.093 Ω.
Step-by-step explanation:
The resistance of a wire can be calculated using the formula:
R = (ρ * L) / A
where:
- R is the resistance
- ρ is the resistivity of the material
- L is the length of the wire
- A is the cross-sectional area of the wire
For the given copper wire, we need to find the resistivity and the cross-sectional area:
The resistivity of copper is approximately 1.68 x 10-8 Ω•m.
The cross-sectional area of the wire can be calculated using the formula for the area of a circle:
A = π * r2
where:
- A is the cross-sectional area
- π is approximately 3.14159
- r is the radius of the wire, which is half of the diameter
Using the given diameter of 2.053 mm, the radius is 1.0265 mm or 0.0010265 m.
Now we can plug in the values into the formula for resistance:
R = (1.68 x 10-8 Ω•m * 20.0 m) / (π * (0.0010265 m)2)
Simplifying the expression:
R ≈ 0.093 Ω
Therefore, the resistance of the 20.0-meter piece of 12-gauge copper wire is approximately 0.093 Ω.