Final answer:
The resistance of a 1.00-km length of 0-gauge copper wire can be calculated using the resistivity of copper, cross-sectional area, and length of the wire. However, the value calculated does not match any of the provided answer options, indicating a potential error in the question.
Step-by-step explanation:
To calculate the resistance of a 1.00-km length of 0-gauge copper wire used for power transmission, we must use the formula for resistance:
R = ρL/A
where R is the resistance, ρ (rho) is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area.
The resistivity of copper at 20°C is typically about 1.68×10⁻⁸ Ω·m. The length of the wire, L, is 1.00 km or 1000 meters. The cross-sectional area, A, can be obtained using the diameter of the wire, which is 8.252 mm, hence the radius r is 4.126 mm or 4.126×10⁻⁸ meters. The area A is calculated using the formula for the area of a circle, πr².
A = π(4.126×10⁻)^2 = 5.346×10⁻⁵ m^2
Now, substituting the values into the formula for resistance:
R = (1.68×10⁻⁸ Ω·m)(1000 m) / (5.346×10⁻⁵ m^2)
R ≈ 0.31 Ω
However, none of the answer options provided (a. 0.04 Ω, b. 0.08 Ω, c. 0.12 Ω, d. 0.16 Ω) match the calculated value. It seems there might be a mistake in the question or the options provided.