25.8k views
2 votes
A copper wire has a square cross section 3.0 mm on a side. The wire is 4.1 m long and carries a current of 4.0 A. The density of free electrons is 8.5×10²⁸ m⁻³. What is the resistance of the wire?

1 Answer

1 vote

Final answer:

The resistance of the copper wire is 7.4 x 10^-2 Ω.

Step-by-step explanation:

To calculate the resistance of the copper wire, we can use the formula R = ρL/A, where ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area of the wire. First, we need to find the cross-sectional area of the wire, which is given as a square with a side length of 3.0 mm. So, the area is A = (3.0 mm)^2 = 9.0 mm^2. Next, we convert the area to meters squared: A = 9.0 mm^2 * (1 m / 1000 mm)^2 = 9.0 x 10^-6 m^2. Now, we can calculate the resistance using the given length of the wire and the resistivity of copper: R = (1.68 x 10^-8 Ω / m) * (4.1 m / 9.0 x 10^-6 m^2) = 7.4 x 10^-2 Ω. Therefore, the resistance of the copper wire is 7.4 x 10^-2 Ω.

User Parsifal
by
7.5k points