What is the resistance of a 4.00 m length of copper wire having a diameter of 2.00 mm at a temperature of 20 degrees?

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To calculate the resistance of a wire, we can use the formula for resistance:

R = (ρ * L) / A

where:
R is the resistance,
ρ is the resistivity of the material (for copper, ρ = 1.7 x 10^-8 Ω·m),
L is the length of the wire,
A is the cross-sectional area of the wire.

First, we need to find the cross-sectional area of the wire. The formula for the area of a circle is:

A = π * r^2

where:
A is the area,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the wire (which is half of the diameter).

Given that the diameter of the wire is 2.00 mm, we can calculate the radius as follows:

r = 2.00 mm / 2 = 1.00 mm = 0.00100 m

Now we can calculate the area:

A = π * (0.00100 m)^2 ≈ π * 1.00 x 10^-6 m^2 ≈ 3.14 x 10^-6 m^2

Next, we can substitute the given values into the resistance formula:

R = (1.7 x 10^-8 Ω·m * 4.00 m) / (3.14 x 10^-6 m^2)

Calculating this expression will give us the resistance of the wire.