Find the resistance of a piece of 8 AWG copper wire 400 Ft long. Assume a temperature of 20 degree C.
The resistance of a wire can be calculated using the formula:
R = (ρ * L) / A
Where:
R = Resistance
ρ = Resistivity of copper
L = Length of the wire
A = Cross-sectional area of the wire
First, we need to find the value of ρ for copper at 20 degrees C. The resistivity of copper at 20 degrees C is approximately 1.724 x 10^-8 Ω·m.
Next, we need to calculate the cross-sectional area of an 8 AWG wire. The cross-sectional area of an 8 AWG wire is approximately 8.37 mm^2.
Converting the length to meters:
400 ft = 400 * 0.3048 = 121.92 m
Finally, we can calculate the resistance:
R = (1.724 x 10^-8 Ω·m * 121.92 m) / 8.37 mm^2
R = (0.0000020947 Ω·m) / (8.37 x 10^-6 m^2)
R = 0.25 Ω
Therefore, the resistance of a piece of 8 AWG copper wire 400 ft long at 20 degrees C is approximately 0.25 Ω.