What is the resistance of 125 m of aluminum wire that has a diameter of 0.8118 mm?
The resistivity of aluminum is 2.824 x 10^-8 (omega) m.
I need help with the set up. we've been using R = V/I, but haven't had anything with resistivity. I don't know where to place this, diameter, etc. Please help. Thank you.
resistance= resisitivyOfAluminum*length/area
figure the area of the crosssection, and look up of resistivity of alumnium
To calculate the resistance of the aluminum wire, you need to use the following formula:
R = (ρ * L) / A
where:
R is the resistance
ρ (rho) is the resistivity of aluminum
L is the length of the wire
A is the cross-sectional area of the wire
First, let's calculate the cross-sectional area of the wire:
1. The wire has a diameter of 0.8118 mm. To find the radius, divide the diameter by 2:
Radius = 0.8118 mm / 2 = 0.4059 mm
2. Convert the radius from millimeters to meters:
Radius = 0.4059 mm * (1 meter / 1000 mm) = 0.0004059 meters
3. Calculate the cross-sectional area of the wire using the formula for the area of a circle:
A = π * r^2
A = π * (0.0004059 meters)^2
Now that we have the cross-sectional area, we can calculate the resistance:
4. The length of the wire is given as 125 m, so plug in the values into the resistance formula:
R = (ρ * L) / A
Substituting the given values:
R = (2.824 x 10^-8 (omega) m * 125 m) / (π * (0.0004059 meters)^2)
5. Simplify and calculate the resistance using a calculator:
R ≈ 0.2205 (omega)
Therefore, the resistance of the 125 m aluminum wire with a diameter of 0.8118 mm is approximately 0.2205 ohms.