An aluminum wire has a diameter of 0.395 mm. What length of the wire has a resistance of 2.60 Ω?
m
To find the length of the wire, we can use the formula:
Resistance (R) = Resistivity (ρ) * Length (L) / Cross-sectional area (A)
Rearranging the formula, we can solve for the length:
Length (L) = (Resistance (R) * Cross-sectional area (A)) / Resistivity (ρ)
First, let's calculate the cross-sectional area of the wire.
The cross-sectional area (A) of a wire can be calculated using the formula:
A = π * (diameter/2)^2
Given: Diameter of the wire = 0.395 mm.
Converting the diameter to meters:
Diameter = 0.395 mm = 0.395 * 10^(-3) m
Now, we can calculate the cross-sectional area (A):
A = π * (0.395 * 10^(-3)/2)^2
Next, we need to determine the resistivity (ρ) of aluminum. The resistivity of a material is typically given in a table or can be found online. For aluminum, the resistivity is approximately 2.65 x 10^(-8) Ω*m.
Now, we have all the required values to calculate the length (L):
Length (L) = (Resistance (R) * Cross-sectional area (A)) / Resistivity (ρ)
Substituting the given values:
Length (L) = (2.60 Ω * A) / (2.65 x 10^(-8) Ω*m)
Calculating the cross-sectional area (A) using the formula above, and substituting it back into the equation:
Length (L) = (2.60 Ω * (π * (0.395 * 10^(-3)/2)^2)) / (2.65 x 10^(-8) Ω*m)
Evaluating this equation will give us the length of the wire in meters.