Aluminum has a resistivity of 2.7*10-8 Ùm. What would be the resistance of 100 m of aluminum wire with a cross-sectional area of 2*10-4 m2?
2.7*10^-8 is the resistivity of Al, in ohm-meters. Call it rho.
The resistance is R = (rho)*length/area
Do the calculation
To calculate the resistance of a wire, we can use the formula:
Resistance (R) = Resistivity (ρ) * Length (L) / Cross-sectional Area (A)
Given:
Resistivity (ρ) of aluminum = 2.7 * 10^-8 Ωm
Length (L) of aluminum wire = 100 m
Cross-sectional Area (A) of aluminum wire = 2 * 10^-4 m^2
We can substitute these values into the formula to find the resistance:
R = (2.7 * 10^-8 Ωm) * (100 m) / (2 * 10^-4 m^2)
Now, let's simplify this expression step by step:
Step 1: Calculate the denominator of the fraction:
(2 * 10^-4 m^2) = 2 * (10^(-4))^2 m^2 = 2 * 10^(-8) m^2
Step 2: Substitute the values:
R = (2.7 * 10^-8 Ωm) * (100 m) / (2 * 10^-8 m^2)
Step 3: Simplify:
R = (2.7 * 10^-8 Ωm * 100 m) / (2 * 10^-8 m^2)
R = (2.7 * 10^-6 Ω) / 2
R = 1.35 * 10^-6 Ω
Therefore, the resistance of 100 m of aluminum wire with a cross-sectional area of 2 * 10^-4 m^2 is approximately 1.35 * 10^-6 Ω.