Calculate the resistance of a 1 mile length of wire if the conductivity (sigma) is 5.7x10^5 (ohm-cm)^-1 and the diameter of the wire is 1 inch. The formula for resistance is R = length/(sigma*Cross-sectional area) but all of the units must be consistent. The correct answer is not listed. Select the answer that is nearest the correct answe
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Use the formula
R = Length/[area*conductivity]
For length, use 1 mile converted to centimeters: 160,934 cm
For area, use pi*D^2/4,converted to cm^2
A = 5.067 cm^2
R = 0.0557 ohms
To calculate the resistance of the wire, we need to ensure that all units are consistent.
First, let's convert the length of the wire from miles to centimeters since the conductivity is given in (ohm-cm)^-1.
1 mile = 1.60934 km = 160,934 cm
Next, let's convert the diameter of the wire from inches to centimeters.
1 inch = 2.54 cm
Now, we can calculate the cross-sectional area of the wire using the formula for the area of a circle:
Area = pi * (radius)^2
The radius (r) can be calculated by dividing the diameter by 2:
r = 1 inch / 2 = 0.5 inch = 1.27 cm
Substituting the values into the formula:
Area = pi * (1.27 cm)^2
Finally, we can substitute the computed values into the resistance formula:
R = length / (sigma * Area)
R = 160,934 cm / (5.7x10^5 (ohm-cm)^-1 * pi * (1.27 cm)^2)
Calculating this, we find that the resistance is approximately 14.62 ohms.
Since the correct answer is not listed, you should select the answer nearest to 14.62 ohms from the given options.