Calculate the resistance of a piece of aluminum wire with a diameter of 100 mils and a length of two miles, at 68°f. hint: be sure to first convert mils to cmils and use the k value for aluminum found in the reference. (round the final answer to two decimal places.)

 

Explanation:

The resistance of an aluminum wire is given by



where:



Since the resistivity is in ohm-meters, we need to convert the length to meters and the area to square meters. But we need to convert mils to cmils first to get the cross sectional area of the wire.

To convert mils to cmils, we get the square of the diameter of the circle in mils because 1 cmil (or circular mil) is the area of the circle whose diameter is 1 mil. So, since the diameter of the wire is 100 mils, the cross-sectional area of the wire in cmils is given by:



Note that we convert the area in terms of scientific notation because the resistivity is expressed in scientific notation and it is easier to multiply very large and very small numbers if they are expressed in scientific notation.

Now, since , the cross sectional area of the wire is equal to 




Since 1 mile = 1,609.344 meters, 2 miles = 2 × 1,609.344 meters = 3,218.688 meters = . . 

Hence the resistance is given by