Answer : The overall resistance of the wire is [tex]6.617\times 10^{-4}ohm[/tex]
Explanation :
First we have to determine the volume of copper wire.
Density of copper wire = [tex]0.00896kg/mm^3[/tex]
[tex]Volume=\frac{Mass }{Density}=\frac{24kg}{0.00896kg/mm^3}=2678.57mm^3[/tex]
Now we have to determine the area.
[tex]Area=\pi r^2[/tex]
where,
r = radius of copper wire = 1.63 mm
[tex]Area=3.14\times (1.63mm)^2=8.343mm^2[/tex]
Now we have to determine the length of the wire.
[tex]\text{Length of the wire}=\frac{\text{Volume of wire}}{\text{Area of wire}}[/tex]
[tex]\text{Length of the wire}=\frac{2678.57mm^3}{8.343mm^2}=321.06mm=3.2106\times 10^{-4}km[/tex]
conversion used : [tex](1mm=10^{-6}km)[/tex]
Now we have to determine the overall resistance of the wire.
[tex]\text{Overall resistance}=\text{Length of wire}\times \text{Resistance of wire}[/tex]
[tex]\text{Overall resistance}=3.2106\times 10^{-4}km\times 2.061ohm/km[/tex]
[tex]\text{Overall resistance}=6.617\times 10^{-4}ohm[/tex]
Therefore, the overall resistance of the wire is [tex]6.617\times 10^{-4}ohm[/tex]
