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