Question

a length of #8 copper wire (radius = 1.63 mm) has a mass of 24.0 Kg and a resistance of 2.061 Ohm per Km. What is the over all resistance of the wire?

Answer 1

V = m / ρ
V = (23,200/8.96) × 1000
V = 2,589,285.71 mm³

Now we have volume and given the radius we can solve for its length.
L = V/πr²
L = (2,589,285.71/(π×1.63²))/1×10^6
L = 0.31 km

So
R = rL
R = 2.061(0.31)
R = .6389 Ω

End.

Answer 2

Answer : The overall resistance of the wire is
`6.617* 10^(-4)ohm`

Explanation :

First we have to determine the volume of copper wire.

Density of copper wire =
`0.00896kg/mm^3`

`Volume=(Mass )/(Density)=(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* (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}=(2678.57mm^3)/(8.343mm^2)=321.06mm=3.2106* 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}* \text{Resistance of wire}`

`\text{Overall resistance}=3.2106* 10^(-4)km* 2.061ohm/km`

`\text{Overall resistance}=6.617* 10^(-4)ohm`

Therefore, the overall resistance of the wire is
`6.617* 10^(-4)ohm`