Question

A common cylindrical copper wire used in a lab is 841 m long. Find the radius (in mm) of a wire necessary to have 0.5 Ohms of resistance. (The resistivity of copper at room temperature is 1.68×10-8  Ohm × meter). Express the answer (only numerical value) to one decimal place.

Answer 1

The relationship between the resistance R of a wire and its resistivity
`\rho` is given by

`R= (\rho L)/(A)`
where L is the length of the wire and A is its cross sectional area.

In the problem, we have
`R=0.5 \Omega`,
`\rho = 1.68 \cdot 10^(-8) \Omega m` and
`L=841 m`. So we can solve the find the area A:

`A= (\rho L)/(R)=2.83 \cdot 10^(-5) m^2`

For a cylindrical wire, the cross sectional area is given by

`A= \pi r^2`
where r is the radius. We know the value of the area A, so now we can find the radius of the wire:

`r= \sqrt{ (A)/(\pi) }= \sqrt{ (2.83 \cdot 10^(-5)m^2)/(\pi) }=0.003 m=3.0 mm`