Question

14 gauge copper wire has a diameter of 1.6 mm. what length of this wire has a resistance of 4.8ω?

Answer 1

The relationship between resistance R and resistivity
`\rho` is

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

The radius of the wire is half the diameter:

`r= (d)/(2)= (1.6 mm)/(2)=0.8 mm=8\cdot 10^(-4) m`
and the cross section is

`A=\pi r^2 = \pi (8\cdot 10^(-4) m)^2=2.01\cdot 10^(-6) m^2`

From the first equation, we can then find the length of the wire when
`R=4.8 \Omega` (copper resistivity:
`\rho = 1.724 \cdot 10^(-8) \Omega m`)

`L= (AR)/(\rho)= ((2.01\cdot 10^(-6) m^2)(1.724 \cdot 10^(-8) \Omega m))/(4.8 \Omega)=7.21 \cdot 10^(-15) m`