The relationship between resistance R and resistivity [tex]\rho[/tex] is [tex]R= \frac{\rho L}{A} [/tex] where L is the length of the wire and A its cross section.
The radius of the wire is half the diameter: [tex]r= \frac{d}{2}= \frac{1.6 mm}{2}=0.8 mm=8\cdot 10^{-4} m [/tex] and the cross section is [tex]A=\pi r^2 = \pi (8\cdot 10^{-4} m)^2=2.01\cdot 10^{-6} m^2[/tex]
From the first equation, we can then find the length of the wire when [tex]R=4.8 \Omega[/tex] (copper resistivity: [tex]\rho = 1.724 \cdot 10^{-8} \Omega m[/tex]) [tex]L= \frac{AR}{\rho}= \frac{(2.01\cdot 10^{-6} m^2)(1.724 \cdot 10^{-8} \Omega m)}{4.8 \Omega}=7.21 \cdot 10^{-15} m [/tex]
