Required information:
Density of copper = [tex]8.96\ \text{g/cm}^3[/tex]
Resistivity of copper = [tex]1.68\times10^{-8}\ \Omega\text{m}[/tex]
Answer:
The length of the wire is 4.9 m.
Explanation:
Volume of copper = Mass of the copper/Density of copper
[tex]V = \dfrac{1.8\ \text{g}}{8.96\ \text{g/cm}^3} = 0.20\ \text{cm}^3 = 2\times 10^{-7}\ \text{m}^3[/tex]
Since it is a cylinder of cross-sectional area, A, and length, l
[tex]Al = 2\times 10^{-7}[/tex]
[tex]A= \dfrac{2\times 10^{-7}}{l}[/tex]
Resistance is given by
[tex]R = \rho\dfrac{l}{A}[/tex]
where l is the length, A is the cross-sectional area and ρ resistivity of copper.
[tex]2 = (1.68\times10^{-8})\dfrac{l}{A}[/tex]
[tex]A = 8.4\times10^{-9}\times l[/tex]
Equating both equations of A,
[tex]\dfrac{2\times 10^{-7}}{l} = 8.4\times10^{-9}\times l[/tex]
[tex]l^2 = 23.809\ldots[/tex]
[tex]l = \sqrt{23.809\ldots} = 4.9\text{ m}[/tex]
