Question

You have a lump of copper with a mass of 1.8 grams. Copper is ductile so you can draw it into a cylindrical wire. You draw it into a wire with length L and diameter D so that it has a resistance of 2LaTeX: \OmegaΩ What is the length of the wire in m?

Answer 1

Required information:

Density of copper = $8.96\ \text{g/cm}^3$

Resistivity of copper = $1.68\times10^{-8}\ \Omega\text{m}$

Answer:

The length of the wire is 4.9 m.

Explanation:

Volume of copper = Mass of the copper/Density of copper

$V = \dfrac{1.8\ \text{g}}{8.96\ \text{g/cm}^3} = 0.20\ \text{cm}^3 = 2\times 10^{-7}\ \text{m}^3$

Since it is a cylinder of cross-sectional area, A, and length, l

$Al = 2\times 10^{-7}$

$A= \dfrac{2\times 10^{-7}}{l}$

Resistance is given by

$R = \rho\dfrac{l}{A}$

where l is the length, A is the cross-sectional area and ρ resistivity of copper.

$2 = (1.68\times10^{-8})\dfrac{l}{A}$

$A = 8.4\times10^{-9}\times l$

Equating both equations of A,

$\dfrac{2\times 10^{-7}}{l} = 8.4\times10^{-9}\times l$

$l^2 = 23.809\ldots$

$l = \sqrt{23.809\ldots} = 4.9\text{ m}$