Copper has a resistivity of 168 Times 108 Ohm m and a densit

Copper has a resistivity of 1.68 Times 10^-8 Ohm m, and a density of 8.96 g/cm^3. If I had 2.0 grams of copper, and wanted to make a wire with a resistance of 2.0 Ohms, determine: The radius of the wire that I would require. The length of the wire that I would get.

Solution

a)

Volume

V=mass/density = 2*10^-3/(8.96*10³)=2.23*10^-7 m³

Since V=AL =2.23*10^-7

A =pi*r²

=>pi*r²*L =2.23*10^-7

r = sqrt[7.1*10^-8/L]

Since resistance is given by

R=pL/A =pL/pi*r²

=>2=(1.68*10^-8)*L/pi*(7.1*10^-8/L)

L²=26.57

L=5.15 m

radius of the wire

r=sqrt[7.1*10^-8/5.15]

r=1.17*10^-4 m or 0.117 mm

b)

Length of the wire

L=5.15 m