Suppose that you wish to fabricate a uniform wire out of 085

Suppose that you wish to fabricate a uniform wire out of 0.850 g of copper. Assume the wire has a resistance R = 0.500 , and all of the copper is used.

(a) What will be the length of the wire? in (m)

    (b) What will be the diameter of the wire? in (µm)

Solution

density copper 8960 kg/m³

Resistance of a wire in
R = L/A
is resistivity of the material in -m
L is length in meters
A is cross-sectional area in m²
A = r², r is radius of wire in m
resistivity Cu 17.2e-9 -m or 17.2e-6 ohm-mm



Use the density number above to convert to volume

0.850 e-3 kg / 8960 kg/m³ = 9.49e-8 m³

cylinder V = r²h
9.49e-8 = r²L

R = L/A
R = L/r²
0.5 = (17.2e-9)L/r²

you have two equations in two unknowns
9.49e-8 = r²L
0.5 = (17.2e-9)L/r²

L = 9.49e-8 / r²
L = 0.5r² / (17.2e-9)

9.49e-8 / r² = 0.5r² / (17.2e-9)
0.5r²(r²) = 9.49e-8(17.2e-9)
r = 9.49e-8(17.2e-9) / 0.5²
r = 3.307691e-16
r = 0.0001349 m or 135 µm so diameter= 270µm

L = 9.49e-8 / r² = 1.66 m