You are working at a company that manufactures electrical wire. Gold is the most ductile of all metals: it can be stretched into incredibly long, thin wires. The company has developed a new technique that will stretch 1.00 g of gold into a wire of length L= 2.40 km and uniform diameter.
a) What is 1 gm in kg, and what is the volume of 1 gm of gold?
The mass density of gold ρ= 1.93 x 10^4 kg/m3. Watch units!
b) What is the length of the wire in m? 1 km = 1000 m.
Treat the wire as a cylinder, the volume V = AL, A = cross sectional area (m2) and L = length (m).
c) With the volume from a), what is the cross sectional area, A,then find the radius of the wire: A =πr2.
The resistivity of gold is ρAu= 2.44 x 10^-8 Ωm
d) Using the area from c), what is the resistance of this gold wire?
This should be a large number. Compare this to a copper wire with the same dimensions.The resistivity of copper is ρCu= 1.7 x 10^-8Ωm
e) Using the area from c), what is the resistance of this copper wire? A copper wire could never be made this small, (Cu is not as ductile as Au), so this is just for comparison.
You are working at a company that manufactures electrical wire. Gold is the most ductile of...
Gold is the most ductile of all metals. For example, one gram of gold can be drawn into a wire 2.08 km long. The density of gold is 19.3 x 103 kg/m2, and its resistivity is 2.44 × 10-8 ?·m, what is the resistance of such a wire at 20.0°C? Your response differs from the correct answer by more than 10%. Double check your calculations. MII
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