Question

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.

Answer 1

m = 1.93x10 4 -5.18x15m3 gel d = 1 3 , L = 2.4 Km) a) m=1gm = 10² kg - volume = mass 103 density b) L = 2.4 km = 2,4x1000 = 2400 m v= freax Length c Area = y = 5-18x16 8 - 2116x16"'2 2400 = - YAX d) Ral t = 2.44x16 & 2400 - 2.7x16x 2.16 -10 -21X1000 e) Ree = faux t Rew = 1.7x100x 2400 = 4.8 x106s 2-16x10-11