Bulk Properties of Copper: Density and Resistivity Answers

1. If you have two identical saucepans, one made of copper and the other of aluminium, how many times heavier will the copper one be?

Just use the ratio of their densities; 8940/2700 = 3.31 times heavier.

2. Compare the resistivities of silver and nichrome alloy. How many times better is silver than nichrome at conducting electricity?

The ratio of resistivity is 1.6 x 10-6 / 1.6 x 10-8 = 100

3. Calculate the resistance of a copper cable 50 mm in diameter and 30 km long.

R = ρ ( L /A)

= (1.7 x 10-8 x 30 x 103)/ (3.14 x 25 x 25 x 10-6)

  = 0.26 Ohms

4. If you had to replace the cable in question 3 with aluminium, what would the diameter need to be to have the same resistance?

RAl = RCu
Al x L) / (π x rAl2) = (ρCu x L)/( π x rCu2)

Cancelling π and L:

2.7 x 10-8 / rAl2 = 1.7 x 10-8/ rCu2
rAl2 = (2.7 x 10-8) / (1.7 x 10-8)  x rCu2
rAl = √ (2.7 x 10-8) / (1.7 x 10-8)  x rCu
rAl = √(2.7/1.7) x rCu  = 31.5 mm

Diameter of the aluminium cable would need to be:  2 x rAl = 63 mm

5. The unit of conductivity is the Siemens m-1. Find out who Siemens was and where you will find his name today.

Werner von Siemens. He founded what is now one of the largest multinational engineering companies in the world.

Resistivities
Material Resistivity
ρ (Ω·m)
Insulators
Teflon 1.0 x 1023
Quartz 7.5 x 1017
Rubber 7.5 x 1017
Glass 7.5 x 1017
Conductors
Nichrome alloy 1.6 x 10-6
Lead 2.2 x 10-7
Iron 9.7 x 10-8
Tungsten 9.7 x 10-8
Aluminium 2.7 x 10-8
Gold 2.2 x 10-8
Copper 1.7 x 10-8
Silver 1.6 x 10-8
Graphene 1.0 x 10-8