A-level Physics (Advancing Physics)/Resistivity and Conductivity/Worked Solutions
1. A material has a conductivity of 106 S m-1. What is its resistivity?
2. A pure copper wire has a radius of 0.5mm, a resistance of 1 MΩ, and is 4680 km long. What is the resistivity of copper?
3. Gold has a conductivity of 45 MS m-1. What is the resistance of a 0.01m across gold connector, 0.05m long?
First, work out resistivity:
Then, substitute everything possible into the resistivity formula:
4. A strand of metal is stretched to twice its original length. What is its new resistance? State your assumptions.
The material does not change, so resistivity is constant. Length doubles, and we know that volume must be constant.
V = AL
A = V/L
When we double L, we get:
We are assuming that ρ and V are constant.
5. Which has the greater resistivity: a plank or a piece of sawdust, made from the same wood?
Sawdust and a plank are artefacts, not materials. Hence, they do not have a resistivity. Even if they did, they are made of the same thing, so they would have equal resistivity.