# A-level Physics (Advancing Physics)/Resistivity and Conductivity/Worked Solutions

**1. A material has a conductivity of 10 ^{6} 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.