# Resistivity and Conductivity Solved numerical problems (Worked Solutions)

In this post, we have compiled a bunch of interesting numerical problems on Resistivity and Conductivity. These are Solved numerical problems (Worked Solutions).

## Resistivity and Conductivity numerical problems (solved worksheet)

1 ) **Gold has a conductivity of 45 MS m ^{−1}. What is the resistance of a 0.01 m diameter gold connector that is 0.05m long?**

**Solution:**

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.**

**Solution:**

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.

3 ) **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?**

**Solution:**

4) **A material has a conductivity of 10 ^{6} S m^{−1}. What is its resistivity?**

**Solution:**