# 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 106 S m−1. What is its resistivity?

Solution: