The conductivity of plasma can be related to its microscopic properties using the Drude model

$ \sigma \approx \frac{n q^2}{m \omega} $

where $ n $ is the number density, $ q $ is the elementary charge, $ m $ is the mass of the electron and $ \omega $ is the collision rate. The latter is given by

$ \omega \approx n \Sigma v $

where $ \Sigma $ is the cross section for collisions and $ v $ is the thermal velocity. To calculate the cross section, we note the impact parameter below which a scattering angle between an electron and a proton will be of order unity

$ b \approx \frac{q^2}{m v^2} $


$ \Sigma \approx b^2 \approx \frac{q^4}{m^2 v^4} $

Finally, the resistivity is given by

$ \eta = \frac{1}{\sigma} \approx \frac{m}{n q^2} n v \frac{q^4}{m^2 v^4} \approx \frac{q^2}{m v^3} \approx \frac{q^2 \sqrt{m}}{\left(k T \right )^{3/2}} $

where $ T \, $ is the temperature and $ k $ is the Boltzmann constant.