In a tokamak, the electron distribution deviates from a Maxwellian because magnetically untrapped electrons run away parallel to the applied electric field. A new method for calculating the dynamics of the electron distribution is presented. This method is novel because it can treat systems with comparable numbers of trapped and untrapped electrons, and an electric field comparable with (but smaller than) the Dreicer field. The electron distribution function and the plasma resistivity are presented for representative values.