In a three-dimensional device like a stellarator, the ambipolar electric field must be determined self-consistently from the ambipolarity constraint and can have a significant effect on transport through the diffusion coefficients. A differential formulation and an algebraic formulation for the electric field are solved, together with the density and temperature equations. The results are compared, and in both cases multiple electric field solutions can exist, with bifurcations occurring between different solutions. It is shown that heating of the electrons encourages bifurcation to the more favourable positive electric field root.