It is possible to move, split, merge, and mix liquids in micro fluidic devices by applying spatially varying electric fields that effectively change the surface tension at specific spatial locations. The phenomena is brought about by a competition between surface tension effects (that cause the droplet to bead up because it has been placed on a hydrophobic surface) and electrical forces in the underlying solid dielectric (which attempt to enlarge the liquid/solid contact area so as to relieve electro static forces). In this paper we primarily present an energy minimization model for the equilibrium shape of electrically actuated droplets. By including a realistic amount of liquid resistance, this model captures the effect of contact angle saturation and predicts the experiment data we observe in the UCLA devices. At the close of the paper we also outline our results in modeling the dynamics of the moving, splitting, and merging droplets. This part includes modeling of the 2-phase low-Reynolds fluid dynamics with electrically actuated boundary conditions.