We report an experimental and theoretical study of the morphology of desiccation cracks formed in deposits of hematite ellipsoids dried in an externally applied alternating current (ac) electric field. A series of transitions in the crack morphology is observed by modulating the frequency and the strength of the applied field. We also found a clear transition in the morphology of cracks as a function of the aspect ratio of the ellipsoid. We show that these transitions in the crack morphology can be explained by a linear stability analysis of the equation describing the effective dynamics of an ellipsoid placed in an externally applied ac electric field.