The effect of the instantaneous application of an electric current during the directional solidification of a binary alloy is considered. The initial state consists of steady-state solidification at constant velocity. It is assumed that the electric current is sufficiently small that its application can be treated as a small perturbation. The problem is solved by Laplace transform techniques and the results are compared to numerical calculations for arbitrary currents. The Laplace transform allows for an understanding of the discontinuities resulting from the discontinuous electric pulse.