Recent work with Lorentz-induced mixing of planar diffusion flames has required an understanding of their behavior when subjected to electric fields. Extensive work with electric currents in premixed flames has been reported, but the current-carrying properties of planar diffusion flames have not previously been characterized. In this work, a cesium-seeded methane/oxygen diffusion flame is investigated under various conditions. A d.c. electric field is applied transverse to the flow direction but parallel to the flame sheet. Two distinct modes of discharge are observed, one sustaining currents an order of magnitude larger than the other. The transition between the modes is described, and the conditions supporting each type of discharge are reported. Comparisons are made with similar observations reported in the literature for premixed flames, and differences are contrasted in light of fundamental differences in the characters of the flames. The effects of electrode gap and location downstream of the burner exit plane are examined. Predictions of the expected temperature rise during each arc mode are made based on theoretical considerations. Optically measured temperatures in the discharge region are reported and compared with predicted values.