When a water droplet is suspended in an immiscible, insulating liquid medium of essentially infinite dimensions and is subjected to a periodically alternating electric field, it will undergo periodic deformation at a frequency twice that of the field. This work examined the periodic deformation and bursting of microsize water droplets in silicone oil moving through a PTFE microchannel with an inner diameter nearly twice that of the droplets, under a periodically alternating electric field normal to the direction of flow. When the sinusoidal electric field was either relatively weak or had a low frequency, the droplets displayed periodic deformation alternating between a prolate ellipsoidal along the electric field direction and a sphere. In contrast, droplets alternated between prolate and oblate shapes when the electric field strength was high or the frequency of the electric field was high. When the applied electric field strength was increased, a constriction formed in the central portion of droplets which had deformed into a prolate ellipsoid. When the electric field strength was further increased, droplets broke into two or more smaller droplets as the result of the inertial force acting on the water in the droplet and the electrostatic force at the interface of the droplet and the surrounding liquid. The majority of the small droplets formed by such breakups subsequently merged into single droplets over the course of time.