Transport of carriers induced in high resistivity materials as a result of a short duration ionizing process is considered for the case where the region of ionization extends throughout the interelectrode distance. A simple one-carrier model, neglecting carrier recombination and diffusion, is used to derive expressions for the induced charge and current flowing through the external circuit, and for the carrier transit time, when the applied field is greater than half the maximum field set up by the immobile carrier space charge. It is concluded that under certain conditions the shape of the current or charge pulses may be used to determine the electron mobility in films and thin crystals of low-mobility solids.