Embodiments of the present disclosure describe techniques and configurations for controlling current in a non-volatile random access memory (NVRAM) device. In an embodiment, the NVRAM device may include a plurality of memory cells coupled to a plurality of bit lines forming a bit line node with parasitic capacitance. Each memory cell may comprise a switch device with a required level of a holding current to maintain an on-state of the cell. A voltage supply circuitry and a controller may be coupled with the NVRAM device. The controller may control the circuitry to provide a current pulse that keeps a memory cell in on-state. The pulse may comprise a profile that changes over time from a set point to the holding current level, in response to a discharge of the bit line node capacitance through the memory cell after the set point is achieved. Other embodiments may be described and/or claimed.