The potential relaxation instability (PRI) can be excited in the magnetized plasma column of a single-ended Q-machine by drawing an electron current to a collector. This can either be the terminating tungsten plate (the cold plate (CP) or a grid (G) inserted in between. The frequency of the PRI, which according to the standard model should be solely determined by the length of the system, in fact also depends on the collector bias, the plasma density and the magnetic field. If, however, the reduction of the system length due to the electron-rich sheath in front of the collector is taken into account, in a certain range the PRI frequency becomes more independent of the external parameters.