The linear stability of a dielectric fluid filling a cylindrical capacitor is analyzed. The outer or the inner cylinders forming the capacitor may rotate with fixed angular velocities, thus generating a Taylor-Couette flow inside the fluid. A weak, moderate or strong injection of charge is assumed to occur at the anode when a high voltage is applied to the electrodes. The physical mechanisms associated to the instability of the steady flow are discussed. Special attention is paid to the case when the mobility of ions is similar to or smaller than the hydrodynamic mobility of the fluid. ©1998 American Institute of Physics.