We report a previously unseen non-ohmic effect in which the resistivity of carbon nanotube fibers immersed in polar liquids is modulated by the applied electric field. This behavior depends on the surface energy, dielectric constant, and viscosity of the immersion media. Supported by synchrotron SAXS and impedance spectroscopy, we propose a model in which the gap distance, and thus the conductance, of capacitive interbundle junctions is controlled by the applied field.