Transient charging currents produced by DC voltage applied to a parallel plate capacitor filled with liquid crystal sample (7CB and 8CB) have been studied experimentally. A discontinuous jump of the current magnitude in the nematic phase has been observed for the first time. The shape of the charging current curves has been shown to depend on the applied of the external magnetic field. Experimental results have been explained with a simple model based on molecular alignment and quasi-one-dimensional conductivity.