A mathematical model that describes the evolution of the current and voltage distributions in a 1D conductor interacting with a system of potentials is presented. The model can be used to describe transient and steady-state harmonic electric processes in a nonmagnetic system. The evolution of voltage in a thin distributed conductor is approximately described using nonuniform diffusion equation with spatially inhomogeneous coefficients. In addition, the formulas that describe the distributions of voltage and current phasors along the conductor are derived for harmonic regimes. The 1D procedure is tested for a hypothetical high-voltage system that contains a distributed conductor and three electrodes. The verification provided solutions to several harmonic and transient problems. The error of the 1D model is studied, and the applicability conditions are formulated.