Non-electrified clouds in the fair-weather part of the Global Electric Circuit (GEC) reduce conductivity because of the limited mobility of charge due to attachment to cloud water droplets, effectively leading to a loss of ions. A high-resolution GEC model, which numerically solves the Poisson equation, is used to show that in the fair-weather region currents partially flow around non-electrified clouds, with current divergence above the cloud, and convergence below the cloud. An analysis of this effect is presented for various types of non-electrified clouds, i.e. for different altitude extents, and for different horizontal dimensions, finding that the effect is most pronounced for high clouds with a diameter below 100 km. Based on these results, a method to calculate column and global resistance is developed that can account for all cloud sizes and altitudes. The CESM1(WACCM) Earth System Model as well as ISCCP cloud data are used to calculate the effect of this phenomenon on global resistance. From CESM1(WACCM), it is found that when including non-electrified clouds in the fair-weather estimate of resistance the global resistance increases by up to 73%, depending on the parameters used. Using ISCCP cloud cover leads to an even larger increase, which is likely to be overestimated because of time-averaging of cloud cover. Neglecting current divergence/convergence around small clouds overestimates global resistance by up to 20%, whereas the method introduced by previous studies underestimates global resistance by up to 40%. For global GEC models, a conductivity parametrization is developed to account for the current divergence/convergence phenomenon around non-electrified clouds. Conductivity simulations from CESM1(WACCM) using this parametrization are presented.