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Unintentional doping of the active layer is a source for lowered device performance in organic solar cells. The effect of doping is to induce a space-charge region within the active layer, generally resulting in increased recombination losses. The impact of a doping-induced space-charge region on the current-voltage characteristics of low-mobility solar cell devices is clarified by means of analytical derivations and numerical device simulations. It is found that in the case of a doped active layer, the collection efficiency of photogenerated charge carriers is independent of the light intensity and exhibits a distinct voltage dependence, resulting in an apparent electric field dependence of the photocurrent. Furthermore, an analytical expression describing the behavior of the photocurrent is derived. The validity of the analytical model is verified by numerical drift-diffusion simulations and demonstrated experimentally on solution-processed organic solar cells. Based on the theoretical results, conditions of how to overcome charge collection losses caused by doping are discussed. Furthermore, the presented analytical framework provides tools to distinguish between different mechanisms leading to voltage-dependent photocurrents.