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Analytical and equivalent-circuit models based on numerical solutions for a-Si:H solar cells are presented. The dependencies among such variables as recombination rate and electrical field on terminal and optical excitation are discussed. Based on our physical interpretation of the numerical solutions, we propose an equivalent-circuit model which separates the currents into photocollected and back injected components. This model clarifies the concept of the limiting carrier and points out that the limiting carrier is the carrier with the least photocollected current. Analytical expressions for uniformly and strongly absorbed light are derived.