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Living systems efficiently use chemical fuel to do work, process information, and assemble patterns despite thermal noise. Whether high efficiency arises from general principles or specific fine-tuning is unknown. Here, applying a recent mapping from nonequilibrium systems to battery-resistor circuits, I derive an analytic expression for the efficiency of any dissipative molecular machine driven by one or a series of chemical potential differences. This expression disentangles the chemical potential from the machine's details, whose effect on the efficiency is fully specified by a constant called the load resistance. The efficiency passes through a switch-like inflection point if the balance between chemical potential and load resistance exceeds thermal noise. Therefore, dissipative chemical engines qualitatively differ from heat engines, which lack threshold behavior. This explains all-or-none dynein stepping with increasing ATP concentration observed in single-molecule experiments. These results indicate that biomolecular energy transduction is efficient not because of idosyncratic optimization of the biomolecules themselves, but rather because the concentration of chemical fuel is kept above a threshold level within cells.