Abstract: The fundamental mechanism of resistance in voltage-biased superconducting films is poorly understood despite its importance as the basis of transition-edge sensors (TESs). TESs are utilized in state-of-the-art microbolometers and microcalorimeters covering a wide range of energies and applications. We present a model for the resistance of a TES based on phase-slip lines (PSLs) and compare the model to data. One of the model's predictions, discrete changes in the number of PSLs, is a possible explanation for the observed switching between discrete current states in localized regions of bias.