Microbial fuel cells (MFCs) serve two main purposes: clean energy production and wastewater treatment. This study examines the impact of different carbon sources on MFC performance and develops a mathematical model to replicate the polarization curve. The biological reactor employed three types of carbon sources: glucose as a simple feed, microcrystalline cellulose (MCC), and a slurry of the organic component of municipal solid waste (SOMSW) as complex feeds. The MFCs were operated in both open and closed circuit modes. The maximum open circuit voltages achieved were 695 mV for glucose, 550 mV for MCC, and 520 mV for SOMSW as substrates. The influence of the substrate in closed circuit mode was also investigated, resulting in maximum power densities of 172 mW/m2, 55.5 mW/m2, and 47.9 mW/m2for glucose, MCC, and SOMSW as substrates, respectively. In the second section, a mathematical model was developed to depict the polarization curve while considering voltage losses, namely activation, ohmic, and concentration loss, with an average relative error (ARE) of less than 10%. The mathematical models demonstrated that the activation loss of voltage increased with the complexity of the substrate and reached its peak value when SOMSW was used as the substrate.