In this study, the lithium-ion (Li-ion) battery type, which has a high-power density and utilizes lithium as the primary conductive terminal, has been employed. Within the scope of this research, a one-dimensional isothermal Li-ion battery model has been investigated under various electrolyte (both liquid and solid) and electrode materials using the COMSOL Multiphysics software. The obtained simulation results have been corroborated with information sourced from the literature and establish a foundational framework for future studies. The average range of electrolyte salt concentration in battery components is slightly higher for batteries utilizing polymer electrolytes compared to those with liquid electrolytes. During discharge at five different C-rates, Li-ion batteries with liquid electrolytes displayed higher voltage than those with polymer electrolytes. On the other hand, the one with the lithium iron phosphate (LFP) positive electrode exhibits the greatest variation in lithium concentration at the surface of the positive electrode at the end of discharge. Conversely, the battery using a LiNiO2 cathode shows the smallest surface lithium concentration variation during the same period. This pattern is similarly observed for the lithium concentration at the center of the electrode particles. The presented model can be used to explore innovative electrolyte and electrode materials to improve the design of Li-ion batteries.