This research investigates the internal resistance and capacitance characteristics of Lithium Iron Phosphate (LiFePO4) batteries utilizing an equivalent circuit model based on resistor-capacitor (RC) networks. The growing integration of batteries in diverse applications, including electric vehicles and renewable energy systems, necessitates robust battery health monitoring strategies. This work employs current and voltage data acquired during battery discharge, subsequently analyzed using MATLAB 2023b software to determine the pertinent RC parameters. A third-order Equivalent Circuit Model (ECM) of RC, comprising three RC pairs, is implemented to enhance the precision of parameter estimation. The results demonstrate a strong correlation between the number of RC pairs and the accuracy of dynamic battery response representation. A higher-order model generally yields more precise estimations of battery performance. However, increasing model complexity can lead to overfitting, potentially diminishing the model's ability to accurately reflect actual battery behavior. This study contributes significantly to the understanding of LiFePO4 battery internal characteristic modeling and underscores the importance of balancing model fidelity with computational complexity.