Hepatitis B virus (HBV) infection is a deadly liver disease. The main aim of this work is to explore the role of cytoplasmic recycling of rcDNA-containing capsids in the hepatitis B virus (HBV) infection. To this purpose, considering the recycling of capsids, a noval mathematical model is proposed in order to understand the dynamics of this viral infection in a better way. Through a rigorous comparison with experimental data obtained from four chimpanzees, the proposed model exhibits a robust alignment with the dynamics of infection. The effects of three parameters (recycling rate, virus production rate, and volume fraction of newly produced capsids) are examined, revealing an interesting observation: the inclusion of recycling reverses the influence of both virus production rate and the volume fraction of newly produced capsids in infection. A comprehensive global sensitivity analysis is conducted to identify the most positively as well as negatively sensitive parameters for each compartment in the model. In conclusion, this study underscores that the accumulation of rcDNA-containing capsids within the infected hepatocyte is a key factor contributing to the exacerbation of the disease. In addition, another major finding of our study is that due to recycling of capsids, the number of released viruses increases in spite of low virus production rate. In other words, the recycling of capsids acts as a positive feedback loop in the viral infection.