In an RC circuit, the current through the capacitor approaches zero after a long period, allowing for the simplification of the circuit by removing the capacitor. The equation q = Q(1-e^{-t/RC}) describes the charge on the capacitor over time. Understanding this behavior is crucial for analyzing circuit dynamics. The discussion emphasizes the importance of recognizing steady-state conditions in circuit analysis. Overall, mastering these concepts is essential for solving RC circuit problems effectively.