In circuit analysis, current from cell E1 and E2 flows through their respective resistors, with the same amount of current passing through each component. Kirchhoff's law is applied to determine the net current in the circuit, emphasizing that only one current flows through a branch despite containing both resistance and cells. The currents can be labeled as I1 for E1, I2 for E2, and I3 for the resistor R. Understanding these relationships is crucial for accurately analyzing the circuit. The discussion highlights the importance of applying fundamental laws to solve circuit problems effectively.