In a circuit with two batteries connected in parallel and a variable resistor (Rh), the current from the 10V battery divides into two paths: one through Rh and the other through the second battery. When adjusting Rh so that the voltage drop across it equals that of the second battery, the current through the second battery can effectively become zero, leading to all current flowing through Rh. This results in the total current from the 10V battery being equal to the current through Rh, while the second battery does not contribute to the circuit. The discussion emphasizes that the two batteries do not cancel each other out; rather, they are in parallel, and the current behavior depends on the resistance and voltage conditions in the circuit. Understanding this relationship clarifies the current flow dynamics in such configurations.