In series circuits, the total voltage is equal to the sum of the voltages across each component, while in parallel circuits, the voltage across each branch remains equal to the voltage supplied by the battery. This is because the voltage between any two points in a circuit does not depend on the path taken. When multiple branches are present, the voltage across each branch is not divided among them; instead, they all maintain the same voltage potential as the battery. Current flow varies across each branch due to differing resistor values, which can be calculated using Ohm's Law. Understanding these principles is essential for analyzing circuit behavior effectively.