I have a question regarding the voltage of two different circuits. In the first circuit there is a 75 volt battery with just one 4 ohm resistor. In a separate second circuit there is a 75 volt battery again, but this time there is a 4 ohm resistor and 9 ohm resistor in series. My question is this: Why is the potential difference across the 4 ohm resistor in the first circuit 75 volts, but not in the second circuit. In the second circuit, according to ohms law, the potential difference across the 4 ohm resistor is 23.08 volts, and the potential difference across the 9 ohm resistor is 51.93 volts, so the total voltage adds up to 75 volts, BUT WHY? I'm wondering how the system as a whole can tell how many resistors are in the circuit. Because the way I am seeing it right now, there is a potential that comes out of the positive terminal of the battery and reaches the 4 ohm resistor the same in both circuits, so why would it take more energy to cross the 4 ohm resistor in the first circuit, but less in the second circuit when the electrons are crossing the same resistor? Is it because of less current flow? Because according to ohm's law, the current flow across the 4 ohm resistor in the second circuit would be less. Can someone explain to why this is? Why does more total resistance in a circuit mean less current flow? I guess big picture: Why is ohm's law the way it is? Why does current * resistance = voltage?