# Why won't all voltage be used up on first resistor in series?

tldr: I am having trouble conceptually understanding voltage between resistors in series, even though I know how to calculate it using Ohm's law. How do the electrons "know" there are more resistors after going through the first one? Why doesn't it use up all the 10V so it's 10V -> resistor 1 -> 0V?

Case A: If a circuit has 1 resistor, the voltage on each side will be completely used up. For example, with a 10V battery and $$5\Omega$$ resistor, the voltage will be 10V -> resistor -> 0V, with a current of 2A.

Case B: However, if we attach another $$5\Omega$$ resistor, then the voltage will be 10V -> resistor 1 -> 5V -> resistor 2 -> 0, with a current of 1A.

From the perspective of the electrons, they don't know that there is another resistor down the line.

So why does the voltage drop across the first resistor 10V in Case A but only 5V in Case B?

I'm probably not understanding something very simple. This is my first circuits class and it's a lot to wrap my mind around! Thanks in advance.

• Hello and welcome to the Physics StackExchange! Are you sure your question is regarding transistors and not resistors? From your description, it sounds more like resistors. Also, you may consider asking this on the Electronics StackExchange instead for more accurate answers. Sep 12, 2021 at 3:34
• Oh you're right! I meant resistors. I started learning it in physics but I can ask there too. Sep 12, 2021 at 4:00

From the perspective of the electrons, they don't know that there is another resistor down the line.

The current is a moving ensemble of electrons, with a group drift velocity, no single electron goes from the positive to the negative pole of a battery. Electrons interact with the lattice and the molecules of the medium they pass through.

If they find a lot of resistance the drift velocity becomes lower, if the resistance is low the drift velocity becomes higher.No need for knowledge of the future path.

It is important to understand Ohm' law

Since both the momentum and the current density are proportional to the drift velocity, the current density becomes proportional to the applied electric field; this leads to Ohm's law.

Think of it this way.

One battery terminal sits at $$10V$$, the other at $$0V$$. The first resistor has one terminal connected to the $$10V$$ pole of the battery.

Now assume, as you did, that the voltage is "all used up" after the first resistor (i.e. if $$2A$$ flows through it). In that case the voltage would be $$0V$$ at that point. That means that the second resistor has both terminals at $$0V$$. Hence there could be no current flowing through that resistor. However, since the resistors are in series, that automatically means the current through the first resistor also has to be $$0A$$.

This is in contradiction with our assumption that $$2A$$ flows through the first resistor. The only way to fix the contradiction is to accept that the same current flows through both, i.e. a total of $$1A$$