Why do series resistors have a single current running through them?

In a circuit such as the following:

The current is the same through all the resistors and is:

V = IReq
9 = I (R1 + R2 + R3)
9 = I (100 + 300 + 50)
9 = I * 450
I = 9/450 or 1/50 Amps


Why is this the case though? For example, why wouldn't there be three or four or two current running through the circuit? Why is all the current equalized with the circuit? Note that I'm looking more into the why (perhaps physics?) behind why this happens and not just so much a link to Ohms law or something.

• think of three garden hoses connected together ... same amount of water passes any point for a given time interval Jan 30, 2020 at 0:19

Suppose some charge exits the right terminal of R1, where can it go besides into the left terminal of R2?

If the current exiting the right terminal of R1 isn't equal to the current entering the left terminal of R2, then charge must be accumulating in the wire between the two resistors.

To model that possibility, we could include a parasitic capacitor between that node and the ground node in our model. Then we'd see that when that happens (assuming the current through R1 is greater than the current through R2), the voltage on that node will increase. Which will cause the current through R2 to increase until things balance out again.

By not including the parasitic capacitor in our model, we're saying that this capacitance is so small as not to matter for the way we're using the circuit. And any capacitive charging needed to get the resistor currents balance happens so fast after connecting the 9 V source that we can ignore it.

In a completed DC circuit, for every mobile electron that leaves one battery terminal another one enters the other battery terminal; very much like a closed plumbing loop connecting the input of a pump to its own output. In that plumbing loop, every drop of water that enters the pipe loop exits the pipe loop because there is nowhere else for it to go. Similarly for an electric circuit, every electron goes through every series element. Current is defined as a (very large) number of electrons passing a point, so the current is equal at all points in the circuit.

• not to go too deep into the plumbing analogy, but what about things like leaks and such? Doesn't some of the charge get absorbed/lost/etc along the way? Jan 30, 2020 at 4:00
• Not in a simple DC circuit. Most of the energy is dissipated in the resistors as heat, and a very small amount is dissipated in the wires as heat. No leaks. AC circuits are very different, but DC circuits in a steady state really do come down to Ohm's Law. Jan 30, 2020 at 4:57
• Note that while power is dissipated in each of the circuit elements in proportion to each element's impedance, this is not the same topic as electron flow (current). 100% of the current goes through 100% of the elements 100% of the time. Jan 30, 2020 at 20:43