Why is current the same when batteries are connected in series?

Question

I struggle to understand why the current remains the same in the circuit when batteries are connected in series.

Update I can reason with it if someone can confirm the update. If the speed of electrons is the same in the circuit, then the despite the quantity of electrons a series power source might generate in total, we can expect the "current"/amount of electron flow to be the same as a single unit.

As they all pass through a conducting material sequentially but the x amount of electron flow stays the same as each component will experience this at a steady phase.

Please point out any flaws in my reasoning.

Let's consider a power source that provides energy E (potential) and generates X electrons through chemical reactions.

My understanding of voltage and current: Voltage is the potential E between two points. Current is the flow of electrons through a component when observed.

Now, when we connect two individual power sources in series, I expect to see a potential of 2E and 2X electrons. Similarly, when connected in parallel, I expect the current to double to 2X electrons.

The current should double.

The explanation based on electron paths doesn't make sense to me because: In series: They are connected end-to-end, creating a single path with a single outlet when connected to the circuit. v1−v2−v3 provides a single path.

Parallel: the positive terminals of the sources are connected together and likewise for the negative terminals and when connected to an electric component they essentially have a single path.

-------------- + --- v1 | v2 | v3 | [ component ] --- single path to travel

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What is happening when electrons travel between batteries. Can some please explain what happens to the amount of electrons in a series connection. Without using any water analogies.

There is an in depth explanation about the chemistry in the following discussion which helped me a bit but the reaction during series is hard for me to understand. https://physics.stackexchange.com/a/421646/406966

Answer 1

I struggle to understand why the current remains the same when batteries are connected in series.

The same as what? The same as when the two batteries are connected in parallel? That premise of your question is in fact not correct. Let's say we have a simple loop circuit with a single resistor of 2 Ohms and the voltage on the positive terminal of either of the batteries is 6 Volts . In the parallel case the the current is $I = V/R = 6/2 = 3 \ \text{Amps} \ $ With the two batteries in series the current is $I = V/R = 12/2 = 6 \ \text{Amps} \ $ which is twice the parallel case.

I see you don't like the hydraulic analogy but it provides such clear simple insight into visualising what is happening I cannot resist presenting the hydraulic analogy anyway. You can think of the battery as a pump that can raise a fluid to a certain head height (where head height is analogous to voltage potential). Lets say we have a single pump that is capable of raising a quantity of fluid to a height of 2 metres. Two such pumps in parallel can raise fluid from a lower reservoir to a common reservoir that is 2 metres higher. If we use one pump to raise he fluid to first reservoir and use a second pump to raise the fluid from the first reservoir to a higher reservoir, we have raised the fluid to a height of 4 metres and there is now a higher head pressure that can provide a greater flow (current) through the circuit for a given resistance. This is effectively the same as putting the batteries in series. It does not matter how many pumps you have in parallel the end result is that they are all topping up the same reservoir at 2 metres and they do not result in a greater head pressure. On the other hand if we had 10 pumps in series each one pumping from a preceding reservoir to a higher reservoir, we can raise the fluid to a height of 20 metres which has a lot higher gravitational potential (higher voltage potential).

Update: I see some comments that suggest you are asking about when two batteries are in series, why is the current through any given battery the same as the other battery it is in series with? The current is simply the number of charges passing a given point per unit time. If the number of electrons entering the negative terminal of the first battery was different to the number of charges leaving the second battery, we would have charge either piling up or depleting in the batteries which is not how batteries work. The amount of charge entering any single component in a circuit is always equal to the amount of charge leaving the component with the exception being a capacitor, where charges accumulate on a plate inside the the capacitor. In the hydraulic analogy of the battery being a pump, it should be intuitive that the amount of fluid entering the suction of the pump should be the same as the amount of fluid that leaves the discharge in a given period of time. Consider what happens if the pumps are designed to pump 100 litres per minute. If the first pump delivers 100 liters per minute to a reservoir between the pumps and the second pump draws 100 liters per minute from the reservoir, then the level in the reservoir does not change over time, then neither pumps affects the performance of the other pump and each pump continues to pump 100 litres per minute when in series. In other words, the pumps operate at the same flow rate as each other, when in series and likewise, the current going through a given battery in series is the same as the current flowing through the other battery.

Answer 2

First, when we say "the current is the same when batteries are connected in series" we mean that the current through battery 1 is the same as the current through battery 2. We don't mean that the current in this configuration is the same as the current in a different circuit with two batteries in parallel connected to the same load. (and the answer by KDP has shown that it isn't in the case of a resistive load)

Now, when we connect two individual power sources in series, I expect to see a potential of 2E and 2X electrons.

If the action of a battery was to admit electrons into its cathode terminal and produce double the amount of electrons exiting its anode terminal, you'd have a problem explaining the behavior of a circuit with a single battery.

Suppose we have a single battery (1 V) connected to a resistor (1 kohms). Now 1 electron leaves the anode and passes through the resistor and returns to the cathode...Our doubling battery then doubles it and sends 2 electrons out the anode...which return to the cathode, producing 4 electrons .... Can you see how this is impossible? 4 electons is not a large charge in the world of circuits but continuous doubling will quickly lead to a dramatic end for either the battery or the resistor, involving flame and smoke.

So this is not what batteries actually do. What they do is take electrons in at the cathode and produce the same number of electrons at the anode, but at a higher potential. That means a combination of two batteries in series has twice the potential of a single battery, but the current through the two batteries is the same.

Answer 3

Let's consider a power source that provides energy E (potential) and generates X electrons through chemical reactions.

Batteries don't generate electrons. The chemical reactions that produce electrons in the negative electrode of a battery and supply them to the external circuit cannot progress without an equal number electrons being supplied by the external circuit and delivered to the positive electrode.

Within the battery, charge is transported through the electrolyte by ionic currents.

when we connect two individual power sources in series, I expect to see a potential of 2E and 2X electrons.

You're half right. The overall voltage is doubled when you connect two batteries in series, but since the batteries do not generate electrons (see above) where would those extra electrons come from? If the current out from a battery must equal the current in, and you've connected batteries in series, then the current in and out from each battery must be equal to the current in and out from its neighbors.

What is happening when electrons travel between batteries?

Kirchoff's Current Law (KCL) tells us that the sum of all of the currents entering a "node" in an electronic circuit must equal the sum of all of the currents leaving it. The wire connecting one member of a series string of components to the next is a "node," and by the very definition of "series," it's a node with only one way in and one way out.

Answer 4

Lets say you have one battery with voltage V and a resistive load R that allows a current I. The power consumed by the load is VI, where I is V/R. Now put an identical battery in series. The voltage is now 2V and the current is 2V/R. The power is (2V)(2I), which is 4 times greater. 4 times because there are twice as many electrons moving and they each have twice as much electric potential (speed).

For the comparison with constant current you need to double the resistance of the load, in which case you get current is 2V/2R and power is 2VI or twice the single battery power. You could say the same number of electrons going twice as fast.

(Drift velocity varies linearly with the electric field strength, which seems a little odd since kinetic energy varies with the square of the velocity. I would check that out.)

Answer 5

Why is current the same when batteries are connected in series?

Batteries have an internal resistance. The equivalent circuit is a pure voltage source in series with the internal resistance. Two identical batteries in series have twice the voltage and twice the internal resistance so the current is identical for two batteries in series.

Answer 6

Gentlemen, thank you all, the answers were there all along; I was lost, but now I am found.

After wrestling with this thought for some time, I have finally arrived at a clear understanding. My initial visualization was incorrect.

While the total number of electrons is indeed doubled when batteries are connected in parallel or series, the orientation of the sources plays a crucial role in how the electrons travel.

In a series circuit, the electrons travel uniformly and sequentially through each component. This means that the amount of electrons flowing through any component at a given time remains the same. There is only one continuous path, so the current (the rate of electron flow) is consistent throughout.

In a parallel circuit, there are multiple paths for the electrons to travel from each battery. These paths merge at the load, and because the electrons also flow uniformly in parallel paths, the number of electrons passing through the load is doubled. This results in a higher total current through the load.

Hallelujah!