# Why is current the same when batteries are connected in series? [closed]

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

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

• If the currents were not the same where would the charges disappear or be created? Commented Jun 16 at 8:49
• @Farcher my understanding of current is that, it is the amount of electrons that are flowing through an electric component when observed, so the the component should experience the sum of the sources in series.
– DPV
Commented Jun 16 at 9:31
• We speak of "charging" and "discharging" batteries in informal conversation, but batteries do not work by storing charge. Think of them as charge pumps. Charge flowing in must equal charge flowing out when averaged over any significant interval of time. Commented Jun 16 at 13:32
• @SolomonSlow I understand that batteries do not store charge, they create potential as a result of the chemical reaction between the electrodes and the electrolyte. Current when observed, is the amount of electrons that are flowing through the component, i included a Update in my question, please share your thoughts on that.
– DPV
Commented Jun 16 at 14:53
• ...So, if we agree that charge flowing in to a battery must equal charge flowing out, can we also agree that charge flowing in to the next battery in a series-connected string of them must equal charge flowing out of the previous one? Current in a string of series connected batteries (or series connected anything else) must be the same everywhere because there is no place else where it can go. en.wikipedia.org/wiki/… Commented Jun 16 at 15:09

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.

• I updated the line "I struggle to understand why the current remains the same when batteries are connected in series." Thank you for trying to explain but you are using a formula as a reasoning but I am trying to understand using the fundamental conecpts.
– DPV
Commented Jun 17 at 1:25
• @DPV I have updated my answer too.
– KDP
Commented Jun 17 at 2:04
• Thank you, @KDP. Yes, current refers to the number of electrons passing through a component. If the electrons move simultaneously, the component will experience the same number of electrons at any given moment. When three sources are connected in parallel, with their positive terminals connected together and their negative terminals connected together to a conductor, the electron movement is simultaneous. Therefore, in this configuration, the same amount of electrons will be observed across the conductor
– DPV
Commented Jun 17 at 2:24

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.

• I provided an update in my question, """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."""
– DPV
Commented Jun 17 at 1:28
• @DPV, speed of electrons is not really relevant. 1000 electrons per cubic cm moving at 1 m/s is the same current as 100 electrons per cubic cm moving at 10 m/s. If you just join a fat wire to a skinny wire and put a current through them you'll have the electrons in the skinny wire on average moving faster than the ones in the fat wire, but still have the same current in both wires. Commented Jun 17 at 2:17
• I understand that current measures the number of electrons flowing through a conducting component. Within a circuit, the electrons are driven by the generated potential. If the electrons move at different speeds, a component might experience a surge in electrons. For example, if electrons from voltage source V2 move alongside electrons from voltage source V1, the conductor will see twice the number of electrons passing through.
– DPV
Commented Jun 17 at 2:31
• @DPV, that's not a good mental model. The electrons experience a force due to the electric field where they are. The electric field is the gradient of the potential. Whether the potential difference is created by one 3 V battery or two 1.5 V batteries in series dosen't matter. It still produces the same potential and thus the same electric field in a circuit that is driven by that potential. There are no "electrons from source 1" and "electrons from source 2". Commented Jun 17 at 2:42
• Even electrons that were initially in the wire when the battery was connected, and have never passed through either battery, are pushed around by the electric field and contribute to the current. Commented Jun 17 at 2:47

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.

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.)

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.

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!