# Ampere hour and voltage

It's been a while since I had to deal with physics, in general, and I try to wrap my head around this and it's confusing.

So as I know, if you wire n batteries in series, Ah remains the same while voltage increases. While wiring them in parallel makes the Ah increase.

So in abstract, a battery can hold infinite Ah as long as the voltage is low enough since, in theory, you could split the battery into virtual ones that have lower voltage and are connected in series, and then you connect them in parallel. Also, this means, in theory, you can create a battery with huge Ah and low voltage. But this sounds to me somewhat infeasible (and limited by atom size).

But can I can't explain to myself why. Can you?

And I think it all starts because I can't completely understand why series batteries combine their Ah, even though is intuitive.

• There’s no way you can “cut” a single battery element as 2 smaller elements in series. But I don’t see any theoretical problem with a battery with 0 voltage and infinite Ah. (By the way, it does exist and it is called a wire.) Commented Mar 20, 2017 at 0:57
• Yes they do it's called inductance. Just drain really quick ;) Commented Mar 20, 2017 at 1:03
• A battery with null voltage would not store energy either. Ampere-hour is not an energy unit, it is a charge unit, like Coulomb (also known as Ampere-second). A charge multiplied by a voltage is an energy. Commented Mar 20, 2017 at 1:04
• The voltage of a cell depends on the chemical reactions in the cell - if you cut a 1.5 volt cell in half, you get two 1.5 volt cells, each with half the Ampere-hour capacity of the original. You could cut a 9 Volt battery in half to get two 4.5 volt batteries, of the same Ah capacity, as a 9 volt battery is made up of 6 1.5 volt cells connected in series. Commented Mar 20, 2017 at 1:54
• "why series batteries combine their Ah" - When charges/electrons flow through the battery the battery gets discharged. In a series installation, every single charge must "travel" through all the batteries, taking that amount of charge from every battery. In parallel setups, an electron can come from any one battery but not from multiple batteries. This is the same as discharging one battery after the other instead of all at the same time for the serial connection. Commented Mar 20, 2017 at 8:11

To explain this to yourself, first you have to reject a common misconception.

Do batteries store Ampere-Hours? Nope. Wrong.

Batteries don't store any electric charge. Instead, batteries are chemically-powered charge pumps. The path for amperes is in through one terminal, through the battery, then out through the other terminal. Batteries are "electricity pumps," and they don't accumulate any coulombs or AH or electrons inside.

In other words, an ideal battery doesn't block the flow of charges. Instead it's a short-circuit. When connected to a load, a battery provides a complete circuit, with no beginning or end.

Doesn't this mean that, during electric currents, the battery DOESN'T provide any flowing charges?!! Yes, exactly right. The charges are provided by the conductors. Within the battery's (very conductive) electrolyte, the dissolved ions are the electric charges (and in lead-acid batteries, the charges are the acid's mobile protons. Flowing protons!) Then, out in the copper wires, the charges are the movable electrons of the copper metal.

So, what does "ampere-hour" really mean? It's a convenient way to express the total amount of coulombs that a fully-charged battery can pump through itself before being exhausted. When the battery is dead and the AH expended, it means that the chemical fuel inside the battery has been consumed, so the pumping-process comes to a halt. The ampere-hour is actually used as a measure of chemical fuel, rather than a measure of amperes or coulombs or electric charge. Fortunately the total of "chemical fuel" being consumed inside the battery is directly related to the number of coulombs pumped through. We don't need to somehow weigh the fuel remaining. Instead we can just watch the flow of coulombs.

So, in rechargable batteries, if we force the charges backwards through each cell, then the chemistry runs backwards, and the "chemical exhaust" gets converted back into fuel again. In a flashlight battery, the zinc chloride is turned back into zinc metal, and chemical energy is stored. Or in a fuel cell, the H2O gets "unburned" and forms new H2 and O2 gas. The battery is again ready to power your devices, converting the "fuel metals" back into solid "exhaust products." The fuel cell again can burn the hydrogen into water, or your Lithium cell burns the lithium metal into lithium salts.

So, notice that a "charged" battery is not full of charge. It's full of chemical energy, full of joules or KWH worth of chemical fuel. And, a "discharged" battery contains exactly the same amount of electric charge as a "charged" battery. Confusing yes! With batteries, the word "charge" refers to a charge of energy, and not an electric charge of electrons or protons. (Similar: when we "charge" a cannon, we give it a charge of gunpowder, not a charge of electricity.)

OK, original question: why do the Amper-Hours remain the same when batteries are hooked in series? It's because each battery only has enough chemical energy to pump a certain number of coulombs through itself. WHen hooked in series, the total number of coulombs don't add up, since the coulombs coming out of one terminal just goes right back into the terminal of the next battery in the chain. That means a certain number of coulombs passes through the entire chain. It doesn't increase as it goes! If one battery passes 1000 coulombs through itself, well, all the following batteries in the chain will do the same. The voltage does stack up, and so does the energy. But series-batteries pump the same total charge through themselves that a single battery does.

Will a water-analogy help. In plumbing, a "battery" is a constant-pressure water-pump that's powered by a mechanical wind-up motor, with some energy stored in the motor's spring. The spring-pump can be rated in flowrate-hours! Each waterpump can only pump a certain number of gallons before its spring totally unwinds. Stacking up many pumps doesn't alter the total gallons that the spring-motors will pump through the chain. (Stacking up many pumps will add up the pressures, which does add up the total energy produced by the chain of pumps.)

Note well that "Ampere-Hours" actually means "Coulombs-per-second times hours," which means the same as "Coulombs times 3600." One ampere-hour is just 3600 coulombs.

Second question: can we swap voltage for AH, while keeping the size of battery constant? Yes, to some extent. But cell-voltage is determined by the "corrosion voltage" where water touches conductor at the plate surfaces. You can alter the metal, and choose battery types between about 0.5V and 4V, but that's all. The voltage comes from the reactivity of the metal, and from the "aggressiveness" of the solvent action of the electrolyte. When water dissolves metal, the dissolving process is halted by the build-up of roughly 4V between water and metal, with the metal having negative polarity and the water being positive. Drop some metal into water and it dissolves furiously ...but the metal immediately charges up to ~4v negative, and the corrosion halts. Once this voltage appears, the water no longer can drag positive ions out of the negative-charged metal. The battery's own voltage is halting the corrosion of the plates. Different metals give different voltage, as do different electrolytes (such as H2O versus molten salt, molten sulfur, etc.)

So, you can have a few volts per cell, down to a few cells per volt, but nothing further. Cell voltage is limited by the chemistry, which is limited by the voltage-steps between electron orbitals in the conductive battery-plates.

On the other hand, you can make the plate-area larger and larger (from AAAA to D-cell, or far larger,) and that increases the total amount of "fuel," and increases the AH rating of each cell. Two or three volts per cell, but use infinitely-wide battery plates for infinite AH rating. Roll the plates into a cylinder for a "DDDDDDDDD"-cell with an infinite number of Ds.

• I can have a few. Commented Mar 20, 2017 at 3:16

Ah ratings are all based on a specific voltage, although it's usually not specified. If you get a battery cell or pack, the Ah rating is assumed to be at some nominal output voltage at the terminals, e.g. 3.7V for a LiPo. But the voltage of a battery drops during discharge, so it's hard to compare by Ah ratings. For a portable battery pack (with output voltage regulation) it's more straightforward. Wh, or total energy would be better ways in my opinion to specify battery capacity.

But keeping in mind that Ah should always be specified at a certain voltage, when you say connecting batteries in series produces the same Ah rating, this is only true if you increase the voltage rating, so essentially they are not the same Ah rating. E.g. two 3.7 1Ah batteries in parallel provide 2Ah at (3.7V) which is easy to follow - the voltage hasn't changed. But in series they provide 1Ah at 7.4V, OR 2Ah at 3.7V (assuming the voltage is converted down at 100% efficiency). It's important to remember the voltage. Again, it's better to think in terms of energy. Two identical batteries will store twice the energy, regardless of how they are wired.

A battery is something that keeps one end more electrically positive than the other, and keeps this up until it runs out of charge. How much more positive is measured in volts, and how long it can keep this up is measured in Ampere-hours.

Suppose you have two 5V, 3Ah batteries, in series. The first one keeps its positive terminal 5V above its negative. Its negative terminal is connected to the positive terminal of the second, which the second keeps 5V above its negative. So, the first battery's positive terminal is 10V above the second battery's negative, and they can maintain this until 3Ah has run though both batteries.

In parallel, they both keep their shared positive terminal 5V above their shared negative terminal. But since the current is split half-and-half between them, the combined battery doesn't run out until 6Ah has passed through it.

"Batteries" with huge Ah and low voltage or the reverse are common. A wire keeps one end 0V higher than the other end, and can keep this up indefinitely. So, a wire is a "battery" with 0V and infinite Ah.

A car body holding a static charge on a dry day can shock you, but only the first time you touch it. That's a "battery" with a few thousand volts, but so little Ah that it runs out after one spark.