# Relationship between voltage and capacity?



## benh (Jan 24, 2006)

Forgive me if this is covered in an FAQ, but I couldn't find an answer by searching.

I'm curious about the relationship (if any) between the nominal voltage of a battery and the mAh (capacity?) of that battery.

Here's what got me thinking about this. Sanyo AAs these days are coming in 2500mAh capacities with a nominal voltage of 1.2v. I was reading about some rechargable 123s that are regulated at 3v output with a capacity of 600mAh. 

A typical Maxell non rechargeable CR123A is rated at 1400mAh. I understand that part of the difference in capacity between the regulated and protected 123 vs the primary is the protection circuit, which takes up space in the cell, but that can't be all of it, can it?

My cellphone takes a LiPo battery at 3.7 volts with a 770mAh capacity. Looking at that battery, seems like it should have a higher capacity that that.

I know that the more mAh a battery is rated for, the more capacity (and thus runtime) it should have, and that capacity is directly related to the size of the cell. Bigger cell = more capacity. But what is the relationship between voltage and capacity?


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## Flash_Gordon (Jan 24, 2006)

Voltage of a cell is determined by the chemistry. NiMh cells are 1.2V whether it is a AAA or an F cell. MAh capacity is a function of physical size more than anything. Basically, how much "stuff" can we put in the container.

Likewise, Lithium primary cells are 3V, whether the smallest coin cell or a CR123.

The batteries you listed in your post are different chemistries therefor different voltages. In any of the chemistries, larger physical size allows higher mAh capacity.

As in many things in life-size matters.

Mark


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## benh (Jan 25, 2006)

That all makes good sense.

It seems to me that there's some relationship between voltage and capacity, though, though I could be totally off. If I had two cells of equal physical size, one a 1.5v cell and one a 3v cell, would the 1.5v cell have greater capacity due to the lower voltage being pulled from the cell?


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## chimo (Jan 25, 2006)

There is a lot of good information here.


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## bguy (Jan 25, 2006)

Do check out the link in post #4 for a more complete explanation.

Basically, a battery creates the power from a chemical reaction. The variations would be in the quantity and quality of the chemicals. So if you took 2 nimh 1/2AA batteries to make 3v in the space of 1 AA, it would have less capacity simply due to lost space of the additional casing. The newest advancements also get put into the AA sized nimh batteries, since they are very common and widley used.

Also, as noted, you refer to NiMH, primary lithium, lithium polymer, lithium ion, and a voltage dropped lithium ion batteries. So different chemistries will have different characteristics.

The rechargeable 123 you refer to is actually a 3.6v Li-ion with built in circuitry to allow it to be used in place of a 3v primary 123, as well as protection from over charging/discharging. That circuitry takes up space, and that space is capacity. So the 3v rechargeable, should generally have less capacity of a standard 3.6v li-ion.

Keep in mind also, the mah ratings are sometimes more of a marketing term. They can give you a general idea of the power available in the battery, but batteries with identical numbers can vary a lot.


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## vandrecken (Jan 25, 2006)

Would this example help explain it ?

Lamp output depends on Power (power's measured in Watts)

Power = Voltage x Current (watts = volts x amps)

So you could get exactly the same output from a 3v lamp drawing 1 amp as from a 1.5v bulb drawing 2 amps.

Now imagine your power supply was two 1.5 volt batteries.

Wire them in series and you have a 3v source that will push out 1 amp for some number of minutes.

Wire them in parallel and you have a 1.5 volt source that will supply 2 amps for the same length of time.

Regardless of the voltage of the "pack" both of these have the same volume of battery, both supply the same power for the same length of time. So all things being equal, the amount of energy available from a given size of battery pack doesn't go up if the voltage is higher.

Now, 

What you can't do is compare alkaline, NiCd, Nimh, Li-Ion side by side like this. Each of these is based on different chemistry. The chemistry dictates the voltage produced by one cell (1.5v for an alkaline cell, 1.2 for NiCd, 3.6 ish for Li-Ion, 1.4v for zinc-air etc) but it also dictates the energy density of the cell (how many millamp-hours can be produced from a certain volume or weight of chemical). Some chemical reactions are more efficient at storing and releasing electrical energy than others. 

It happens that Li-Ion chemistry has the highest energy density among the rechargeable cells i've listed. That's why it's been developed commercially. It also happens that Li-Ion chemistry generates the higher voltage per cell, but it's the chemistry that dictates the voltage per cell, it's not a law of chemistry that a higher voltage per cell will automatically mean a higher energy density too.

For comparison, NiMH cells have around 1.5x the gravimetric (weight) energy denisity of NiCd for the same voltage, reusable alkaline cells have only half that of NiMH despite a higher voltage per cell, Li-Ion batteries have 3x greater voltage per cell than NiMH but energy density is only 30% more at around 160 watt-hours / kg. Jumping across to non rechargeables, zinc air batteries are now pushing above 350 watt-hours / kg yet only produce 1.4v per cell. 

Equivalent information will be around comparing energy density by volume instead of weight.

Hope this helps,


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## altis (Feb 11, 2006)

I often read that lithium-ion has the highest energy density of any battery chemistry yet, when I actually compare cells, I get different results.

For example, go to the GP Batteries site and look up the data sheets for the GP1450L70 lithium-ion rechargable and the GP260AAHC NiMh rechargable. Fortunately, although they have different chemistries, they are both AA sized.

GP1450L70 (lithium-ion)
nominal output voltage = 3.7V
typical capacity = 700mAh
therefore, typical power capacity = 3.7 * 0.7 = 2.59Wh

GP260AAHC (NiMh)
nominal output voltage = 1.2V
typical capacity = 2500mAh
therefore, typical power capacity = 1.2 * 2.5 = 3.00Wh

Now, I know my estimate for the power capacity is flawed - I should calculate the power by multiplying the current and voltage all along the discharge curve - but I haven't got the information for that. However, I think it is a reasonable estimate and shows that there is really little difference between the two energy densities.

NiMh cells can source current an order of magnitude higher than Li-ion, have a flatter discharge curve, can be recharged in minutes rather than hours and generally come in non-proprietary packages. So I can't see why everyone is so positive about Li-ions.

http://www.gpbatteries.com.hk/


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## chimo (Feb 11, 2006)

altis said:


> I often read that lithium-ion has the highest energy density of any battery chemistry yet, when I actually compare cells, I get different results.
> 
> For example, go to the GP Batteries site and look up the data sheets for the GP1450L70 lithium-ion rechargable and the GP260AAHC NiMh rechargable. Fortunately, although they have different chemistries, they are both AA sized.



I believe that they use a different definition of energy density. You are using Energy Density per battery volume (Wh/volume unit), they are using Gravemetric Energy Density (Wh/kg). 

That would explain why the numbers don't jive.  

Paul


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## SilverFox (Feb 11, 2006)

Hello Altis,

When I think of energy density, I add in weight.

The GP1450L70 Li-Ion cell weighs 19g and has an energy density of around 136 Wh/kg.


EDIT Someday I will learn to read the numbers in a table correctly. The GP260AAHC NiMh cells do not weigh 245g (that number was next to the weight column, and actually reflects that the standard charge current is 245 mA), but actually weighs 31g. This gives an energy density of about 97 Wh/kg.

The GP260AAHC NiMh cell is quite a bit heaver at 245g, and has an energy density of about 12 Wh/kg.

When you add weight to the equation, the difference is dramatic. Well, it is a bit less dramatic if you use the correct numbers... END EDIT

Tom


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## jtr1962 (Feb 11, 2006)

The difference isn't as dramatic if we're talking about Wh per liter. The lithium cells are no better than NiMH cells, at least in the smaller sizes. Sure, they're lighter but for flashlight use that's irrelevant. You can just eat a little less breakfast and save the same amount of weight. Now if you're talking lots of cells, as in an EV, then lithium offers a huge advantage.


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## MrAl (Feb 11, 2006)

Hi there,

Weigh certainly matters -- think of space applications.

Also, Li-ion cells have a MUCH lower self discharge rate and NiMH cells basically
bite the big uno here  That sometimes makes the call between using one or
the other.
Also also, i havent found many NiMH cells that live up to their package stamped
ratings yet either, and i've purchased quite a few now.

Li-ions are more expensive, but they have higher voltage and much lower self 
discharge, as well as being lighter in weight...this is why so many people like them.
Their charge termination method is much simpler than with NiMH too, so it's much
more reliable. Anyone can build an Li-ion charger with transistors and ic's while
to charge NiMH cells you need special ic's to get it right.
I designed and built an Li-ion charger that runs from any wall wart (6v to 24vdc)
and only gets slightly warm even when charging my biggest cell. Charging the AA
size cell the warmth is hardly even noticable. No large heatsink required. It's very
nice to be able to grab just about any wall wart and be able to charge your cell
with it (with the circuit board too of course) and not have to worry about heat at all !
I was thinking of eventually offering to the CPF community.


Take care,
Al


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## altis (Feb 13, 2006)

Erm, the GP260AAHC does not weigh 245g - that's over 8oz! The data sheet says 31g so that brings the specific energy density to 97Wh/kg vs 136 for the Li-ion. Yes, that's an advantage to the Li-ion but the difference is not enormous. Note that these are crude estimates of the energy density based on a flat approximation of the discharge curve.

But for many applications, weight is not an issue. As it happens, I don't live in space and am quite happy carrying my AA-powered camera around all day. Also remember that NiMh chemistry offers many advantages over Li-ion. The NiMh is good for 7.35 amps while the Li-ion can only manage 0.7A. The discharge curve of NiMh is flatter. You can recharge a NiMh in 15 minutes but a Li-ion takes 2 to 3 hours. But, for me, the most significant advantage is that the cells are readily available in standard sizes. 

Almost all of our portable electronic equipment uses AA cells rather than a host of proprietary Li-ion rechargables. This makes stocking and carrying spares a breeze.

When I'm away from the mains for any length of time, for example while trekking in Nepal, then I take out the NiMhs and pop in some non-rechargable Lithium-iron-disulphides (eg Enegizer L91, 14.5g, 3000mAh, 1.5V, 15 year shelf life, -40C to +60C operating temperature) and carry some spares. That's 310 Whr/kg, the best of the lot by a wide margin - when weight *is* important to me.

If a low self-discharge rate is important to you then check out the new Sanyo Eneloop cells. These use NiMh chemistry but discharge by only 15% over a year.


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## MrAl (Feb 13, 2006)

Hi there,


Sure, there are good and bad points for each. I've even heard of Li-ions exploding,
but i dont think i've ever heard of a single NiMH exploding (just leaking).

I use both myself, but if the Li-ions were cheaper i'd use them exclusively.

Since there are new battery chem's coming out in the future i guess the decision
will also start to depend on how well these cells *really* perform (as opposed to
how the manufacturers *say* they will). If the new ones work as good as 
projected, i'll probably turn to them in devices that can take their size/voltage.


Take care,
Al


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## SilverFox (Feb 13, 2006)

Hello Altis,

Oops, I am not sure what I was thinking... At 245g, those would be some very dense AA cells. I have edited my post to reflect something closer to reality...

I think you have a very good point. NiMh chemistry has improved greatly and is getting closer to Li-Ion performance. It is also a more robust chemistry. If I were traveling in remote areas, I would go for AA cells.

On the other hand, I usually find devices require several AA cells to operate, whereas others can operate on a single Li-Ion cell. However, if weight and bulk are not an issue, that argument falls flat.

I'm with Al, there are good and bad points for each.

Tom


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