# Charging a low voltage battery with a higher one of same Ah

Keanthon
Let's say both battery have the same charge capacity of 3Ah
Battery A has voltage of 3V and B has voltage of 6V. Battery A is completely discharged while B is completely charged.
If I charge battery A with battery B, wouldn't B be completely drained because they hold the same amount of charge? If so, where did the missing electrical potential energy go since originally the energy stored is 18Wh and now is 9Wh

## Answers and Replies

Homework Helper
Hello Keanthon,

Fairly easy to answer if you consider what the driving force is: the voltage difference. Once that's dropped to zero, nothing happens any more. If that means A is half full, then B should be at the same point ...

This completely depends on the charger circuitry. (It is not a good idea to do this without proper charger - that would most likely end with both battery wrecked).
If the charger is just some linear regulator (LDO) based circuit, then the current drawn will be ~ the same as the current provided, and the energy difference will be dissipated on the charger circuit. The 3V battery will be full, the 6V battery will be depleted.
If the charger is some switching type regulator with 80% efficiency, then the energy drawn will be ~ 125% of the energy provided and at the end the 3V battery will be full and the 6V one will have ~ 1.12Ah charge left. The energy difference will be dissipated on the charger circuit.
If your battery is that special (hypothetical) type which would survive the direct connection then the energy would be dissipated on the internal resistance and the wires.

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Homework Helper
@Rive : there is no mention of a separate charger in the scenario ...

@BvU : exactly that's why I mentioned it...

BvU
Gold Member
2021 Award
@Rive : there is no mention of a separate charger in the scenario ...

@BvU : exactly that's why I mentioned it...

exactly, because he should be using a charger circuit between them

connecting a 6V battery directly to a 3V battery ( or any other very different voltage situations) is, generally, not wise

Homework Helper
@Keanthon: I took the "let's say" as indication you refer to the 'hypothetical' battery @Rive mentions. He and Dave jumped on this rightfully for practical reasons: connecting two different ideal voltage sources leads to infinite current -- not a good idea.
My answer was more to reassure you re energy balance, aside from the losses that occur in practice.

Are things a bit clearer for you now, or would you like some more explanation ?

Keanthon
@BvU @Rive sorry I'm relatively new to this topic, but why would Battery B not be depleted if they have the same charge capacity of 3Ah. Doesn't battery store energy by storing charge in electrodes. If they are both rated as 3Ah, don't they have the same total charge capacity and when charging an empty A with B, shouldn't it be a direct transfer of charge. Assume 100% transfer of charge wouldn't that result in a loss of energy?

Homework Helper
Gold Member
Lets suppose you used an ideal dc-dc converter to step down the 6V to 3V. If you draw 1A from the 3V side the converter would draw 0.5A from the 6V battery.

The power into the converter 0.5*6 = 3W equals the power out 1*3 = 3W.

When the 3V battery is fully charged the 6V battery will still be half full.

In practice it won't be quite like that because dc-dc converters aren't ideal, they have losses. The charging process isn't 100% efficient either, some is turned into heat.

This situation is hypothetical as you would in practice never do this for a number of reasons. The charging of a battery requires the rate to be monitored and adjusted as the battery is charged otherwise damage will occur. Additionally the starting voltage to charge a battery cannot be too high again could result in damage. So some charging device is necessary to control the charging current and voltage as mentioned above.

@BvU @Rive sorry I'm relatively new to this topic, but why would Battery B not be depleted if they have the same charge capacity of 3Ah. Doesn't battery store energy by storing charge in electrodes. If they are both rated as 3Ah, don't they have the same total charge capacity and when charging an empty A with B, shouldn't it be a direct transfer of charge. Assume 100% transfer of charge wouldn't that result in a loss of energy?

Batteries are complex devices and simple theoretical discussions are fraught with errors. The first error is that the charging battery cannot transfer all its stored energy since some must be used to do the work in charging the other battery.

Staff Emeritus
@BvU @Rive sorry I'm relatively new to this topic, but why would Battery B not be depleted if they have the same charge capacity of 3Ah. Doesn't battery store energy by storing charge in electrodes. If they are both rated as 3Ah, don't they have the same total charge capacity and when charging an empty A with B, shouldn't it be a direct transfer of charge. Assume 100% transfer of charge wouldn't that result in a loss of energy?

I think you are confusing batteries and capacitors. Also confusing charge with energy. Study the Wikipedia article on those four words, them return to your original question.

Homework Helper
Gold Member
@BvU @Rive sorry I'm relatively new to this topic, but why would Battery B not be depleted if they have the same charge capacity of 3Ah.

The Ah "capacity" of a battery is only useful if you are comparing two batteries with the same voltage.

To properly compare two batteries you need to know how much energy they store. Energy is measured in Joules, Watt Seconds or kWh.

To convert from Ah to Joules multiply the Ah figure by 3600 and by the battery voltage.

russ_watters
Homework Helper
Gold Member
Not a very good analogy but.. the Ah rating is like the flow available from a Dam (so many gallons for so many hours). You can only use that to compare the energy in two Dams if they are the same height above the turbine.

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Mentor
@BvU @Rive sorry I'm relatively new to this topic, but why would Battery B not be depleted if they have the same charge capacity of 3Ah. Doesn't battery store energy by storing charge in electrodes. If they are both rated as 3Ah, don't they have the same total charge capacity and when charging an empty A with B, shouldn't it be a direct transfer of charge. Assume 100% transfer of charge wouldn't that result in a loss of energy?
EDIT -- Others are faster at typing than I am...

You are mixing terms, which is part of your confusion. The Amp*Hour (Ah) rating is a measure of Energy stored (EDIT -- see my comment about this in my next post), not charge. If you want to ask about exchanging charges between a charged and uncharged capacitor, that is a different question (do a search of the PF to find those discussions).

If you want to discuss charging a 3V battery from a 6V battery, you would include the efficiency of the DC-DC buck voltage converter that you connect between them. That efficiency can be around 90%, so you would be able to convert about 90% of the higher voltage battery's energy content into energy stored in the 3V battery.

Well, except that for real batteries, taking that last 20% of their energy out often damages the battery, so it would be a fairly destructive experiment.

But not nearly as destructive as directly connecting a 6V battery to a 3V battery in real life. Other posters have been kind in saying that it's not a good idea. It would likely result in a fire and ruptured batteries.

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Homework Helper
I have to admit I misread the original post -- I figured two identical batteries and A empty ( showing only 3 V) and B full.
Casually skipped over the infinite current issue too. Not a good show.

Mentor
To properly compare two batteries you need to know how much energy they store. Energy is measured in Joules, Watt Seconds or kWh.
The Amp*Hour (Ah) rating is a measure of Energy stored, not charge.
Good point by @CWatters -- the Ah rating of the battery only refers to Energy if the battery voltage is assumed. I omitted mentioning that (bad habit).
Casually skipped over the infinite current issue too.
I think things will explode a bit before we get to infinite current...

BvU