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If I wire 2 AA cells with a nominal capacity of 2 Ah and a nominal voltage of 1.5V each in series, then I'll get 3V with 2 Ah, right? Is that, thus 6 Wh?

If I wire them in parallel, I get 1.5V with 4 Ah? Is that also 6 Wh?

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    \$\begingroup\$ More like 5 Wh. You don't use 1.5V when calculating Wh because the battery voltage declines during discharge. The average voltage is more like 1.3V or 1.25V. \$\endgroup\$
    – user57037
    Oct 28, 2018 at 4:41
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    \$\begingroup\$ What AA cells? NiMH, alkaline, zinc chloride...? And what is the current draw? Continuous use or intermittent? \$\endgroup\$
    – Indraneel
    Oct 28, 2018 at 6:09
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    \$\begingroup\$ @Indraneel Which of those AA's you mention are 1.5V? Which would have a capacity of 2000 mAh? \$\endgroup\$ Oct 29, 2018 at 14:25
  • \$\begingroup\$ @Indraneel, they're alkaline and we're pulling 150 mA intermittently. There's a 400 mA spike during startup, then about 25 seconds at 150 mA. Most of the time, the components are in deep sleep and draw substantially less current. \$\endgroup\$
    – D. Patrick
    Oct 29, 2018 at 14:30

2 Answers 2

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Initial answer: Yes Possibly: No: see update Formula: Power Capacity [Wh] = #Batteries * Voltage * Electric Charge [Ah] Divided in Series/Parallel:

Connection   Voltage            Electric Charge [Ah]  Power Capacity [Wh]
----------   -----------------  --------------------  -------------------
Series       2 * 1.5 V = 3   V  1 * 2 Ah = 2 Ah       3   V * 2 Ah = 6 Wh
Parallel     1 * 1.5 V = 1.5 V  2 * 2 Ah = 4 Ah       1.5 V * 4 Ah = 6 Wh
  • This means by using batteries in series, the voltage is increased (sometimes needed by the circuit).

  • Using batteries parallel extends the 'running time' of the circuit without the batteries to be replaced/charged.

  • Of course combinations are possible (e.g. using a set of batteries with 2 parallel sets of 3 batteries in series, resulting in 4.5 V, 4 Ah).

Update

It seems it is load dependent. My knowledge about batteries is not so high, and it seems Misunderstood's answer shows more insight.

However, I rather will keep my answer for all useful comments below.

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    \$\begingroup\$ Pfew. Finally some of this is making sense. Thanks so much!! \$\endgroup\$
    – D. Patrick
    Oct 25, 2018 at 23:42
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    \$\begingroup\$ It's worth noting that it's not quite this simple. This is a pretty good estimate, but battery voltage isn't constant, so it's not exact. Not to mention that battery capacity can vary based on discharge rate. \$\endgroup\$
    – Hearth
    Oct 26, 2018 at 0:16
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    \$\begingroup\$ @D.Patrick: you figure out the step up/step down conundrum by looking at how efficient regulators are. Synchronous buck converters are generally best, but modern boost converters aren't far behind. Note, however, that most dry cells (and, incidentally, NiMH cells) are good down to 0.9V/cell -- leave much more than that on the table and you're throwing away energy. So if you're going to step down to 3.3V, start with four cells (0.9V * 4 = 3.6V, which is enough headroom for a synchronous buck). \$\endgroup\$
    – TimWescott
    Oct 26, 2018 at 0:19
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    \$\begingroup\$ @D.Patrick, there is information in this unrelated answer which may be helpful regarding the regulators. You can skip the first third of the answer :) \$\endgroup\$
    – bitsmack
    Oct 26, 2018 at 0:33
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    \$\begingroup\$ An alkaline AA's capacity is rated from 1.5V down to 0.8V. So is 3V or 1.5V the voltage that should be used to calculate Wh? The same that you cannot say you can get 1.5V @ 100 mA for 20 hours from a 2,000 mAh alkaline. So I do not believe the OP can get 6Wh. \$\endgroup\$ Oct 27, 2018 at 20:04
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2 AA cells with a nominal capacity of 2 Ah and a nominal voltage of 1.5V each in series, I'll get 3V with 2 Ah, right? Is that, thus 6 Wh?

The 1.5V of an AA is not like the nominal 1.2V of a NiMH. The estimation of Wh by V x capacity works much better for NiMH and Li-ion where the nominal voltage is mid point in the discharge curve. NiMH fresh charge voltage is 1.6V and Li-ion 4.2V, and cutoffs 1V and 3V. AA fresh voltage is 1.5V and cutoff is 0.8V, very unlike NiMH and Li-ion.

So no, 8 Wh would not be correct for an alkaline AA. It would be 6 Wh if the battery voltage was a constant 3V over the lifespan of the battery. Notice, in the MilliAmp-Hours Capacity bar chart below, it says "Continuous discharge to 0.8V". The 2 Ah is not at a constant 3V. An AA has a 2 Ah capacity only with a specific load.

Both the capacity and voltage are dependent on the load and therefore the Wh is also load dependent.

More information is needed. Need to know the instantaneous current and voltage over the lifetime of the battery. Even at that it is not easy to calculate the watt hours used.

An empirical approach would be easier. Continuously record the current and voltage of the battery while your device is operating. Then calculate the Wh for small periods of time and sum the results.



The capacity of an AA varies with load's current draw and whether or not it is a continuous load.

enter image description here
Source: Energizer E91 AA Datasheet


The voltage and discharge curve is also load dependent.

enter image description here
Source: Energizer E91 AA Datasheet


If the load is not continuous the discharge curve is much different than a continuous curve.

enter image description here
Source bossmanbattery.com

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