Battery life calculation parallel vs series

Question

When I'm calculating battery life in series do I add up the mah or is is the same as a single unit? Ex. If I take 10x 3.2v cells @3000 mah and concert them in series, I will have 32 v @ 30,000mah or 3000mah. How does this work for parallel circuits. Thanks

Answer 1

Think of it this way, you get what you pay for, and you're paying for Joules, watt.hours, energy. This is, if you like, the financial restatement of Conservation of Energy. When in doubt in physics, follow the energy!

A 3.2v 3Ah cell holds 9.6Wh. If you have 10 of them, you will have a total of 96 Wh available. It doesn't matter how you rearrange the cells, you will still have the same total energy available.

If they are in series, then 96Wh at 32v is 3Ah, the same as a single cell. As the current has to pass through each in turn, that makes sense.

If they are in parallel, then 96Wh at 3.2v is 30Ah. As their currents all add up in parallel, this too makes sense.

It still holds if you make a (say) 2s5p array of 6.4v, which will show 15Ah for the same 96Wh energy.

Answer 2

Here is a set of "rules"/Guidelines for combining batteries.
This should be used as an aide-memoir and the underlying principles MUST be understood if disaster is to be avoided.

eg I say for parallel cells - "Limiting max allowed current is sum of allowed currents BUT hard to ensure correct division = mA_max_sum." This is correct, but if you parallel say an AA and a Dcell, the variation in voltage with discharge energy is such that the AA cell may be treated badly by both charge and discharge processes.

Care and understanding is needed in both cases below.

Series:

Volts add = Vsum.

Current is the same in all. Limiting allowed current is that of the smallest = Ixxx_min.
(eg Ichg_min or Iout_min)

mAh are that of the smallest = mAh_min

Power capability out is Vsum x Iout_min

Energy capability = mAh_min x Vsum

Parallel:

Great care needed.

Volts: Batteries in parallel with different voltage ratings = bad juju.
For identical voltage batteries volts = volts = Vbat BUT must be same state of charge when combined and same capacity and condition.

Current is the sum of currents from/to each. If charging in parallel current division may cause problems.

Limiting max allowed current is sum of allowed currents BUT hard to ensure correct division = mA_max_sum.

mAh is sum of mAh = mAh_sum but ideally all have identical mAh.

Power capability out is Vbat x mA_max_sum

Energy capability = mAh_sum x Vbat

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Re example given:

You say

10 x 3.2v cells @3000 mah

That sounds like LiFePO4 cells - possibly 26650 size.
If so, combining cells affects how they are charged and balanced.
VBased on your queries re achieved capacity, you may also need to ask about balancing and charging.