# Series and parallel Lipo question (20,000mAh capacity)

I got a battery bank from China and it says in the back that the rated capacity is 20,000mAh (3.7V). After some use (charging my laptop) I decided to open the thing and I noticed four cells of 5000mAh connected in series at 14.8V. The battery bank offers two ports: 1 USB port of 5V,2A(max) and one DC output of 19V/4A(max). I contacted the people and they said that the configuration of 4x5000mAh in series (achieving 14.8V) is the same as the 20,000mAh at 3.7V (4x5000mAh in parallel), because the power is the same.

How can that be? are they flat out lying? shouldn't a parallel connection give you more capacity than the series connection? even if the power at any given instant is the same, the capacity should be 5000mAh and not 20,000mAh, wouldn't it? or is it that the DC-DC converter design requirements inside the product make the two configurations equivalent?

I think inside there is this configuration: 14.8V stepped down to 5V@2A and 14.8 stepped up to 19V@4A. Since stepping up from 3.7V to 19V and still give 4A(max) would ideally require more current from the 20,000mAh battery than from the 5000mAh battery (since the voltage step would be from 14.8 to 19, not so big), is it then that the two configurations (series and parallel) are similar/equal and the reason they are marketing their product as 20,000mAh?

I would really hope you guys could help me with this puzzle and point any mistakes I've made. Thanks in advance!

## What batteries actually store

Batteries don't store charge, they store energy. That energy can be used to move charge. When a battery is being discharged it is receiving as much electrical charge at one terminal as it is emitting at the other terminal. There's no net loss or gain of electrical charge.

The energy stored is V * I * t (though you really need to integrate since voltage will be a function of time as the battery is discharged)

The numbers in your question are equivalent:

• 3.7 * 20,000 = 74,000 units of energy†
• 14.8 * 5,000 = 74,000 units of energy

## Battery Capacity

A battery's capacity is the amount of electric charge it can deliver at the rated voltage.

Charge, as we know, is measured in coulombs, an amp is a coulomb per second, so you can also express charge in amp-seconds (or amp-hours or milliamp-hours etc)

If you reconfigure the cells of the battery so that the battery has a higher rated voltage, the capacity (by this definition) is correspondingly reduced (since the overall energy available must be the same as before reconfiguration).

The energy is V * I * t so if you increase V you must decrease I * t

(which is what battery makers call the capacity - measured in amp-seconds although they usually apply a constant so they can express it in amp-hours or milliamp-hours for the convenience of consumers)

## The claim in question

Lets look at the claim you seem to be disputing

"the power is the same". How can that be?

It's just sloppy language. They are trying to say that 20,000 mAh * 3.7 V delivers the same energy as 5,000 mAH * 14.8V - which is correct.

You can of course increase power by increasing V or I - however you thereby decrease t in inverse proportion.

## Footnotes

Units of energy

1 watt = 1 joule per second
1 watt x 1 second = 1 joule
V * I = watts
1 volt * 1 amp * 1 second = 1 joule

The units in my answer are not joules (since the times are hours not seconds and the currents are milliamps not amps) but that's just a scaling factor that is the same for both numbers.

• I know that the energy stored is the same, but the capacity isn't. Thanks for the answer though. Oct 11 '13 at 8:19
• @Antonio: I'm unsure whether you consider your question to be answered? Oct 11 '13 at 9:23
• @Antonio: Capacity is really in Joules but since most batteries have a fixed nominal voltage, the battery industry uses a convenient lie and state capacity in terms of electrical charge (amp-hours) without expressly saying "at the specified nominal voltage". It's a convenient lie but don't let it confuse you. I'd attribute the rest of the confusion to language difficulties with your specific battery maker representative. Oct 11 '13 at 10:27
• I don't think I get yet...wouldn't one assume that if the package says 20,000mAh it could charge devices longer than a 5,000mAh product, cause the user doesn't know what's inside. The user just sees that the USB port is 5V and 2A(max) and the capacity. Isn't it a bit deceiving? Oct 11 '13 at 10:38
• Sorry, I didn't notice you answered already, I pressed enter by mistake and posted that previous comment Oct 11 '13 at 10:39