batteries
When combining battery cells in series, the voltages of the cells are added to get the voltage of the final circuit.
Do the mAh add up, or stay the same?
For example, suppose you have two 3.7V cells, each with 200 mAh capacity. When connected in series, will the resulting battery will be a 7.4V, 200mAh battery?
Cells in devices that you do not wish to be a flaming ruin MUST have protection.
Having protection circuits does not guarantee it will not happen.
Cells without protection are intended for use by either manufacturers or experts or enthusiasts who add their own or for suckers.
Whole device protection and cell protection are complementary and serve overlapping but different roles.
4,000 mAh 18650 LiIon batteries are ~~~= 99.9% +0.1% - 0.0% sure to be rubbish.
ie not just < 4000 mAh but << 4000 mAh and low quality.
The people who bogus label cells
almost never feel an obligation to use the best cells they can and
almost always decide to add injury to insult by using junk as well as lying.
Real world experience shows that the value of 'almost' is very high in both cases.
Higher capacity cells can usually be fitted OK.
MUCH higher capacity will lead to long CC tails and overcharge but not an issue here as mAh_new is < to << 4000 mAh.
Notice that in this ad and all their other ads they ALWAYS show non-brand-label views of the battery.
However, you may find that the racing stripes and general colour scheme a good match for the well known "Ultrafire" brand batteries. This may in fact be a real brand and these may be real examples of it BUT you can buy empty shrink wrappers to apply to the battery of your choice with this (or other) branding on it , so caveat emptor. Better nullius emptor I'd hazard.
These ones are a stunning 6800 mAh - a steal at the price. Available here
You'll find others similarly arrayed here and
here - 3000 mAh and 4000 mAh and
and unspecified but with GENUINE CREE 2000 lumen {so 20+ Watt} flashlight for $9.27 and
only 4000 mAh and
that's better - 4200 mAh
and .............
Flee!
It does! The capacity of a battery is correctly measured in watt hours (or equivalently, joules), not amp hours. A rough approximation of a battery's capacity in watt hours is its rating in amp hours multiplied by its nominal voltage.
Putting two 1V 1AH batteries in series results in a 2V 1AH battery - which has twice the nominal capacity. If you were to use the battery as an input to a buck regulator (known as a BEC in RC hobbyist terminology), you'd be able to draw 1V with 2AH, before accounting for losses in the voltage regulator.
Best Answer
Summary
mAh stay the same when you connect cells in series - provided that cells are all of the same mAh capacity.
Special and unusual case If two cells are connected in series and they have differing mAh capacities the effective capacity is that of the lower mAh capacity cells. This is not normally done, but it can sometimes make sense to do so.
mAh add when you connect cells in parallel (but there are technical issues which mean that doing this may not be straightforward.)
The answer can be deduced by considering what mAh capacity means:
While there are (as ever) complications, this means that eg, a 1500 mAh cell will provide 1500 mA for one hour or 500 mA for 3 hours or 850 mA for 2 hours or even 193.9 uA for one year ( 193.9 uA x 8765 hours = 1500 mA.hours).
In practice the capacity of a cell varies with loading. A cell will generally produce its rated capacity if loaded at its C1 = 1 hour rate. eg 1500 mAh = 1500 mA for one hour. BUT a 1500 mAh cell loaded at say 5V (5 x 1500 = 7500 mA = 7.5A) will NOT do this for 1/5 hour = 12 minutes - and may not produce 7.5A at all even on short circuit. A load of say C/10 = 150 mA or C/100 = 15 mA may produce more than 1500 mAh overall BUT a load of say 150 uA = 10,000 x as long = 10,000 hours = about 14 months may produce less than 1500 mAh if the battery self discharges rapidly with time.
BUT
If a cell will produce say 2000 mA for 1 hour at 3.7V (a typical rating for liIon 18650 cells) then two identical cells will do the same thing if tested independently. If instead of using 2 loads you connect the cells in series and draw the same current as before the identical current flows through both cells. You can still here only draw 2000 mA for one hour BUT the available voltage has doubled.
If you use 2 x 3.7V, 2000 mAh cells in parallel to drive a 3.7V nominal load, one cell can provide 2000 mA for one hour or 200 mA for 10 hours etc AND the other cell can do the same. So the mAh ratings add.
If one cell has more mAh than the other, the mAh TEND to add when connected in parallel. Say you have 1000 mAh and 2000 mAh cells in parallel, each rated at 3.7V nominal, as the smaller battery loses capacity it will tend to reduce in voltage faster so the larger battery will provide more current so they will TEND to balance. YMMV and this is usually not good practice without specific design of what happens.
In the special case I mentioned above, you may have a 12V 7AH sealed lead acid "brick" battery beloved of the alarm industry. You may want to use an N Channel high side switch which needs a gate voltage of say 4V above the +12 rail. If you use a 9 Volt PP3 "transistor radio battery" and connect its negative terminal to +12 V then the PP3 positive terminal will be at 12+9 = 21 V initially. The N Channel MOSFET needs 12+4 = 16V so the PP3 + SLA combined followed by a regulator will operate it until the combined voltage falls to under 16V. This should be never happen, as the PP3 "dead voltage " = 6V and the Sla should not be under say 11V so minimum Voltage available = 11+6 = 17 V.
If you use this occasionally, and disconnect battery when not in use, the PP3 will last a long time. If the PP3 is rated at say 150 mAh, and if the FET high side cct takes a steady 10 mA when oj then the PP3 will last for ~~= 150/10 = 15 hours. This may be acceptable or not depending on the application.
BUT the SLA has a 7Ah = 7000 mAh capacity BUT the combination can only provide 150 mAh at >= 17 Volts. So the mAh effectively is that of the much smaller PP3. This is for the task which needs the combined voltage - the 12V output still has the full 7Ah capacity.