Mixing batteries in series : no real problem, right?

Factual Questions
1

Ok, so if you search google for “mixing rechargeable batteries and alkaline”, you get a huge amount of posts from various forums. Pretty much everyone parrots some bullshit about incorrect battery chemistry or ‘pushing’ too much current or other nonsense. From what I understand, this is complete bs, but maybe my analysis is wrong.

Ok, so a battery can be thought of as a voltage source and a resistor. Any battery only 'see’s the rest of the circuit, which is some amount of resistance. When the device is off, resistance is infinite, and no current flows.

Case 1 : You mix 2 batteries of different types in series in a device. Both batteries are healthy.

Each battery just sees the resistance of the rest of the circuit, which is just Other_Battery + Load. Whether the other battery is a lower resistance NiMH, a lithium, something exotic, or what, it doesn’t matter. V=IR, and a certain amount of current will flow. Some battery types don’t handle being shorted, but in any safe battery powered device, the load itself will have significant resistance so even if the other battery were a paperclip, it wouldn’t matter to the battery.

Case 2 : One of the mixed batteries dies first, as would be expected.

See above. So now the dead battery has high internal resistance. So almost no current flows from the still remaining battery. Device no longer works. Batteries are fine, nothing has exploded, user just needs to remove both batteries and recharge any rechargeables and replace any disposables.

As for the device : as long as the voltage remains high enough even when the load resistance is low because the device is operating, device doesn’t care. Some really low end devices do require a minimum battery voltage to work, and might not work unless they are loaded with fresh alkalines, but that’s a device fault and mixing batteries still won’t do anything bad.

But hey, I’m no expert in batteries. Anyone else want to weigh in on the straight dope on this? A lot of bad information out there.

2

No.
If you put different capacity rechargeable batteries in series, the weak battery gets wrecked, because it gets reverse charged when it runs flat.

3

As above. The danger is that you reverse the voltage across a weak cell. To see this you need to add the load resistance to your Thevenian analysis. If you increase the equivalent series resistance past a certain point for one cell you will see that the voltage across that cell will reverse. Remember the entire cell is both voltage source and it’s internal resistance.

4

Yep.

I ran a simple simulation for the OP:

Folder
Excel file
Results

As can be seen, the voltage across a weak cell can indeed go negative.

5

Wow! Thanks for performing the sim! This might not always happen, my logic was that if the failed cell is resistive enough, the load voltage just won’t be high enough, and the (electronic) gadget would just not start. But in something like a conventional flashlight, this would definitely happen. Not sure about some gadget where it’s a micro-controller and a linear voltage regulator, though.

6

There’s are lots and lots of variables, obviously. In some scenarios a weak or mismatched cell can have a reverse voltage across it, while in other scenarios there will not be a reverse voltage across a weak or mismatched cell.