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Ok. I have searched everywhere and can't find a definite answer on this:

My first question, Is, Can you mix 2 lithium batteries of different sizes together? (Like mixing an 18650 lithium battery with a 3v coin cell lithium battery). would that be be damaging? What effects would it have?

My second question is if it would be ok to mix 4 lithium batteries of the same size and brand together. What about NiMh batteries? How many of the same brand and size of that battery type are ok to mix?

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    \$\begingroup\$ Never never never mix any kind of batteries. They do not have the same voltage discharge characteristics. At best the low power ones will drain the high power ones, at worst something will smoke and blow up. \$\endgroup\$ – Kyle B Aug 12 '20 at 1:28
  • \$\begingroup\$ If the batteries are 'identical' they can be mixed. That means they are all the same age and preferably same manufacturers lot. Don't screw around with lithium cells though. Fire is a very real possibility with them. Buy a manufactured battery pack if you need to \$\endgroup\$ – Kyle B Aug 12 '20 at 1:30
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    \$\begingroup\$ Not sure why you can't find an answer....every battery made says exactly that right on it. \$\endgroup\$ – Kyle B Aug 12 '20 at 1:31
  • \$\begingroup\$ The preference is to match the required voltage and current compliance using a single battery cell, whenever that's an option. You don't put them in series or in parallel if you can avoid it. But that's not always possible. So you can use identical-manufacture batteries in series where the current compliance of any one of them matches your need. Or, if the batteries are all at the same level of charge (never happens) you could try and use them in parallel to increase the current compliance. These things get more dangerous with high current batteries and safer with very low current ones. \$\endgroup\$ – jonk Aug 12 '20 at 1:33
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    \$\begingroup\$ In cases where they are rechargeable, recharge them individually whenever that's possible, as well. But in the case you mention, with one 18650 and the other say a CR2032, this would be very bad to attempt. The two batteries aren't of the same type, the same manufacture, and they certainly don't have the same current compliances. So that's a very definite "don't do, ever." For parallel cases, the reason low current batteries are safer is, well, because they are low current. They usually have a higher internal resistance which better allows them to match up with each other, serving the load. \$\endgroup\$ – jonk Aug 12 '20 at 1:34
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All high energy and high power density battery chemistries are dangerous by definition. Do not mix batteries of different sizes. Do not mix different battery chemistries of any type.

Even cells of the same chemistry, size, and brand cannot be connected together in parallel before carefully matching their voltages or else they will try and charge each other, and for batteries that need careful charging (like lithium batteries) this is dangerous.

You've heard of smartphone battery fires, right? That's what happens when you do not charge lithium polymer properly or mis-used. Radio-controlled models use particularly large versions of the same battery and they are extra careful and use expensive chargers. Models, homes, and lives have been lost from mischarged and over-discharged lithium polymer batteries. For their batteries with series connected cells, the battery chargers basically monitor and charge each cell individually so it does not differ from the other cells. They are not blindly charged as a group.

Also, a 18650 lithium battery is not the same as a 3V coin cell lithium battery, not even in chemistry. That's almost like calling both NiCd and NiMh nickel batteries. There are at least several different kind of "lithium" batteries out there. If all you know about a battery is that it is "lithium" then you don't know anything about the battery. There's Lithium ion, lithium polymer, lithium iron phosphate, and whatever crappy non-rechargeable AA and AAA batteries labelled Lithium are. They're all different.

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