Can I connect 2 batteries in series and parallel?

Hi. I am building a project using 2 18650 Batteries. To power the Arduino and the servos, I have to connect them in series. I also have the TP4056 board to charge the batteries. So for the batteries to charge with this board, I have to connect them in parallel. So if I connect the two batteries in series and parallel, will it work?
If not what can I do to solve it? I don't want to add any extra components like step-up transformer and such.
Thank you!

You can, but not at the same time, lol. Try drawing the schematic for such a connection. Notice any shorts?

I had tried to do the same for my GM328A using two TP4056 chargers (one for each battery).
It is currently on hold until i find a suitable 6-pin switch (two independent groups of 3 pins) to toggle between serial and parallel connection of the charger outputs.

I was planning to use a switch like this--

So its a 2-way switch which can toggle between series and parallel connection. Do you think this will work?

Sorry, it's 2 AM here and i have trouble comprehending that (and the handwriting).

I quickly threw this together in some online editor, hope it's easy to understand.
circuit
One position of the switch is for charging, the other is for normal use, can't do both.
There may be something i overlooked, i haven't tested it yet.

You can’t connect them at once like that as it will create short circuits (you see how the red and blue wires touch each other at the terminals?). I guess the easy was would be to use 2 TP4056 boards and add switchs to disconnect them when charging

I don't see where it would short circuit. When its in series connection, the blue wire doesn't connect to the + of the second battery. So then, both the arduino and the TP4056 will be connected to the batteries in series. How will that short circuit?

So what switch can i use in this? A 4-Way switch?

I think it is called DPDT switch.

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Is there any other way(preferably cheaper) to do this? Thanks!

It's a 6 pin dpdt switch right?

Could also be a rotary switch.
Paul

Get an old 2-cell laptop battery and replace the cells.

How will it work if I want the batteries in series? I couldn't get the right connections.

oh, nvmd. I actually found one on the internet.

So like in the given diagram above, could I add two more wires, one connected to 4 and the other to 5 (for parallel circuit) and connect that to a board that needs parallel connection while simultaneously using the 2 given output wires just for series connection?

No, you can't use them like that.
It is either in series or in parallel, you select it with the switch.
Can you make the switch be in both positions simultaneously? (hint - don't try or a battery will catch fire).

P.S. that circuit on your picture is not exactly the same as mine, i think you may need to connect the charger to the output (only in parallel position of the switch!)
On my circuit the output pins of the two chargers will be connected in place of the batteries.

If you can find some old (working, but not holding much charge) 2-cell laptop battery (about 7.8V on the label) for cheap, it would be the easiest way. You need only the controller PCB to use it with the cells you already have.
A battery designed for more cells may or may not work with only 2 cells. Worth a try if you find it in a scrap pile, but better not risk spending money for one, lol.

So the circuit in that image won't work?

Also, what I did was that I had connected the output pins to both the arduino and the TP4056 charger. So when the circuit is in parallel, the batteries would change and I would just put a small code that if the voltage is less than 5, then switch off the arduino. And when it is in series, the arduino has the necessary power and even though it is connected to the TP4056, as the circuit isn't closed(as the board isn't plugged into a wall charger) it doesn't matter.
So I had planned built the circuit like that.

No, it should still work.