Electrical Circuit to run a DIY Speaker

I need to build an electrical circuit that can allow me to run a DIY speaker set up I’m building.

This is what I have for components:
* 1 - Amplifier Board 2 x 100 W 4 Ω
* 2 - 12 V 9800 mAh DC rechargeable batteries
* 1 - Kicker KS 5.2 series component speaker

All of those pieces work when i put them together with alligator clips, and the 3 batteries in series to give me 36 V at a completely full charge. Before I continues I have to ask: in that arrangement do I now have 29,400 mAh of capacity or is it still only 9800 mAh just at 36 V? When I plug it into the wall it will both play music immediately no matter how much charge is still remaining in the batteries and recharge the batteries at the same time. I also need to incorporate a UBS rechargeable bluetooth receiver into this circuit as well as power switch to it off and on. I don’t think the circuit is to overly complex at least not in my head but I don’t know how to accomplish it, I know very little above using alligator clips to connect the light bulb to the battery that we all got in junior high, so if someone could lay it all out for me id be extremely appreciative!!

Jamie,

Sounds like fun! First, your battery capacity will still be 9800mAh as you've put the batteries in series. If you had them in parallel, you'd have 29,400 mAh but at only 12V. Some quick math will show you that either setup will give you the same amount of power, but if your circuit requires 36V, then that's the right thing to do.

The power switch is easy - just put a Single Pull, Single Throw (SPST) switch in series with your power - between the battery and the amplifier.

The USB rechargeable bluetooth receiver - what is this for? What is it integrating with? And USB output is 5V, so you need to be careful when mixing voltages here. Just give a little bit more info on what you're doing with this so we can help you out.