![]() If these components and the Uno part of a system that requires 12v for some other components, I'd suggest using 2 power supplies, 12v for the components that need it, and 7 volts into Vin (or 5v, if well regulated, into the 5v pin) on your Uno. We can only guess without the specs but it sounds like these components would be pushing your Uno's regulator pretty hard. Try measuring it with the batteries attached and at low, medium, or almost fully charged. I'm guessing you measured your charger's output voltage with no load. I didn't find a spec for the charger, but in automotive use, Lead/Acids are charged at 14.2 volts. ![]() The batteries are 12V 7.2 Ah and they are PK12V7.2 as the product name. You need to know more about the charger and the batteries. ![]() A battery charger has to apply a higher voltage than the present voltage of the battery it is trying to charge, in order to drive current into the battery against its (the battery's) voltage. We can't know without knowing the specs on the particular batteries and charger. And if the power supply provides any more than 12 volts, it will exceed regulator's spec. The Uno's voltage regulator has to waste - as heat - a good deal of power in reducing the voltage to 5v. However, a 12v power supply (batteries, charger, or both) are at, or very close to the maximum input voltage spec the Uno. Just for clarity: your diagram shows the Arduino, the batteries, and the charger connected in parallel - which is correct for what you want to do.
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