I have a project with an arduino uno connected to a smartphone as a display to output data.
My question is if it's safe to connect a external battery to arduino's jack input to avoid drawing the smartphone battery? Is it safe to have 2 sources of power?
Yes, 7V - 12 V on the jack of an Uno will block the power coming from the USB. Be aware that you can draw a limited amount of power from the onboard regulator (that converts the barrel voltage to 5V) so if your display is a big consumer, it might not work. The closer to the 7V the better from that perspective.
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