Can an Arduino Uno R3 run with a 12v 1A DC power supply along with an rgb strip without an additional power supply for the strip ? Do I need to take any precautions ?
WS2812B is 5 volts.
Review this:
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With 300 LEDs at 60mA per LED you need to supply 18000 mA, that is 18A so no you can not power it with a 1A supply.