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Can I use the Arduino with an External wall-wart and the USB at the same time? I need to power more LEDs, and the USB on my computer can only supply so much. But, I didn't want to destroy my computer because I had the USB and the external plugged in.

I saw this,

External power supply?

But I am still unsure. The reason I want to at all is because when I connected this circuit, the Arduino would cease to be recognized on the USB. I don't know if it is because there wasn't enough power to the LED, if I short-circuited something, or something else. I do not wish to break my laptop though.

What happens if I power the Arduino with both the USB and external power voltage simultaneously?

These all seem to indicate you don't just "plug in" with both, and you need some other kind of regulator or something. But in that same answer, one person says,

https://arduino.stackexchange.com/a/896/69706

And that indicates when the power is plugged in the USB is cut off. Again, my fear is breaking my laptop, and that is the main question. Especially in light of this,

Is supplying 5V from both external 5V and USB harmful?

The external power is this,

9 VDC 1000mA regulated switching power adapter

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    don't use the arduino as a power supply for the LEDs – jsotola Oct 24 '20 at 18:29
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    Don't I power the Arduino and run the wires through the GPIO? – learntofix Oct 24 '20 at 18:33
  • you do if you want to use the arduino as an expensive fuse .... GPIO pins have a limited current source/sink capacity .... the internet has many examples of controlling high current devices with a microcontroller – jsotola Oct 24 '20 at 18:46
  • Besides the limits of the signal pins, the 5V pin on the arduino cannot supply as much current as your 9V 1A wall wart. Question is, how you power more LEDs ? – DataFiddler Oct 28 '20 at 22:19
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Yes, you can simultaneously connect external power supply and USB. As explained in one of the answers, that you linked, the Arduino chooses it's power input through the supplied voltage on Vin/barrel jack. Vin has no direct connection to the VUSB, so the USB port will not get any voltage from the external supply, thus it does not get damaged.

BUT: Your thinking is wrong. Clearly your LEDs need more than 500mA. This current should never flow through the Arduino. You can easily fry the protection diode or the voltage regulator (which is an inefficient linear regulator), if you connect all the LEDs to the 5V pin. One GPIO pin can only provide about 20mA (40mA at absolute max, you should stay below 20mA) and only 100mA through all GPIOs together. They are not made to provide power, but for switching.

Instead you should connect the LEDs outside of the Arduino to the power supply. If you want to use the specified 9V power supply, you need to buy a buck switching voltage regulator, which gets the voltage down to 5V for you. Make sure, that this regulator is rated for a current significantly higher, than what you need.

How to control the LED then? That depends on your LEDs. If you just have some bare LEDs, you could use a transistor to switch the higher voltage from the Arduino. If you have a plain LED strip you can also use a transistor. Best use a MOSFET for this. If you have an addressable LED strip, just connect the power lines to the 5V output of your new switching regulator and the data line to the Arduino.

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