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Why will my Arduino not power up when I use an external power supply for my Ramps 1.4?

I am working on my 3D printer and I am using the Arduino Mega 2560 with the Ramps 1.4 board. when I power the ramps board the Arduino will not power up and operate. I have tried moving the header pin across VCC and the other connecter but there is not effect. I have to power the Arduino separately Via USB. is there something I am hooking up wrong or is there damage that I have to fix on the board itself.

Without knowing how you wired it and what power supplies were used it is quite pointless to give advice.
The Arduino works with up to 15V on the power input, above that and it is toast.
So if all is connected correctly you should not have the problem.

You have to be extremely careful moving the power jumpers around on a RAMPS board, it is entirely possible to inflict mortal damage to the Ramps and/or the Arduino.

What voltage are you applying to the Ramps ?

Have you connected the supply ground of the Ramps to the Arduino ground ?