Electronic – How to duplicate Apple’s tiny USB power adapter

You have a couple of easy options here: feed in an unregulated voltage, like the 12v, to the Arduino's Vin pin (on the Arduino headers), and let the Arduino regulate it, or feed in 5v to the 5v pin. In either case, of course, you should connect the ground pin to your PSU's ground rail. From the Arduino schematic, you can see that Vin is only used to feed the 5v regulator and the comparator for the USB/Vin switch, so if you power the Arduino over the 5v rail, you should not connect anything to the USB port.

Assuming you have a fairly stable and clean 5v source, feeding the 5v is the more efficient option.

You are correct that the Arduino is powered over USB only when no DC supply is present. This is implemented with a comparator, comparing half the voltage on the Vin pin to the 3.3v rail - so the switch will work correctly as long as power is supplied to Vin.

You can do this with direct conversion. Simply use a rectifier, followed by a mains-rated capacitor, then connect this to your LED in series with a very large resistor. You don't need to generate 5 or 12 volts - the series resistor will limit current through the LED. Something like this:

^{simulate this circuit – Schematic created using CircuitLab}

You could go even lighter weight and use a single resistor and capacitor but for two issues: it would flicker at 60Hz, and most LEDs aren't rated to withstand mains voltage in reverse bias.

Things to look out for:

• Remember that rectified mains is 1.41 times the RMS voltage, so spec the DC part of your circuit for 338 (169) volts, not 240 (120).
• Size R1 appropriately to the amount of current you want through the diode. In the schematic above, I've sized it to allow 2mA through for 240V mains.
• Make sure R1 can handle the power dissipation; in this case it'd be 0.67 watts, so make sure you use a power resistor.
• Mains voltages everywhere! Take care, and make sure it's well insulated.