Why do most layouts show a 4.7k resistor?

[PRR]

> Shockley's equation, EEK!

It is quite simple. Double the current is 20mV more voltage.

OK, the full equation has a term for Temperature. For room-temp work, sometimes you can ignore this. For reference, voltage drops 2mV per degree C.

And it has charge on an electron, but since that never changes it is just a "magic number", no different than "12" for figuring inches from feet.

[darron]

Just to add to discussion.

As mentioned, the LED is a special purpose kind of regular diode. If your circuit always gets the same voltage then you could use another special diode, the Zener diode, to shave some further voltage off and make it more efficient:

http://www.dazatronyx.com/tech/low-battery-led-fading/