DerekErb:
I now understand that the resistor can be connected on the cathode pin or the anode pin.If I am running a wire from the digital, or analog, output pin on the Arduino to the cathode wire of the LED I assume it is the digital, or analog, output pin on the Arduino which is sending the current to the LED. If I am using one of these output pins, rather than the 5V or 3.3V pins, how do I know how many volts are going to the circuit and therefore which resistor calculation to use?
For calculation purposes you can just assume a digital output pin set to HIGH will have the same voltage as the Vcc value powering the chip, so +5vdc for a 5 volt board and +3.3 volts for a 3.3 volt board.
Note your above:
If I am running a wire from the digital, or analog, output pin on the Arduino to the cathode wire of the LED I assume it is the digital, or analog, output pin on the Arduino which is sending the current to the LED.
Yes, however:
Normally one wires the led anode to the output pin and the cathode/resistor end to a ground pin so that a digitalWrite HIGH will turn on the led. If you wire the cathode to the output pin then the other end of the led/resistor must wire to the +5V pin and the led will only light if you set the digital output pin LOW.
Lefty