Your average Arduino, or Arduino clone has a built in voltage regulator. Think of it as a variable load resistor.
Take for instance, my Boarduino sitting here. Using the coaxial connector, I can hook it up to a 12V, 2A power supply. The on board regulator through an internal pass transistor drops that to 5V. Same thing happens if I hook up a 9V, 850mA power supply, the measured voltage on the board is 5V.
Now lets put this Arduino into a portable circuit. Because passing the input voltage through a regulator burns all the excess off as heat which is a waste of good electricity, we decide to hook up four 1.25V NiMH rechargeable batteries for a total voltage of 5V. Works pretty good because we can connect this directly to the GND and 5Vdc pins. So we decide to run a motor and 5V just doesn’t cut it and we forget we’re running unregulated to save on battery drain. What happens if we put together a battery pack with six D Cell 1.5V Alkalines for a total voltage of 9 Volts. Our Arduino’s ATMega chip is only rated for 5.5 Vdc Max and the higher voltage forces more current through it than it was designed to handle, probably quickly frying it.
Remember that Ohm’s Law states that Current = Voltage / Resistance. With this 9V D-cell pack, we could put a series dropping resistor, or a two resistor voltage divider in place to lower the input voltage to our 5Vdc port on the Boarduino so it sees a proper input voltage less than 5.5V. (We also need to put some decoupling/noise filter capacitors in there to handle brush hash from the motor, but that’s a whole other topic)
Using what we learned about why a 12V 1A power supply won’t burn up the Arduino if the power is applied to the proper port, we now see that over-voltaging any circuit will cook it. Voltage regulators, dropping resistors, load resistors, voltage dividers all are used to reduce voltage to acceptable levels.
Now let’s take that LED. Depending on the material used for the PN junction, it can be anywhere from a 1.3 to 4.6 volt device. If you supply exactly this voltage to it, you won’t need a load/current limiting resistor because the proper current will flow through it, however, with semi-conductor junctions, the current increases exponentially to the applied voltage, unlike a resistor which has a linear increase in current. If you supply more than that voltage, you need to put a resistor in series, typically 1k will let it light, but if you want full brilliance without burning up the LED, you need its data sheet to know its operating voltage and current rating.
Luxeon recommends this website’s resistor calculator for determining the exact value of this current limiting resistor:
A good web page for explaining LED circuits:
Resistor = (Voltage - LED Spec Voltage) x LED Spec Current