Resistor Value for LED

source : http://www.sparkfun.com/
Limiting current into an LED is very important. An LED behaves very differently to a resistor in circuit. Resistors behave linearly according to Ohm's law: V = IR. For example, increase the voltage across a resistor, the current will increase proportionally, as long as the resistor's value stays the same. Simple enough. LEDs do not behave in this way. They behave as a diode with a characteristic I-V curve that is different than a resistor.
For example, there is a specification for diodes called the characteristic (or recommended) forward voltage (usually between 1.5-4V for LEDs). You must reach the characteristic forward voltage to turn 'on' the diode or LED, but as you exceed the characteristic forward voltage, the LED's resistance quickly drops off. Therefore, the LED will begin to draw a bunch of current and in some cases, burn out. A resistor is used in series with the LED to keep the current at a specific level called the characteristic (or recommended) forward current.

Using the circuit above, you will need to know three values in order to determine the current limiting resistor value.

i = LED forward current in Amps (found in the LED datasheet)
Vf = LED forward voltage drop in Volts (found in the LED datasheet)
Vs = supply voltage

Once you have obtained these three values, plug them into this equation to determine the current limiting resistor:

Also, keep in mind these two concepts when referring to the circuit above.

1. The current, i, coming out of the power source, through the resistor and LED, and back to ground is the same. (KCL)
2. The voltage drop across the resistor, in addition to the forward voltage drop of the LED equals the supply voltage. (KVL)