Setting up this website, I have certain requirements. Superscript, subscript, equation display, logical picture display, charts, formatting that I like and presents information in a manner I think works1. This is the useful test post to evaluate all of these capabilities. The subject below is covered in several other places on the wide wide webz.
Calculating current-limiting resistor for an LED
An LED is a great thing. It makes a great deal of light with relatively little heat and over a long life. However, LEDs are also a bit more sensitive to power requirements and more easily damaged than other indicators and/or illuminators6. LEDs require a minimum amount of voltage before they will turn on, producing any illumination, and have a maximum amount of current they can tolerate before their lifespan is degraded (or they fry; I consider this a notable degradation of the expected life of the product).
Refer to the diagram to the right. An LED is a diode; as such there is a voltage threshold below which no current will flow and above which current will. This forward voltage drop of the diode, defined as Vf, varies depending on the type of LED used2. Once voltage exceeding the forward voltage is applied across the LED, current will flow. The LED has a maximum forward current (and/or typical, and minimum, too) given by If, where the LED will emit light of the specified intensity and frequency for the given lifetime. If the datasheet or part spec does not indicate if this is a typical or maximum value, assume it is maximum.
Note: exceeding the maximum current level of an LED will not necessarily fry it immediately. Too, it will be brighter. However, exceeding it will decrease the lifespan and luminous efficiency3.
A current limiting device must be used to protect the LED. The simplest way to limit current is to add a resistor, R, in series with the LED.