Determining the Value of the Current Limiting Resistor -
A Maple  Simulation
L. Van Warren MS CS, AE
WDV
May 3, 2009
Preamble:
REDO THIS DOCUMENT WITH THE CORRECT KVL model for the DIODE. THIS MODEL IS WRONG. ESTABLISH WHY BY SHOWING HOW R CHANGES with V.

Whenever we start a document in Maple, we want the machine in a known state:

Consider the simple case of Ohm's Law, which relates current (i), voltage(v) and resistance(R):

A current limiting resistor splits R into two parts  for the LED resistance and  for the limiting resistance.
We will denote the maximum permissible LED current by 

Substituting the values used in the simulation we compute the equivalent resistance of the LED:

Having computed equivalent resistance used by the simulation we now solve the equation for .

The nearest resistance in the standard values table at www.elexp.com/t_eia.htm is 100 ohms. 
We want to know the current that will result in the LED and that is:

In practice a higher resistance would be used to insure a longer life of the LED.
We can derate the part by setting to 15 mA. It is critical to keep our units straight, or Ohm's law fails!

Which is our new resistance that makes the LED dimmer, but gives it longer life.

To use this approach for multiple LED's in series we must modeling their series resistance. In this case Ohm's law becomes:

where  is the number of LED's in series and  is the effective internal resistance of the LED.

If n is unavailable, one can compute the total resistance by measuring the current with a known applied voltage and a convervatively valued (large value) series resistor, so the LED segment or array is not damaged.