I need to derive an equation for the current through the led in the given circuit. The resistor R is a variable resistor.

I know I need to do a simple KVL, solve for current, and there we go. But I'm not sure if I need to use the Shockley diode equation or not. Should I assume the current through the diode is the same as the current through the resistors, just treating the led kind of as a resistor? This is what I'm thinking: iR + 100i + iR - 5v = 0. Any help is appreciated.

 

You need the Vf drop of the LED. This spec is extremely depended on how the LED was made, there is no easy answer except the component spec sheet.

I've started an article on the subject...

http://forum.allaboutcircuits.com/showthread.php?t=18277

In general, LEDs can be thought of as similar to zener diodes, only with forward bias. They can be as little as 1.5V Vf, and as much as 3.8V Vf.

 

Vf, If is question there is no set of forward current or forward volttage . what you must learn is every device is limited by power dissipation and that cannot be exceeded. A led sitting outside in the tropics will require a different Vf-If from the same LED sitting in the artic. To solve these problem a limiting resistance is put in series to limit the current. Since the LED is a diode of sort it will follow an exponentail curve like a diode.