I'm having a bit of trouble understanding currrent limiting resistors in simple LED circuits. I know that I can determine the optimal resistor like so:
\$\displaystyle R=\frac{V_{s}-V_{f}}{I_{f}}\$
But I'm having a hard time understanding how this one value modifies the voltage and the current to the correct values for the LED. For example, if my calcuations for a super bright blue LED (with \$V_{f}\$ being 3.0-3.4 V and \$I_{f}\$ being 80 mA, and a voltage source of 5 V) gives me 25 ohms (using the lower bound of the forward voltage), that's fine. So the current throughout should be 80 mA and the voltage drop for the resistor and LED should be 2 and 3 volts, respectively.
But what if I used a 100 ohm resistor instead? Or any other value—how would I calculate the voltage drops and current? Would I assume one of them stays the same?