Resistor requirement for 3.3v

An LED has a point where the terminal voltage applied causes a significant rise in the current taken and if you increase that voltage by even as little as 0.1 volts, the current taken by the LED could be beyond its operational rating.

Because that voltage (for your LED) might be OK set at 3.3 volts, it doesn't mean you won't blow the back off it at 3.4 volts. This is why we put a current limit resistor in series. If your LED takes 100 mA at 3.3 volts (for instance) you would need to drop 1.7 volts from 5 volts with a resistor.

That means a resistor of value 1.7 volts / 100 mA = 17 ohm.

Now, if your 5 volt rose to 5.1 volts, the 100 mA would rise to no more than 1.8 volts / 17 ohm = 106 mA. If your LED is rated at a maximum current of 120 mA, you could in fact allow the 5 volts to rise to 5.34 volts before being on the cusp of exceeding its ratings.

Do you see how adding a resistor protects your LED from over-current?

For pull-down resistors on switches you need to ensure that if there is a wetting current requirement to be met, the resistor is low enough to allow that current to flow.

Quick answer

If you were using to 220 ohms from 5 V and you drop the supply to 3.3 for a 2.1V RED then 5-2.1=2.9 or R reduces to 2.9/220*R=1.2V difference

and R=1.2 /2.9×220= answer

Very accurate method which I use to estimate R and determine the voltage threshold for dim at 10% Imax which is often 10% below the rated forward voltage . Then use the difference voltage between the supply and that threshold Vt to determine the total series resistance.

The LED resistance is I have found inverse to its power rating so a 1/16W is ~ 16 ohms , a 1 W is approximately 1 ohms or less. Thus the added Series R changes with power of the LED.

This may sound complicated but with practice it’s trivial. The total series resistance you would need to drop from 3.3 V just depends on the LED curve ESR plus the series resistance to get exact desired current with reasonable tolerances. If you search my answers in the window at the top of this page you will find I have written dozens of examples on this topic.

Also compute I^2R for high current LEDs

You may learn how to do this or not is your choice.

E.g. in search tab above type or paste user:"Tony Stewart" LED ESR R quote marks are needed due to space in "my name" . I see I have 63 hits for these keywords.

For users wanting to check self, enter "user:me" .... key words