The need of a resistor in an LED is to limit the current in the LED to a safe value. LEDs are semiconductors or diodes in particular. The current flowing in an LED is an exponential function of voltage across the LED. As a result what happens is that a small change in voltage can produce a huge change in current. That is the most important concept of why resistors are used in LEDs. Resistors have specific properties. The current and voltage in a resistor are linearly related. That means that a change in voltage will produce a proportional change in current. Current versus voltage is a straight line for a resistor but not at all for an LED. Because of this, you can’t say that LEDs have resistance. Resistance is defined as the constant ratio of voltage to current in a resistive circuit element. Even worse, there is no real way to figure out exactly the relationship between current and voltage for any given LED across all possible voltages other than direct measurement. The exact relationship varies among different colors, different sizes, and even different batches from the same manufacturer. When you buy an LED, it should come with a rating. That rating will look like something 5.5V @ 20 mA. That gives you a general point on the operating curve. This is normally a safe operating point. In addition you may get a maximum rating. Which can be in the form of either a voltage or current . For example, a lot of people report buying 5V blue LEDs. These are really not rated to operate continuously at 5V in most cases. The other thing that is very important to mention is the idea that it’s more useful to talk about driving an LED with a current of a particular size, instead of a voltage. If you know the voltage across an LED, you cannot determine the current flowing in it, unless you are operating it at the exact point along the curve that’s described in the specs. More over being if you are being off by a little then the forward voltage can have a drastic effect in the current. So the approach that one should prefer is to select a current-limiting resistor in order to achieve a target current in the LED. Most 3mm and 5mm LEDs will operate close to their peak brightness at a drive current of 20 mA. This is a conservative current it will not exceed most ratings ,your specs may vary, or you may not have any specs, in this case 20 mA is a good default guess. In most cases, driving the LED at a higher current will not produce substantial additional light. Instead, the junction which is the working parts of the LED has to dissipate the excess power as heat. Heating the junction will decrease its useful life, and can reduce the output of the LED substantially. Heating it enough will cause catastrophic failure producing a dark emitting diode. All these factors explain how and why LEDs require resistors for proper working.
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