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The value of the resistor is simple to calculate: subtract the LED's forward voltage from your supply voltage, and this is the voltage that must be across the resistor. Then, use Ohm's law to find the resistance necessary to get the current desired in the LED.

Any power in the resistor is power not used to make light. So why don't we make the supply voltage very close to the LED voltage, so we don't need a very big resistor, thus reducing our power losses? Because if the resistor is too small, it won't regulate the current well, and our circuit will be subject to large variations in current with temperature, manufacturing variation, and supply voltage, just as if we had no resistor at all. As a rule of thumb, at least 25% of the voltage should be dropped over the resistor. Thus, one can never achieve better than 75% efficiency with a series resistor.

You might be wondering if multiple LEDs can be put in parallel, sharing a single current limiting resistor. You can, but the result will not be stable, one LED may hog all the current, and be damaged. See Why exactly can't a single resistor be used for many parallel LEDs?.

The value of the resistor is simple to calculate: subtract the LED's forward voltage from your supply voltage, and this is the voltage that must be across the resistor. Then, use Ohm's law to find the resistance necessary to get the current desired in the LED.

Any power in the resistor is power not used to make light. So why don't we make the supply voltage very close to the LED voltage, so we don't need a very big resistor, thus reducing our power losses? Because if the resistor is too small, it won't regulate the current well, and our circuit will be subject to large variations in current with temperature, manufacturing variation, and supply voltage, just as if we had no resistor at all. As a rule of thumb, at least 25% of the voltage should be dropped over the resistor. Thus, one can never achieve better than 75% efficiency with a series resistor.

You might be wondering if multiple LEDs can be put in parallel, sharing a single current limiting resistor. You can, but the result will not be stable, one LED may hog all the current, and be damaged. See Why exactly can't a single resistor be used for many parallel LEDs?.

An LED requires a minimum voltage before it will turn on at all. This voltage varies with the type of LED, but is typically in the neighborhood of 1.5V - 4.4V. Once this voltage is reached, current will increase exponentially with voltage. Consequently, any voltage much higher than this will result in a very huge current through the LED, until either the power supply is unable to supply enough current and its voltage sags, or the LED is destroyed.

The value of the resistor is simple to calculate: subtract the LED's forward voltage from your supply voltage, and this is the voltage that must be across the resistor. Then, use ohm's law to find the resistance necessary to get the current desired in the LED.

Here's how it works: Q2 gets its base current through R1. As Q2 turns on, a large current flows through D1, through Q2, and through R2. As this current flows through R2, the voltage across R2 must increase (ohm's law). If the voltage across R2 increases to 0.6V, then Q1 will begin to turn on, stealing base current from Q2, limiting the current in D1, Q2, and R2.

So, R2 controls the current. This circuit works by limiting the voltage across R2 to no more than 0.6V. So to calculate the value needed for R2, we can just use ohm's law to find the resistance that gives us the desired current at 0.6V.

The neat thing about this is it doesn't matter what our supply voltage is, or what the forward voltage of D1 is. In fact, we can put many LEDs in series with D1 and they will still light, even if the total forward voltage of the LEDs exceeds out supply voltage.

An LED requires a minimum voltage before it will turn on at all. This voltage varies with the type of LED, but is typically in the neighborhood of 1.5V - 4.4V. Once this voltage is reached, current will increase very rapidly with voltage, limited only by the LED's small resistance. Consequently, any voltage much higher than this will result in a very huge current through the LED, until either the power supply is unable to supply enough current and its voltage sags, or the LED is destroyed.

The value of the resistor is simple to calculate: subtract the LED's forward voltage from your supply voltage, and this is the voltage that must be across the resistor. Then, use Ohm's law to find the resistance necessary to get the current desired in the LED.

Here's how it works: Q2 gets its base current through R1. As Q2 turns on, a large current flows through D1, through Q2, and through R2. As this current flows through R2, the voltage across R2 must increase (Ohm's law). If the voltage across R2 increases to 0.6V, then Q1 will begin to turn on, stealing base current from Q2, limiting the current in D1, Q2, and R2.

So, R2 controls the current. This circuit works by limiting the voltage across R2 to no more than 0.6V. So to calculate the value needed for R2, we can just use Ohm's law to find the resistance that gives us the desired current at 0.6V.

The neat thing about this is it doesn't matter what our supply voltage is, or what the forward voltage of D1 is. In fact, we can put many LEDs in series with D1 and they will still light, even if the total forward voltage of the LEDs exceeds the supply voltage.

The value of the resistor is simple to calculate: subtract the LED's forward voltage from your supply voltage, and this is the voltage that must be across the resistor. Then, use ohm's law to find the resistance necessary to get the current desired in the LED.

The value of the resistor is simple to calculate: subtract the LED's forward voltage from your supply voltage, and this is the voltage that must be across the resistor. Then, use ohm's law to find the resistance necessary to get the current desired in the LED.