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I'm using an LED that is rated at (0.06W) current is 20mA and voltage is at 3V. I did some wrong calculations, and the resistors I'm using are not enough to limit the current to the diodes.

schematic

simulate this circuit – Schematic created using CircuitLab

The current is 0.024A now, can the LED work without blowing up? I'm maxing it with higher power would it manage?

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    \$\begingroup\$ It won't blow up, but it may die young. I'd suggest 0.24A for "die a lot faster" and perhaps 24 amps (with plenty of volts to maintain an arc after internal parts expire) if you really want to have it "blow" nicely. ;^> \$\endgroup\$ – Ecnerwal Dec 10 '15 at 2:53
  • \$\begingroup\$ There are part tolerances in your LED, resistor and meters, even small errors can shift the operating point of and LED in such a circuit. If the LED is never getting too hot to hold between your fingers it will likely live a long time (less than the rated but not much). Also note max current may already be more than operating current which you should be aiming for. \$\endgroup\$ – KalleMP Dec 10 '15 at 8:46
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Unless you are grossly overloading the device, it will not blow immediately. However, as with all devices too much heat will kill it eventually. If you can add a bit of heatsinking (usually not possible with common LEDs) then it will be fine, otherwise derate the MTBF of the device accordingly.

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If the LED current is 24 mA, and the recommended maximum current is 20 mA, you can probably expect a somewhat reduced life for the LED, but it is unlikely to be destroyed instantly.

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If the values you placed are correct \$ Vled=3V, R1=200\Omega, V1=4.8V \$ your actual current is:

\$ Iled=\frac{V1-Vled}{R1}=9mA \$

Therefore, no overload. Check your values and/or your circuit.

If you keep the junction within reasonable temperatures the LED will not die immediately but you will accelerate the aging process.

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It seems your error is serendipetous and you're actually pushing less current through the LED than it's rated for. :)

If you don't exceed the LED's recommended forward current, it'll last for a long, long time.

To determine the value of the ballast resistor, you can do this:

$$ R1 = \frac {V1-VfLED}{IfLED} = \frac {4.8V - 3V}{0.02A} = 90 \text{ ohms} $$

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