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Adafruit's article ( https://learn.adafruit.com/rgb-led-strips/usage ) states that transistor IRLB8721 can be used with 3.3V or 5V gate voltage to drive LED strip. However, in IRLB8721 datasheet ( https://cdn-shop.adafruit.com/datasheets/irlb8721pbf.pdf ) On-Resistance vs. Gate Voltage diagram shows no data for resistance for 3.3V (most likely resistance is to high to show it in used scale). So when driving the transistor with 3.3V voltage, wouldn't it heat too much? Is it a mistake in their article or maybe I'm missing something?

enter image description here

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    \$\begingroup\$ Threshold gate-source voltage on the datasheet is listed at 2.35V. At 3.3V the Drain to source resistance might be a lot higher than 30mOhm but apparently still low enough that the manufacturer considers the fet "on". \$\endgroup\$ – Wesley Lee Dec 7 '18 at 8:51
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If you examine your picture it is for a drain current of 31 amps: -

enter image description here

And clearly, if you look at figure 1 in the DS you will never get gate-source voltages of 3 volts or 3.5 volts able to produce a drain current of 31 amps.

enter image description here

So when driving the transistor with 3.3V voltage, wouldn't it heat too much? Is it a mistake in their article or maybe I'm missing something?

With a 3 volts gate source voltage and a more moderate drain current of (say) 1 amp the DS volt drop will be typically 0.1 volts and the power dissipated will be 0.3 watts. Use the 2nd picture for detailed analysis of power dissipation with different gate-source voltages.

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