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I have a Raspberry PI 3 B+, and when I activate the GPIO 4 as output and checking agains a multimeter I get its 3.3V as expected.

If I connect the GPIO4 to one end of a coil (http://www.electronicoscaldas.com/datasheet/JQC-3F-T73-Series_Liming.pdf) the voltage drops significantly, from 3.3V to 0.99V, and of course, the relay doesn't change it state.

I thought that the coil had a huge resistor and again checking with the multimeter I could verify that it has only 24Ω.

When using the pin 1 (3.3V continuosly) I see that the relay gets activated.

What's wrong with GPIO4? Is there another GPIO which I can replace this with?

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    DO NOT connect a GPIO directly to an inductive load like a relay coil or a motor. You will destroy the GPIO and then the Pi. – joan Jun 16 at 20:30
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There is nothing wrong with the GPIO, it just can't supply enough current for your coil.

If the coil has just 24Ω, at a 3,3V the GPIO would need to supply 137mA.

This source at raspberrypi.org says that the maximum current it 51mA for all GPIOs together and 16mA per GPIO.

You can connect the GPIO to a transistor that can supply the necessary 137mA.

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@RalfFriedl is right, but I found some relays which are done for raspberry and arduino.

https://www.youtube.com/watch?v=My1BDB1ei0E

Now the circuit works.

@joan do you think that this kind of relay will destroy the board?

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