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I'm going to use a 5V relay ( DIP05-1A72-12D Datasheet), and my supply voltage is 5V, do I need a resistance in series with the relay coil not to burn the relay?

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The direct answer is that you do not need a resistance in series when powering a 5 volt relay coil from 5 volt power supply. -- For more in depth understanding, go to the data sheet that you linked, and look at the coil data. -- From the coil data, you can calculate the amount of current required for the coil. ---- Lots of in depth analysis can be made depending upon how you drive the relay coil.

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Marla answered your question (+1). One caution is that the model you have incorporates a catch diode, and if you get the polarity backward you will experience some "burning" type symptoms.

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  • \$\begingroup\$ good catch Spehro. It is always the little details that will get ya. Also, not all of the relays shown have the diode. \$\endgroup\$
    – Marla
    Commented May 11, 2014 at 15:18

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