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I am using a Omron relay for DC voltage control circuit. The rated coil voltage is 48 V DC whereas the max tolerance is 110%.

However at site I just realized the measured voltage is 54 V DC, i.e. 1 V DC higher than the max coil voltage. Will it burn the relay? The relay is not used in continuous and is for synchronizing application where it is used once every few months. I am running out of lead time to purchase another relay.

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You did not give us a datasheet for the relay, so it's difficult to give a specific answer, but a general answer may be useful. Here's a random 48V-coil Omron relay.

The coil rating is as follows: enter image description here

Note the "at 70°C". At a lower ambient temperature, a slightly higher voltage is permissible. That's the temperature in proximity to the relay, not the temperature in the room or outside. Power increases with voltage squared, so even a slight overvoltage results in a much higher power dissipation. For example, 20% over results in a 44% increase in dissipation over nominal. It is possible to allow a bit higher than the 110% if you limit the ambient temperature to less than 70°C. However, that does not allow for changes in the supply voltage that the 110% spec is intended to allow for, so if you get another 10% due to high line voltage, you'll be at more than 50% above nominal dissipation.

The real limitation is the temperature capability of the insulation in the coil, but one must be ever-careful if bending the rules (and even the 110% "spec" is not safe if that's your nominal unregulated voltage).

If you cannot guarantee that the supply voltage will not sometimes go considerably higher, then I would suggest simply adding a small resistor in series with the relay coil to knock the coil voltage down to something closer to nominal.

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