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You will need to know the amount of current flowing through the coil when 220 volts is applied across it. A resistor in series with the coil will limit the current so that the coil only sees 220 volts. The resistor will need to drop 57 volts. So, 57 volts divided by the current in amps will give you your required resistance. You will need a resistor with a high power dissipation rating with 57 volts across it. Your resistor will probaly need to dissipate several watts. For example: A 220 volt coil with 300 milliamps (.3 amps) will require a resistor of 733 ohms. The power dissipation of the resistor would need to be 17.1 Watts! You might try using a light bulb as a series resistor. Ensure that it can handle 57 volts. To complicate matters, is that AC or DC you are using? AC relays have inductance build in, in order to increase the specific "ac resistance", thus the same coil could use as little as 0,001A so you will need a very low value resistor. Anyway, if any 220V relay uses as much as 300mA, I doubt if you will be able to pick it up with one hand! Such a relay coil will draw about 66W of power! I have a 16A rated contact 230V relay. Its current is 0,0015A that is equivelant to 0.33W at 220V!

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Q: What size resistor is needed to allow a 220 volt coil in a relay operate on 277 volts?
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