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For an overload relay on a magnetic starter, what should the overload current be set at? I'm not sure whether this should be set to the rated running current of the motor, or an approximation of the inrush current upon starting.

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You must read the instructions for the specific overload relay you have. Some require that you set them at exactly the motor FLA, the allowable "pick-up point" is already built-into the design. Others have you adjust the values based upon the motor design type, especially if you are in North America where we have "Service Factor" for motors.

That said, you NEVER set the OL relay for the inrush current of the motor. Never...

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A motor overload relay is intended to protect the motor from overheating due to a mechanical overload or failure to start. It should be set just above the motor's rated running current, usually 115% to 125% depending on the motor design. The maximum setting is dictated by electrical safety codes. The tripping time should be designed such that a higher current during starting will not cause the overload to trip. If the overload trips during starting, an alternative type of protection can be used, or the overload can be shunted during starting. Other remedies may be available. Consult the applicable electrical code for details.

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