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"Rated current" is the current the device (motor or transformer?) is designed to handle at full load. "Tripping current" is the current where a protective device (fuse, breaker) will open to protect the device from overload/overheating. "Tripped current", may be the current the tripping device measured prior to making the decision to trip, if you are reading this from a digital protective device like a relay or OCR.

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