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RRL (Ramp-Rate Limitation) is caused by current nonuniformity during magnetic field change. Although current nonuniformity is determined only by contact resistance between strands, cable inductance and field ramp rate, current redistribution process is induced by joule heating from current sharing mode and heat transfer to adjacent liquid helium. Experiment was performed to investigate electro-magnetically and thermo-hydraulically coupled RRL with 2.6 m long two-strand superconducting cable at maximum field to 6 T with a rate of 3 T/s. This paper describes the detailed strand current redistributions during quench process under magnetic field ramps. Heat transfer effect as well as electrical characteristics to current redistribution was also investigated with the measured strand temperatures, currents and quench voltages.