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Dynamic resistance can be observed in a superconducting tape carrying a DC current which is exposed to an oscillating magnetic field. This effect is attributed to the interaction between the transport current and moving fluxons, and can occur in various superconducting components including high temperature superconducting (HTS) flux pumps, fast-ramping magnets and HTS rotating machines. Although conventionally expressed in terms of a DC ‘resistance,’ the phenomenon is inherently transient in nature, and the voltage drop across the superconductor follows a time-dependent periodic waveform. Here we present experimental measurements of the dynamic resistance of different REBCO tapes carrying a DC current and exposed to an oscillating perpendicular field. Measurements of both the transient voltage waveforms and the time-averaged DC resistances are compared with numerical finite element simulations obtained using the H-formulation. We observe clear variations between the voltage response from different tapes, which can be understood in terms of their differing J c(B, θ) dependence. In particular, a key feature of the experimentally measured waveforms is the emergence of a split ‘double peak’ at higher applied fields. Graphical visualisations of the finite element data show that this coincides with a periodic increase in J c(B, θ) throughout the tape. This occurs during each cycle at those times when the applied field falls below the shielding threshold of the tape (as the penetrating field within the tape then approaches zero). Our findings show that models which assume a constant J c irrespective of local field strength cannot capture the full range of behaviour observed by experiment. This emphasises the importance of employing experimentally measured J c(B, θ) data when simulating transient effects in HTS materials.