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In case of a plasma current disruption in a tokomak the conductor of the toroidal field coil may be subjected to a field varying exponentially with a time constant as low as a few milliseconds. Expressions of losses produced by the transverse component of the changing field can be written in the form Where θ is the time constant of the coupling currents in the superconducting multifilament composite and τ the time constant of the magnetic field. The value of the time constant θ evaluated in other theories is discussed For small τ, the outer layers of filaments saturate leading to some decrease of the coupling losses together with the appearance of hysteretic losses in these layers. Both losses are calculated for this case. Measured losses are within 20% of the theoretical predictions, in both two and three component composites. There is a noticeable decrease of losses in rectangular composites when the field is parallel to the broad face of the conductor and the presence of a transport current does not lead to a significant increase of overall losses.