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For pt.I see ibid., vol.29, p.3 (1989). The critical size of Y1Ba2Cu3O7-x (YBCO) has previously been determined from the magnetic stability criterion. Based on the result, composite conductors of YBCO and copper are designed assuming critical current densities of 1.0*109 A m-2 at 77 K and 1.0*1010 A m-2 at 20 K. A multifilamentary composite of 4 mm in diameter can be operated up to the critical current at 77 K but, at lower temperatures, the self-field instability limits the maximum current. A composite tape conductor is also designed: the thickness of YBCO is 25 mu m and the total thickness of copper is 100 mu m. The analysis shows that the tape conductor is quite stable when the wide face is exposed to the coolant. A tape of 20 mm width can attain its critical currents of 500 A at 77 K and 5000 A at 20 K without suffering from magnetic instability.