The energy loss in a torus vessel during startup is now an important factor in a power-producing tokamak design. The torus design cannot be based on a system which minimizes the conductivity with resistive structures as in present experimental devices. If the resistivity of the torus is too high, the reactors are subject to damage from an uncontrolled fast shutdown such as a disruption. The thermal and magnetic stored energy due to the plasma current loop is several hundred megajoules, which can produce melting of the torus wall. To prevent excessive damage, a low resistance passive circuit must be provided close to the plasma edge. Another desirable design feature is to make all vacuum seals as far away from the plasma as practical. Thus, the reactor torus designs need an inner low resistance shell and an outer high resistance shell. In addition, the superconducting dewar and coil support structures provide paths for toroidal currents to flow. The calculations provided in this paper can be used to determine the size and cost of the systems as a function of the resistances of the structures. The results can thus be used to guide the preliminary concepts for the electromagnetic characteristics of a tokamak.