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The electrical boundary layer between an isothermal, weakly ionized plasma and a plane electrode is discussed. Following a formulation of the complete problem, the governing equations are solved in the quasi-neutral continuum approximation to give explicit results for the ionization nonequilibrium layer. This allows three critical current densities to be identified: the first when a cathode must emit electrons; the second at which the anode potential fall changes sign from negative to positive; the third at which the anode must emit ions. The neglected space charge and inertia terms are evaluated to give conditions distinguishing collision-dominated and collisionless sheaths. Using an estimation for the location of the plasma-sheath boundary, the potential falls associated with the ionization nonequilibrium layer are evaluated. The results are illustrated for the case of combustion MHD plasmas.