An analytical study is presented for an one-dimensional, steady-state plasma bound between two perfectly absorbing walls that are biased with respect to each other. Starting from a description of the plasma sheaths formed at both walls, an expression relating the bulk plasma potential to the wall currents is derived, showing that the plasma potential undergoes an abrupt transition when currents cross a critical value. This result is confirmed by numerical simulations performed with a particle-in-cell code. [http://dx.doi.org/10.1063/1.4745863]