Bubbles play an important role in the productivity of an electrolysis cell. They induce flow in the cell and increase the overvoltage, which is still two times greater than the thermodynamic voltage. Their contribution to the total electrical resistance of the electrolyte must be known for several reasons such as the energy efficiency and control. A computationally efficient mathematical model has been proposed that computes the total resistance of the electrolyte by using the concept of parallel-connected current tubes. The resistance of the individual current tubes has been determined earlier by the solution of the Laplace equation around the bubbles by the finite element method. Both electrical resistance models take into account the morphology (position, size and shape of each bubble) of the bubble layer. The current-tube model has been compared to the solutions obtained by a finite element method (FEM) for several real and hypothetical situations, using a large number of bubbles. The agreement between the results obtained by the proposed model and the FEM is very good. The difference between the two approaches is around 5% for a covering factor of 50%.