This paper presents theoretical and experimental studies of the process of electrochemical generation of hydrogen and oxygen with a parallel and serial connection of electrodes in one electrolyte volume. This study is based on the laws of conservation of mass, thermodynamics, electrical engineering, electrochemistry, using data obtained from the methods of mathematical and physical modeling. Data on the development and research of two designs of electrode assemblies, namely, with a parallel and series connection of electrodes, and with the subsequent placement of each assembly in one electrolyte volume. Experimental and calculated data revealed the regularities of the electrochemical reaction of decomposition of the liquid electrolyte into hydrogen and oxygen, the distribution of voltage when the electrodes are connected in parallel and in series in one electrolyte volume. A change in the electric potential between the internal electrodes was also found. Voltage measurement was performed from electrode 1 to electrode 4. The results of experimental studies were displayed graphically. The graphs show that the voltage at the terminals of the internal electrodes is lower than necessary for the electrochemical reaction of decomposition of the liquid electrolyte with the generation of gaseous hydrogen and oxygen. To implement the concept of placing a series (bipolar) connection of electrodes in one electrolyte volume, it is necessary to focus on the design of the electrolyzer that will be able to disconnect the electrodes electrically and provide galvanic isolation between them (separately isolated electrolyte volumes for each electrode pair). This will increase the operating pressure of the generated hydrogen and oxygen to 20.0 MPa, reducing the current load of the electrolysis process when using alternative energy sources.