A household appliance incorporating an electrolyzer for electrolysis of water to H2 and O2 and an electrolyzer therefor. The appliance may include a burner for the hydrogen produced and an electric conductive member to provide household current to the electrolyzer. The electrolyzer comprises an outer housing defining a chamber which houses at least one cathode and at least one anode. The electrolyzer may comprise a plurality of field electrodes and the field electrodes may comprise first and second field electrodes which are electrically connected together and spaced apart to define an intra cell gap. Field electrodes may then be spaced apart to define an inter cell gap between electrodes of adjacent field electrodes. At least one of the anode and cathode may be connected to an electrically conductive member that is molded in situ in the housing and at least some of the electrodes may be configured to dimensionally stabilize the electrodes during operation of the electrolyzer. The number of field electrodes may be from 40 to 60 if a voltage of 120 V is supplied to the electrolyzer, 80 to 120 if the voltage is 240 V, or 4 to 6 if the voltage is 12 V. The gap between adjacent electrodes may vary between top and bottom and the electrolyzer may incorporate a plastic heat sink.