of the applied voltage v 39 and capacitance c 39 2 in one of the high resistance regions 9 are very small so that the electric current flowing through the region 9 becomes smaller and hence the local concentration of electric current is prevented as a result there is caused no local heating as seen in the case of merely flowing direct current through the solid electrolyte in the conventional oxygen concentration regulator or the case of applying alternating current within a low frequency range from the point a to the point b so that even when the electrodes are arranged on both sides of a plate shaped solid electrolyte the whole of this solid electrolyte can uniformly be heated moreover the frequency from the point b to the point c depends upon the composition temperature and shape of the solid electrolyte the shape of the electrode and the like and is not constant in the oxygen concentration regulator as shown in fig1 when a pair of platinum electrodes are arranged on inner and outer wall surfaces of a bottomed cylindrical ceramics produced by adding 3 parts of clay to 100 parts of a mixture of 95 mol of zro 2 and 5 mol of y 2 o 3 and having an outer diameter at its closed end of 3 5 mm an effective length of 10 mm and a thickness of 0 75 mm the frequency at 350 u00b0 c is 10 hz at the point b and more than about 50 khz at the point c as the solid electrolyte to be used in the oxygen concentration regulator according to the present invention mention may be made of zirconia ceramics thoria ceramics ceria ceramics and the like each containing yttrium oxide ytterbium oxide calcium oxide magnesium oxide or.