u2212 soc fig4 shows a theoretical curve based upon this assumption the agreement between the theoretical curve and the experimental points is seen to be excellent the observed variation of g 3 with soc can be exploited to determine soc from measurements of g 3 inverting the theoretical g 3 soc curve leads to a quadratic equation for soc g 3 this quadratic equation has two roots identified as soc and soc u2212 for g 3 400s in fig4 the soc root in fig4 corresponds to approximately 85 soc and the soc u2212 root corresponds to about 15 soc thus if one knows which root is the correct root one can determine soc from measurements of g 3 introducing a single piece of auxiliary information such as battery voltage single frequency conductance or the value of one of the other elements of the equivalent circuit can readily identify the correct root fig5 discloses plots of measurements of conductance i e the real part of the complex admittance obtained at two different frequencies u2014 8 hz and 22 hz these results were obtained by sequentially discharging a battery while measuring the conductance and the specific gravity after each discharge the data are plotted as functions of the battery electrolyte 39 s mean specific gravity although the effect is not as pronounced one notes the same type of behavior at both frequencies as was noted above with reference to fig4 that is the measured conductance is smallest at both full charge and at full discharge and reaches maximum near 50 soc this suggests that if accuracy is not too important one may be able to determine an approximation.