Potentiostatic oxidation of Pb-1.7%Sb alloy used in the manufacture of grids of lead-acid batteries over the potential range from -1.0V to 2.3V in 5M $H_2SO_4$ in the absence and the presence of 0.4M $H_3PO_4$ and the self-discharge characteristics of the oxide layer formed is studied by electrochemical impedance spectroscopy (EIS). Depending on the potential value, sharp variations in resistance and capacitance of the alloy are recorded during the oxidation and they can be used for identification of the various substances involved in passive layer. Addition of $H_3PO_4$ is found to deteriorate the insulating properties of the passive layer by the retardation of the formation of $PbSO_4$. $H_3PO_4$ completely inhibits the current and impedance fluctuations recorded in $H_3PO_4$-free solutions in the potential range 0.5 V-1.7 V. These fluctuations are attributed to the occurrence of competitive redox processes that involve the formation of $PbSO_4$, $PbOSO_4$, PbO and $PbO_2$ and the repeated formation and breakdown of the passive layer. Self-discharge experiments indicate that the amount of $PbO_2$ formed in the presence of $H_3PO_4$ is lesser than in the $H_3PO_4$-free solutions. The start of transformation of $PbSO_4$ into $PbO_2$ is greatly shortened. $H_3PO_4$ facilitates the diffusion process of soluble species through the passive layer ($PbSO_4$ and basic $PbSO_4$) but impedes the diffusion process through $PbO_2$.