Electrical resistance of both the electrodes of a lead-acid battery increases during discharge due to formation of lead sulfate, an insulator. Work of Metzendorf [1] shows that resistance increases sharply at about 65% conversion of active materials, and battery stops discharging once this critical conversion is reached. However, these aspects are not incorporated into existing mathematical models. Present work uses the results of Metzendorf [1], and develops a model that includes the effect of variable resistance. Further, it uses a reasonable expression to account for the decrease in active area during discharge instead of the empirical equations of previous work. The model's predictions are compared with observations of Cugnet et al. [2]. The model is as successful as the non-mechanistic models existing in literature. Inclusion of variation in resistance of electrodes in the model is important if one of the electrodes is a limiting reactant. If active materials are stoichiometrically balanced, resistance of electrodes can be very large at the end of discharge but has only a minor effect on charging of batteries. The model points to the significance of electrical conductivity of electrodes in the charging of deep discharged batteries.