Lead acid battery experiment reaction

[litszyenvin]

My set up was simply putting two lead plates into a beaker of sulphuric acid, then connect the lead plates to a power supply. What is the reaction for charging and discharging the cell? All equations I could found contain lead (IV) oxide... Is the reactions of my set up differ from a real commercial lead acid battery?

 

[m.medhat]

of course it differs