Write the reactions for the following:
$1.$ Oxidation and reduction reactions of a lead storage cell.
$2.$ Cell reaction of a $Ni-Cd$ cell.
$3.$ Anode,cathode,and overall reaction of a mercury cell.

$1.$ Lead storage cell:
Anode (Oxidation): $Pb(s) + SO_4^{2-}(aq) \rightarrow PbSO_4(s) + 2e^-$
Cathode (Reduction): $PbO_2(s) + SO_4^{2-}(aq) + 4H^+(aq) + 2e^- \rightarrow PbSO_4(s) + 2H_2O(l)$
$2.$ $Ni-Cd$ cell:
Cell reaction: $Cd(s) + 2Ni(OH)_3(s) \rightarrow CdO(s) + 2Ni(OH)_2(s) + H_2O(l)$
$3.$ Mercury cell:
Anode (Oxidation): $Zn(Hg) + 2OH^-(aq) \rightarrow ZnO(s) + H_2O(l) + 2e^-$
Cathode (Reduction): $HgO(s) + H_2O(l) + 2e^- \rightarrow Hg(l) + 2OH^-(aq)$
Overall reaction: $Zn(Hg) + HgO(s) \rightarrow ZnO(s) + Hg(l)$