In a cell that utilizes the reaction $\text{Zn}(s)+2{\text{H}}^{+}(aq)\to {\text{Zn}}^{2+}(aq)+{\text{H}}_2(g)$, the addition of ${\text{H}}_2{\text{SO}}_4$ to the cathode compartment will:

Adding ${\text{H}}_2{\text{SO}}_4$ increases the concentration of ${\text{H}}^{+}$ ions in the cathode compartment.According to the Nernst equation, increasing the concentration of a reactant (in the reduction half-cell) increases the cell potential ($E$).According to Le Chatelier's Principle, increasing the concentration of a reactant shifts the equilibrium toward the product side (to the right).