In a cell that utilizes the reaction $Z{n}_{\left(s\right)}+2H^{+}\left(aq\right)\to Z{n}^{2+}\left(aq\right)+H_{2\left(g\right)}$ addition of $H_{2}S{O}_4$ to cathode compartment, will

The correct option is A Increase the E and shift equilibrium to the right

$Z{n}_{\left(s\right)}+2H_{\left(aq\right)}^{+}\rightleftharpoons Z{n}_{\left(aq\right)}^{2+}+H_{2\left(g\right)}$
$E_{cell}=E_{cell}^{\circ }-\frac{.059}{2}log\frac{\left[Z{n}^{2+}\right]}{[H^{+}{]}^2}$
When $H_{2}S{O}_4$ is added then $\left[H^{+}\right]$ will increase therefore $E_{cell}$ will also increases and equilibrium will shift towards right.