Statement I: The tangent galvanometer can be made more sensitive by increasing the number of turns of its coil.

Statement II: Current through tangent galvanometer is proportional to the number of turns of coil.

In tangent galvanometer, the current through the coil is given by

$\mathrm{I}=\frac{2\mathrm{R}}{{\mathrm{n\mu }}_0}.{\mathrm{B}}_{\mathrm{H}} \tan \mathrm{\theta }\Rightarrow \tan \mathrm{\theta }\propto \mathrm{n}/\mathrm{r}$

i.e., by reducing its radius or by increasing number of turns of coil we can increase the sensitivity of tangent galvanometer.

Also, sensitivity, $\mathrm{S}\propto \mathrm{\theta }$

$\Rightarrow \mathrm{S}\propto \frac{\mathrm{n}}{\mathrm{r}}$