The current sensitivity is simply the deflection per unit current so if we double the no of turns it will also double the resistance but not half the current still we not connect it to a battery (or apply any constant potential difference). suppose we connect the given galvanometer turned ammeter in the circuit (I=V/R) the current becomes I=V/R+r and here r is negligible so no change whether be doubled or halved not change the current appreciably but change the deflection angle.

The current sensitivity is simply the deflection per unit current, so if we double the number of the turns, it will also double the resistance. But not half the current still we not connect it to a battery (or apply any constant potential difference). Suppose we connect the given galvanometer turned ammeter in the circuit ($I=\frac{V}{R}$) the current becomes $I=\frac{V}{R}+r$. Here $r$ is negligible, so no change whether be doubled or halved not change the current appreciably but change the deflection angle.