In a galvanometer, when the number of turns N becomes 2 N and resistance R becomes doubled, then

Current sensitivity of galvanometer is deflection per unit current i.e
$\frac{\varphi }{\mathrm{I}}=\frac{\mathrm{NAB}}{\mathrm{k}}\dots \dots \dots \dots \dots ....\text{ (i) }$
Similarly voltage sensitivity is deflection per unit voltage

$\frac{\varphi }{\mathrm{V}}=\frac{\mathrm{NAB}\text{ I }}{\mathrm{k}\mathrm{V}}=\frac{\mathrm{NAB}1}{\mathrm{k}\mathrm{R}}\dots \dots \dots \dots \dots \dots ..\text{ (ii) }$

Voltage sensitivity = current sensitivity X(1/resistance)
Now if current sensitivity is doubled, then the resistance in the circuit also
be doubled since it is proportional to the length of the wire

then voltage sensitivity will remain unchanged.