The voltage sensitivity of a moving coil galvanometer remains constant when the number of turns is doubled due to counteracting effects. Current sensitivity (SI) is defined as deflection per unit current: SI = $\frac{\theta}{I}$. Voltage sensitivity (SV) is deflection per unit voltage: SV = $\frac{\theta}{V}$. Since V = IR, SV can be expressed as SV = $\frac{\theta}{IR}$ = $\frac{\theta/I}{R}$ = $\frac{SI}{R}$. Doubling the number of turns (N) doubles the current sensitivity, so SI' = 2 ⋅ SI, assuming area and magnetic field are constant. This would suggest voltage sensitivity becomes SV' = $\frac{SI'}{R}$ = $\frac{2 \cdot SI}{R}$ = $2 \cdot \frac{SI}{R}$. However, doubling the number of turns also approximately doubles the coil's resistance, so R' = 2 ⋅ R. Therefore, the new voltage sensitivity is SV'' = $\frac{SI'}{R'}$ = $\frac{2 \cdot SI}{2 \cdot R}$ = $\frac{SI}{R}$ = SV. Consequently, the voltage sensitivity remains unchanged.