Explanation:

To understand why the voltage sensitivity of a galvanometer remains unchanged when its current sensitivity is doubled, we need to understand the relationship between the two sensitivities.

Current Sensitivity:
The current sensitivity of a galvanometer refers to the change in its current for a given change in the quantity being measured (e.g., voltage, temperature, etc.). It is typically represented by the symbol "S".

Voltage Sensitivity:
The voltage sensitivity of a galvanometer refers to the change in its output voltage for a given change in the quantity being measured. It is typically represented by the symbol "V".

Relationship between Current Sensitivity and Voltage Sensitivity:
The voltage sensitivity (V) of a galvanometer is directly proportional to its current sensitivity (S) and the resistance (R) of the galvanometer coil. Mathematically, it can be expressed as:

V ∝ S × R

This equation shows that the voltage sensitivity depends on both the current sensitivity and the resistance of the galvanometer coil. Doubling the current sensitivity (S) will only affect the current flowing through the galvanometer, not the resistance.

Effect of Doubling Current Sensitivity on Voltage Sensitivity:
When the current sensitivity (S) of the galvanometer is doubled, it means that for the same change in the quantity being measured, the current through the galvanometer will be twice the original value. However, since the resistance (R) of the galvanometer coil remains unchanged, the voltage sensitivity (V) will also remain unchanged.

Therefore, the correct answer is option 'C': the voltage sensitivity of the galvanometer will remain unchanged when its current sensitivity is doubled.