The relation between voltage sensitivity $\left( {{\sigma _v}} \right)$ and current sensitivity $\left( {{\sigma _i}} \right)$ of a moving coil galvanometer is (resistance of galvanometer is G).
$
  A.\dfrac{{{\sigma _i}}}{G} = {\sigma _v} \\
  B.\dfrac{{{\sigma _v}}}{G} = {\sigma _i} \\
  C.\dfrac{G}{{{\sigma _v}}} = {\sigma _i} \\
  D.None{\text{ of the above}} \\
 $

Hint: In order to solve this question, firstly we will understand the concept of current sensitivity and voltage sensitivity. Then we will use ohm’s law i.e. $V = IR$ to find the relation between voltage sensitivity $\left( {{\sigma _v}} \right)$ and current sensitivity $\left( {{\sigma _i}} \right)$of a moving coil galvanometer.

Complete step-by-step solution -

A galvanometer is an electromechanical device which is used to detect and indicate electrical current. In response to electrical current flowing through a coil in a continuous magnetic field, a galvanometer acts as an actuator by generating a rotary deflection.
We do learn in a galvanometer,
Current sensitivity- The deflection produced in the galvanometer when a unit current flows through it is known as \[{\sigma _i} = \dfrac{\theta }{I}\], where $\theta $ is the deflection produced.

Voltage sensitivity- It is defined as the deflection produced in the galvanometer when a unit voltage is applied across two terminals,${V_s} = \dfrac{\theta }{V}$.
But we know that ohm’s law which shows-$V = IR = IG$
As we are given G is the resistance of the galvanometer.
Therefore, ${\sigma _v} = \dfrac{\theta }{{IG}} = \dfrac{{{\sigma _i}}}{G}$
i.e. Voltage sensitivity is calculated by dividing current sensitivity to resistance.
The above relation means that the voltage sensitivity will remain unchanged if the current sensitivity increases as well as the resistance increases in the same order.

Hence, option A is correct.

Note- While solving this question, we should know the ohm’s law which states that the voltage or potential difference between two points is directly proportional to the current or electricity passing through the resistance.