What is the relation between voltage sensitivity `S_(v)` and the current sensitivity S of a moving coil galvanometer ? (Given that G is the resistance of the galvanometer.)

Options

A. `S_(v) = G S_(1)`
B. `S_(v) = S_(1)//G`
C. `S_(v)S_(1) = G`
D. `S_(v)S_(1) = G_(2)`

Answer

To find the relationship between voltage sensitivity \( S_v \) and current sensitivity \( S \) of a moving coil galvanometer, we can start by defining both terms mathematically.

1. **Define Voltage Sensitivity \( S_v \)**:
Voltage sensitivity is defined as the deflection per unit voltage applied to the galvanometer. Mathematically, it can be expressed as:
\[ S_v = \frac{NAB}{K \cdot R} \]
where:
- \( N \) = number of turns in the coil,
- \( A \) = area of the coil,
- \( B \) = magnetic field strength,
- \( K \) = torsional constant of the galvanometer,
- \( R \) = resistance of the galvanometer.

2. **Define Current Sensitivity \( S \)**:
Current sensitivity is defined as the deflection per unit current flowing through the galvanometer. It can be expressed as:
\[ S = \frac{NAB}{K} \]

3. **Relate Voltage Sensitivity to Current Sensitivity**:
To find the relationship between \( S_v \) and \( S \), we can take the ratio of \( S_v \) to \( S \):
\[ \frac{S_v}{S} = \frac{\frac{NAB}{K \cdot R}}{\frac{NAB}{K}} = \frac{1}{R} \]

4. **Rearranging the Equation**:
From the above ratio, we can express current sensitivity \( S \) in terms of voltage sensitivity \( S_v \):
\[ S = R \cdot S_v \]

5. **Final Relationship**:
Therefore, the relationship between the current sensitivity \( S \) and the voltage sensitivity \( S_v \) of a moving coil galvanometer is:
\[ S = G \cdot S_v \]
where \( G \) is the resistance of the galvanometer.

### Summary:
The current sensitivity \( S \) is equal to the resistance \( G \) of the galvanometer multiplied by the voltage sensitivity \( S_v \).

---