The relation between voltage sensitivity ` 'sigma_(V)'` and current sensitiviy `sigma_(i)` of moving coil galvanometer if its resistance is `'G'` is

Options

A. `sigma_(i)/G=sigma_(v)`
B. `sigma_(v)/G=sigma_(i)`
C. `G/sigma_(v)=sigma_(i)`
D. `G/sigma_(i)/G=sigma_(v)`

Answer

To find the relation between voltage sensitivity \( \sigma_V \) and current sensitivity \( \sigma_I \) of a moving coil galvanometer with resistance \( G \), we can follow these steps:

### Step 1: Define Current Sensitivity
Current sensitivity \( \sigma_I \) is defined as the deflection produced per unit current. Mathematically, it can be expressed as:
\[ \sigma_I = \frac{\phi}{I} \]
where \( \phi \) is the deflection and \( I \) is the current.

### Step 2: Express Current Sensitivity in Terms of Physical Quantities
For a moving coil galvanometer, the current sensitivity can be expressed in terms of the number of turns \( n \), magnetic field \( B \), area \( A \), and the torsional constant \( C \):
\[ \sigma_I = \frac{nBA}{C} \]

### Step 3: Define Voltage Sensitivity
Voltage sensitivity \( \sigma_V \) is defined as the deflection produced per unit voltage applied across the galvanometer. This can be expressed as:
\[ \sigma_V = \frac{\phi}{V} \]
where \( V \) is the voltage.

### Step 4: Relate Voltage to Current
Using Ohm's law, the voltage \( V \) across the galvanometer can be expressed in terms of current \( I \) and resistance \( G \):
\[ V = I \cdot G \]

### Step 5: Substitute Voltage in Voltage Sensitivity
Substituting \( V \) in the expression for voltage sensitivity:
\[ \sigma_V = \frac{\phi}{I \cdot G} \]

### Step 6: Express Voltage Sensitivity in Terms of Physical Quantities
We can express \( \phi \) in terms of the same physical quantities used for current sensitivity:
\[ \sigma_V = \frac{nBA}{C \cdot G} \]

### Step 7: Relate \( \sigma_V \) and \( \sigma_I \)
Now, we can relate \( \sigma_V \) and \( \sigma_I \):
\[ \sigma_V = \frac{nBA}{C \cdot G} = \frac{\sigma_I}{G} \]

### Conclusion
Thus, the relation between voltage sensitivity \( \sigma_V \) and current sensitivity \( \sigma_I \) is:
\[ \sigma_V = \frac{\sigma_I}{G} \]