The ratio of voltage sensitivity `(V_S)` and current sensitivity `(I_S)` of a moving coil galvanometer is

Options

A. `1/G`
B. `1/(G^2)`
C. `G`
D. `G^2`

Answer

To find the ratio of voltage sensitivity `(V_S)` to current sensitivity `(I_S)` of a moving coil galvanometer, we can follow these steps:

### Step 1: Define Current Sensitivity
The current sensitivity `(I_S)` of a moving coil galvanometer is defined as the deflection produced per unit current. Mathematically, it can be expressed as:
\[ I_S = \frac{\phi}{I} = \frac{n \cdot B \cdot A}{C} \]
where:
- \( \phi \) = deflection,
- \( I \) = current,
- \( n \) = number of turns of the coil,
- \( B \) = magnetic field induction,
- \( A \) = area of the coil,
- \( C \) = torsional constant.

### Step 2: Define Voltage Sensitivity
The voltage sensitivity `(V_S)` of a moving coil galvanometer is defined as the deflection produced per unit voltage applied across the terminals. It can be expressed as:
\[ V_S = \frac{\phi}{V} = \frac{n \cdot B \cdot A}{C \cdot G} \]
where:
- \( V \) = voltage,
- \( G \) = resistance of the galvanometer.

### Step 3: Find the Ratio of Voltage Sensitivity to Current Sensitivity
To find the ratio of voltage sensitivity to current sensitivity, we divide the expression for voltage sensitivity by the expression for current sensitivity:
\[ \frac{V_S}{I_S} = \frac{\frac{n \cdot B \cdot A}{C \cdot G}}{\frac{n \cdot B \cdot A}{C}} \]

### Step 4: Simplify the Expression
When we simplify the above expression, we notice that \( n \cdot B \cdot A \) and \( C \) cancel out:
\[ \frac{V_S}{I_S} = \frac{1}{G} \]

### Conclusion
Thus, the ratio of voltage sensitivity to current sensitivity of a moving coil galvanometer is:
\[ \frac{V_S}{I_S} = \frac{1}{G} \]