A moving coil galvanometer coil has a coil of area A, number of turns N. The radial magnetic field present is B. the moment of inertia of the coil is I about its rotation axis. The torque is applied by the magnetic field on the coil of the galvanometer when current `I_(0)` passes through it and produces a deflection of `pi//2` of the pointer. Then answer the following questions based on the paragraph.
The sensitivity of the instrument is

Options

A. `pi//2`
B. `pi//10`
C. `pi//2I_(0)`
D. `2 pi//I_(0)`

Answer

To find the sensitivity of the moving coil galvanometer, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Sensitivity**:
The sensitivity of a galvanometer is defined as the deflection produced per unit current. Mathematically, it is given by:
\[ \text{Sensitivity} = \frac{\phi}{I_0} \]
where \(\phi\) is the deflection in radians and \(I_0\) is the current passing through the coil.

2. **Identify Given Values**:
From the problem statement, we have:
- Deflection, \(\phi = \frac{\pi}{2}\) radians
- Current, \(I_0\) (the current is unspecified, but we will keep it as a variable for now).

3. **Substitute the Values into the Sensitivity Formula**:
Now, substituting the known values into the sensitivity formula:
\[ \text{Sensitivity} = \frac{\frac{\pi}{2}}{I_0} \]

4. **Final Expression for Sensitivity**:
Thus, the sensitivity of the galvanometer can be expressed as:
\[ \text{Sensitivity} = \frac{\pi}{2 I_0} \]

### Conclusion:
The sensitivity of the moving coil galvanometer is \(\frac{\pi}{2 I_0}\).

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