A conducting wire of given length is used to prepare the 'coil' of a moving coil galvanometer. To have maximum sensitivity the shape of the coil should be :

Options

A. circular
B. elliptical
C. rectangular
D. square

Answer

To solve the question regarding the shape of the coil in a moving coil galvanometer for maximum sensitivity, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Context**:
- A moving coil galvanometer uses a coil of conducting wire placed in a magnetic field to measure current. The sensitivity of the galvanometer depends on how effectively the coil can deflect in response to a current.

2. **Identifying Coil Shapes**:
- The question provides four shapes for the coil: circular, elliptical, rectangular, and square.

3. **Analyzing the Magnetic Field**:
- In a moving coil galvanometer, a radial magnetic field is produced by the magnets. For maximum sensitivity, the coil should experience a uniform magnetic field across its entire area.

4. **Evaluating Each Shape**:
- **Circular Coil**:
- The distance from the center to any point on the coil is constant (the radius), which means that the torque experienced by the coil will be uniform across its entire length. This leads to maximum sensitivity.
- **Elliptical Coil**:
- The distance from the center to the points on the coil varies, leading to non-uniform torque and thus lower sensitivity.
- **Rectangular Coil**:
- Similar to the elliptical coil, the distance from the center to the corners of the rectangle varies, resulting in non-uniform torque.
- **Square Coil**:
- Although the square has equal sides, the distance from the center to the corners is not uniform, leading to lower sensitivity compared to a circular coil.

5. **Conclusion**:
- Given that the circular coil provides uniform distance from the center to all points on the coil, it will experience uniform torque in the radial magnetic field, resulting in maximum sensitivity.

### Final Answer:
The shape of the coil that should be used in a moving coil galvanometer for maximum sensitivity is **circular**.