If 'r' is the radius and 'n' is number of turns of coil of a T.G, then to double its sensitivity

Options

A. both r and n should be doubled
B. both r and n should be halved
C. r alone should be doubled
D. 'n' alone should be doubled

Answer

To solve the problem of how to double the sensitivity of a tangent galvanometer, we need to analyze the relationship between sensitivity, the number of turns (n), and the radius (r) of the coil.

### Step-by-Step Solution:

1. **Understanding Sensitivity**:
The sensitivity (S) of a tangent galvanometer is defined as the change in deflection angle (dθ) per unit current (di). Mathematically, it can be expressed as:
\[ S = \frac{d\theta}{di} = \frac{\mu_0 n \cos^2 \theta}{2r H} \]
where:
- \( \mu_0 \) is the permeability of free space,
- \( n \) is the number of turns of the coil,
- \( r \) is the radius of the coil,
- \( H \) is the horizontal component of the magnetic field.

2. **Analyzing the Formula**:
From the formula, we can see that sensitivity (S) is directly proportional to the number of turns (n) and inversely proportional to the radius (r). This means:
\[ S \propto n \quad \text{and} \quad S \propto \frac{1}{r} \]

3. **Doubling Sensitivity**:
To double the sensitivity (S), we can either:
- Double the number of turns (n), or
- Halve the radius (r).

4. **Evaluating Options**:
- **Option 1**: Both r and n should be doubled - Incorrect, as this would not double the sensitivity.
- **Option 2**: Both r and n should be halved - Incorrect, as this would increase sensitivity but not necessarily double it.
- **Option 3**: r alone should be doubled - Incorrect, as this would decrease sensitivity.
- **Option 4**: n alone should be doubled - Correct, as this would directly double the sensitivity.

5. **Conclusion**:
Therefore, to double the sensitivity of the tangent galvanometer, the correct approach is to double the number of turns (n) alone.

### Final Answer:
To double the sensitivity of a tangent galvanometer, **n alone should be doubled**.

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