(A) : The tangent galvanometer can be made more sensitive by increasing the number of turns of its coil.
(R) : For a given P.D current through galvanometer is inversely proportional to the number of turns of coil.

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. 'A' is true and 'R' is false
D. 'A' is false and 'R' is false

Answer

To solve the question, we need to analyze both the assertion (A) and the reason (R) provided in the question regarding the tangent galvanometer.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "The tangent galvanometer can be made more sensitive by increasing the number of turns of its coil."
- Sensitivity in a tangent galvanometer is defined as the ratio of the deflection angle (θ) to the current (I) flowing through the coil.
- The sensitivity can be expressed as \( S = \frac{\theta}{I} \).

2. **Understanding the Reason (R)**:
- The reason states that "For a given P.D, the current through the galvanometer is inversely proportional to the number of turns of the coil."
- The relationship can be derived from the formula for current in the galvanometer, which is given by:
\[ I = \frac{2\pi r B \tan \theta}{\mu_0 N} \]
where \( r \) is the radius of the coil, \( B \) is the magnetic field, \( \mu_0 \) is the permeability of free space, and \( N \) is the number of turns.
- From this equation, we can see that if the number of turns \( N \) increases, the current \( I \) decreases, indicating that \( I \propto \frac{1}{N} \).

3. **Analyzing the Sensitivity**:
- Since \( S = \frac{\theta}{I} \) and \( I \propto \frac{1}{N} \), we can conclude that:
\[ S \propto N \]
- This means that increasing the number of turns \( N \) increases the sensitivity \( S \) of the galvanometer.

4. **Conclusion**:
- The assertion (A) is correct because increasing the number of turns increases the sensitivity of the galvanometer.
- The reason (R) is also correct because the current is inversely proportional to the number of turns.
- However, the reason does not adequately explain the assertion. Therefore, while both statements are true, the relationship between them is not directly explanatory.

### Final Answer:
- **Assertion (A)** is true.
- **Reason (R)** is true but does not explain (A).
- Thus, the correct option is that both A and R are true, but R does not explain A.