(A) : Increasing the current sensitivity of an MCG may not necessarily increase the voltage sensitivity.
(R) : Increasing the number of turns of an MCG, increases the resistance of the coil of MCG.

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 the assertion (A) and the reason (R) provided and determine their validity.

### Step 1: Understanding Current Sensitivity
Current sensitivity (S) of a moving coil galvanometer (MCG) is defined as the deflection (θ) per unit current (I). Mathematically, it can be expressed as:
\[ S = \frac{\theta}{I} \]
For an MCG, this can be related to the number of turns (N), magnetic field (B), area (A), and spring constant (K):
\[ S = \frac{N B A}{K} \]

### Step 2: Understanding Voltage Sensitivity
Voltage sensitivity (V) is defined as the deflection (θ) per unit voltage (V). According to Ohm's law, voltage is related to current and resistance (R) as:
\[ V = I R \]
Thus, voltage sensitivity can be expressed as:
\[ V = \frac{\theta}{V} = \frac{\theta}{I R} \]
Substituting the expression for current (I) from the current sensitivity:
\[ V = \frac{N B A}{K} \cdot \frac{1}{R} \]

### Step 3: Analyzing the Relationship Between Current and Voltage Sensitivity
From the above expressions, we can see that:
- Current sensitivity is directly proportional to the number of turns (N).
- Voltage sensitivity is inversely proportional to the resistance (R), which is also dependent on the number of turns (N).

### Step 4: Understanding Resistance in Relation to Number of Turns
The resistance (R) of the coil in an MCG is given by:
\[ R \propto N \]
This means that as we increase the number of turns (N), the resistance (R) also increases.

### Step 5: Conclusion on Assertion and Reason
- Assertion (A) states that increasing the current sensitivity of an MCG may not necessarily increase the voltage sensitivity. This is true because while current sensitivity increases with more turns, the resistance also increases, which could balance out the effect on voltage sensitivity.
- Reason (R) states that increasing the number of turns of an MCG increases the resistance of the coil. This is also true.

Since both the assertion and the reason are true, and the reason correctly explains the assertion, we conclude that both (A) and (R) are true.

### Final Answer
Both Assertion (A) and Reason (R) are true, and R is the correct explanation for A.

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