`Assertion:` current sensitivity of a galvanometer is directly proportional to the current through the coil.
`Reason:` Voltage sensitivity is inversely proportional to voltage.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is the correct explanation of assertion.
C. If assertion is true but reason is false
D. If both assertion is false but reason is true

Explanation

To solve the question regarding the assertion and reason statements about the current sensitivity and voltage sensitivity of a galvanometer, we will analyze each statement step by step.

### Step 1: Understanding Current Sensitivity
- **Assertion:** Current sensitivity of a galvanometer is directly proportional to the current through the coil.
- **Current Sensitivity Formula:** The current sensitivity (IS) is defined as:
\[ IS = \frac{\theta}{I} \]
where \(\theta\) is the angular deflection and \(I\) is the current through the coil.

### Step 2: Analyzing the Assertion
- From the formula, we can see that current sensitivity (IS) is inversely proportional to the current (I). This means that as the current increases, the current sensitivity decreases.
- Therefore, the assertion that current sensitivity is directly proportional to the current through the coil is **false**.

### Step 3: Understanding Voltage Sensitivity
- **Reason:** Voltage sensitivity is inversely proportional to voltage.
- **Voltage Sensitivity Formula:** The voltage sensitivity (Vs) can be expressed in terms of current sensitivity and resistance (R):
\[ Vs = IS \cdot R \]
Substituting the expression for current sensitivity, we have:
\[ Vs = \frac{\theta}{I} \cdot R \]
This can also be expressed as:
\[ Vs = \frac{\theta}{V} \]
where \(V = I \cdot R\) (Ohm's Law).

### Step 4: Analyzing the Reason
- From the above expression, we can see that voltage sensitivity (Vs) is inversely proportional to the voltage (V). This means that as the voltage increases, the voltage sensitivity decreases.
- Therefore, the reason that voltage sensitivity is inversely proportional to voltage is **true**.

### Conclusion
- The assertion is **false** while the reason is **true**. The reason does not correctly explain the assertion because the assertion itself is incorrect.

### Final Answer:
Assertion is false, Reason is true.

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