Assertion : In series `L-C-R` circuit, if a ferromagnetic rod is inserted inside an inductor, current in the circuit may increase or decrease.
Reason : By doing so `X_L` will increase.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided:

### Step 1: Understand the Assertion
The assertion states that in a series L-C-R circuit, if a ferromagnetic rod is inserted inside an inductor, the current in the circuit may either increase or decrease.

**Hint:** Consider how the insertion of a ferromagnetic material affects the inductance of the inductor.

### Step 2: Understand the Reason
The reason states that by inserting a ferromagnetic rod, the inductive reactance \(X_L\) will increase.

**Hint:** Recall the relationship between inductance and inductive reactance.

### Step 3: Analyze the Effect on Inductance
When a ferromagnetic material is inserted into an inductor, the inductance \(L\) of the inductor increases. The inductive reactance \(X_L\) is given by the formula:
\[ X_L = \omega L \]
where \(\omega\) is the angular frequency of the AC source. Therefore, if \(L\) increases, \(X_L\) will also increase.

**Hint:** Remember that \(X_L\) is directly proportional to inductance.

### Step 4: Consider the Impedance in the Circuit
The total impedance \(Z\) in a series L-C-R circuit is given by:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
where \(X_C\) is the capacitive reactance.

**Hint:** Think about how changes in \(X_L\) and \(X_C\) affect the overall impedance \(Z\).

### Step 5: Evaluate Current in the Circuit
The current \(I\) in the circuit can be expressed as:
\[ I = \frac{V}{Z} \]
where \(V\) is the voltage across the circuit.

**Hint:** Consider how changes in \(Z\) affect the current \(I\).

### Step 6: Analyze Different Scenarios
1. **Case A:** If \(X_C\) is greater than \(X_L\) initially, and \(X_L\) increases after inserting the rod, the difference \(X_L - X_C\) could decrease, leading to an increase in impedance \(Z\) and thus a decrease in current \(I\).

2. **Case B:** If \(X_L\) is initially greater than \(X_C\), and \(X_L\) increases further, the difference could increase, leading to an increase in impedance \(Z\) and a decrease in current \(I\).

**Hint:** Think about how the relationship between \(X_L\) and \(X_C\) determines the behavior of the current.

### Step 7: Conclusion
Since the impedance \(Z\) can either increase or decrease depending on the values of \(X_L\) and \(X_C\), the current \(I\) can also either increase or decrease. Thus, the assertion is true. However, the reason provided does not adequately explain the assertion, as it only states that \(X_L\) increases without considering the effect of \(X_C\).

**Final Answer:** Both the assertion and reason are true, but the reason is not the correct explanation of the assertion.