Assertion: Inductive reactance of an inductor in DC circuit is zero.
Reason: Angular frequency of DC circuit is zero.

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 not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To analyze the given assertion and reason, let's break it down step by step.

### Step 1: Understanding Inductive Reactance
Inductive reactance (XL) is defined as the opposition that an inductor offers to the change in current. It is given by the formula:
\[ X_L = \omega L \]
where:
- \(X_L\) is the inductive reactance,
- \(\omega\) is the angular frequency (in radians per second),
- \(L\) is the inductance of the inductor (in henries).

### Step 2: Angular Frequency in DC Circuits
In a Direct Current (DC) circuit, the current flows in one direction and does not vary with time. Therefore, the frequency of the current is zero. Since frequency is related to how often the current changes direction (or varies), in a DC circuit:
\[ \text{Frequency} = 0 \]
This implies that the angular frequency (\(\omega\)) is also zero because:
\[ \omega = 2\pi f \]
where \(f\) is the frequency. If \(f = 0\), then:
\[ \omega = 0 \]

### Step 3: Calculating Inductive Reactance in DC
Substituting \(\omega = 0\) into the formula for inductive reactance:
\[ X_L = 0 \times L = 0 \]
This shows that the inductive reactance in a DC circuit is indeed zero.

### Step 4: Evaluating the Assertion and Reason
- **Assertion**: "Inductive reactance of an inductor in a DC circuit is zero." This statement is **true**.
- **Reason**: "Angular frequency of a DC circuit is zero." This statement is also **true**.

### Step 5: Conclusion
Since both the assertion and the reason are true, and the reason correctly explains the assertion, we conclude that the assertion is valid and supported by the reason.

### Final Answer
Both the assertion and the reason are correct, and the reason is the correct explanation for the assertion.

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