Assertion : in case of DC circuit , current through the branch of capacitor is zero .
Reason : Reactance of the capacitor is 1/`omega`C and `omega` for the DC source can be assumed to the zero, hence reactance of capacitor for DC circuit becomes infinite .

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion
B. If both assertion and reason are correct but reason is not the correct explanation of assertion
C. If assertion is correct but reason is incorrect
D. If assertion is inncorrect but reason is correct

Answer

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

**Assertion:** In case of a DC circuit, the current through the branch of a capacitor is zero.

**Reason:** The reactance of the capacitor is given by \( X_c = \frac{1}{\omega C} \), and for a DC source, \( \omega \) can be assumed to be zero. Hence, the reactance of the capacitor for a DC circuit becomes infinite.

### Step-by-Step Solution:

1. **Understanding DC Circuits:**
- In a Direct Current (DC) circuit, the current flows steadily in one direction. The voltage is constant over time.

2. **Capacitor Behavior in DC Circuits:**
- A capacitor stores electrical energy when connected to a voltage source. Initially, when connected to a DC source, it allows current to flow until it is fully charged.

3. **Reactance of a Capacitor:**
- The reactance \( X_c \) of a capacitor is defined as:
\[ X_c = \frac{1}{\omega C} \]
- Here, \( \omega \) is the angular frequency of the AC source, and \( C \) is the capacitance.

4. **Angular Frequency in DC Circuits:**
- For a DC source, the frequency is zero (\( f = 0 \)), which means:
\[ \omega = 2\pi f = 0 \]

5. **Calculating Reactance for DC:**
- Substituting \( \omega = 0 \) into the reactance formula:
\[ X_c = \frac{1}{0} \rightarrow \infty \]
- This indicates that the reactance of the capacitor in a DC circuit is infinite.

6. **Implication of Infinite Reactance:**
- An infinite reactance means that the capacitor behaves like an open circuit. Hence, no current can flow through the capacitor branch in a DC circuit.

7. **Conclusion:**
- Therefore, the assertion that the current through the branch of a capacitor in a DC circuit is zero is correct.
- The reason provided is also correct as it explains why the current is zero due to the infinite reactance of the capacitor when connected to a DC source.

### Final Statement:
Both the assertion and the reason are correct, and the reason provides a correct explanation for the assertion.

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