Assertion: In an `AC` circuit, potential difference across the capacitor may be greater than the applied voltage.
Reason : `V_C=IX_C`, wheereas `V= IZ` and `X_C` can be greater than `Z` also.

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 the assertion and reason provided regarding an AC circuit involving a capacitor.

### Step-by-Step Solution

1. **Understanding the Assertion**: The assertion states that in an AC circuit, the potential difference across the capacitor (Vc) may be greater than the applied voltage (V). This suggests that the voltage across the capacitor can exceed the total voltage supplied in the circuit.

2. **Understanding the Reason**: The reason given is that \( V_C = I X_C \) and \( V = I Z \), where \( X_C \) is the capacitive reactance and \( Z \) is the impedance of the circuit. It is stated that \( X_C \) can be greater than \( Z \).

3. **Analyzing the Relationships**:
- The voltage across the capacitor is given by \( V_C = I X_C \).
- The total voltage in the circuit is given by \( V = I Z \).
- The impedance \( Z \) can be expressed in terms of resistance \( R \) and reactance \( X \) (which includes both inductive and capacitive reactance).

4. **Using the Pythagorean Theorem**: In an AC circuit, the relationship between the voltages can be expressed as:
\[ V = \sqrt{V_R^2 + (V_L - V_C)^2} \]
where \( V_R \) is the voltage across the resistor, \( V_L \) is the voltage across the inductor, and \( V_C \) is the voltage across the capacitor.

5. **Example Calculation**: Let's consider an example where:
- \( V_R = 50 \, \text{V} \)
- \( V_L = 100 \, \text{V} \)
- \( V_C = 100 \, \text{V} \)

Plugging these values into the equation:
\[ V = \sqrt{50^2 + (100 - 100)^2} = \sqrt{2500} = 50 \, \text{V} \]
Here, \( V_C \) (100 V) is greater than the applied voltage \( V \) (50 V).

6. **Conclusion on Assertion**: Since we have shown that \( V_C \) can indeed be greater than \( V \), the assertion is true.

7. **Conclusion on Reason**: The reason states that \( X_C \) can be greater than \( Z \). If \( X_C \) is indeed greater than \( Z \), it implies that the voltage across the capacitor can be significantly high, supporting the assertion.

8. **Final Statement**: Both the assertion and the reason are true, and the reason correctly explains the assertion.

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

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