Assertion : AC circuit derives maximum power when it is in a state of resonance.
Reason: Power factor of the circuit becomes zero in case of reasonance.

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 reason provided:

**Assertion**: An AC circuit derives maximum power when it is in a state of resonance.

**Reason**: The power factor of the circuit becomes zero in case of resonance.

### Step-by-Step Solution:

1. **Understanding Resonance in AC Circuits**:
- In an AC circuit, resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC). This condition can be expressed as:
\[ XL = XC \]
- At resonance, the impedance (Z) of the circuit is minimized and is equal to the resistance (R) of the circuit:
\[ Z = R \]

2. **Current at Resonance**:
- The current (I) in the circuit can be expressed as:
\[ I = \frac{V_{rms}}{Z} \]
- Since \(Z = R\) at resonance, the current reaches its maximum value:
\[ I_{max} = \frac{V_{rms}}{R} \]

3. **Power in AC Circuits**:
- The average power (P) consumed in an AC circuit is given by:
\[ P = V_{rms} \cdot I_{rms} \cdot \cos \phi \]
- Where \(\phi\) is the phase difference between the voltage and current. At resonance, the power factor (\(\cos \phi\)) is 1 because the voltage and current are in phase.

4. **Conclusion about the Assertion**:
- Since the power factor is 1 at resonance, the average power is maximized:
\[ P_{max} = V_{rms} \cdot I_{rms} \]
- Therefore, the assertion that an AC circuit derives maximum power when it is in a state of resonance is **correct**.

5. **Analyzing the Reason**:
- The reason states that the power factor becomes zero in case of resonance. This is incorrect because, as established, the power factor at resonance is actually 1 (not zero).
- Thus, the reason is **incorrect**.

### Final Conclusion:
- The assertion is correct, but the reason is incorrect. Therefore, the correct answer is that the assertion is true, and the reason is false.