Assertion: At resonance, power factor of series L-C-R circuit is zero.
Reason: At resonance, current function and voltage functions are in same phase.

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

### Step 1: Understand the Assertion
The assertion states that "At resonance, the power factor of a series L-C-R circuit is zero."

- **Power Factor (PF)** is defined as the cosine of the phase angle (φ) between the current and voltage in an AC circuit. Mathematically, it is given by:
\[ \text{Power Factor} = \cos(\phi) \]

### Step 2: Analyze the Condition at Resonance
At resonance in a series L-C-R circuit:
- The inductive reactance (X_L) and capacitive reactance (X_C) are equal, which leads to the total impedance (Z) being purely resistive.
- This means that the phase angle (φ) between the current and voltage is zero (φ = 0).

### Step 3: Calculate the Power Factor at Resonance
Using the definition of power factor:
- Since φ = 0 at resonance, we can calculate the power factor:
\[ \text{Power Factor} = \cos(0) = 1 \]
Thus, the power factor at resonance is 1, not zero.

### Step 4: Understand the Reason
The reason states that "At resonance, current function and voltage functions are in the same phase."

- This is indeed true because at resonance, the phase difference between the voltage and current is zero. Therefore, they are in phase.

### Conclusion
- The assertion is **false** because the power factor is not zero at resonance; it is actually 1.
- The reason is **true** because the current and voltage are indeed in phase at resonance.

### Final Answer
The correct option is that the assertion is false, but the reason is true.

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