Assertion: At resonance, power factor of L-C-R series circuit is 1.
Reason: At resonance, `X_(C) = X_(L)`

Options

A. (a) If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true but Reason is false.
D. (d) If Assertion is false but Reason is true.

Explanation

To solve the question, we will analyze both the assertion and the reason given in the problem statement.

### Step-by-step Solution:

1. **Understanding Resonance in L-C-R Circuit**:
- In an L-C-R series circuit, resonance occurs when the inductive reactance \(X_L\) is equal to the capacitive reactance \(X_C\). This condition can be expressed mathematically as:
\[ X_L = X_C \]
- At resonance, the total impedance \(Z\) of the circuit is minimized.

2. **Condition for Resonance**:
- The inductive reactance \(X_L\) is given by:
\[ X_L = L \omega \]
- The capacitive reactance \(X_C\) is given by:
\[ X_C = \frac{1}{\omega C} \]
- Setting these two equal for resonance gives:
\[ L \omega = \frac{1}{\omega C} \]

3. **Calculating Impedance at Resonance**:
- The total impedance \(Z\) in an L-C-R circuit is given by:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
- At resonance, since \(X_L = X_C\), we have:
\[ Z = \sqrt{R^2 + 0^2} = R \]

4. **Power Factor Calculation**:
- The power factor \(PF\) is defined as:
\[ PF = \cos \phi = \frac{R}{Z} \]
- Substituting the values we found:
\[ PF = \frac{R}{R} = 1 \]

5. **Conclusion**:
- Therefore, at resonance, the power factor of the L-C-R series circuit is indeed 1, and the reason provided (that \(X_C = X_L\)) is the correct explanation for this assertion.

### Final Answer:
- **Assertion**: True
- **Reason**: True
- The reason correctly explains the assertion.