At resonance, the value of the power factor in an LCR series circuit is

Options

A. Zero
B. 1
C. `(1)/(2)`
D. Not defined

Answer

To find the value of the power factor in an LCR series circuit at resonance, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Resonance in LCR Circuit**:
At resonance in an LCR series circuit, the inductive reactance (X_L) is equal to the capacitive reactance (X_C). This means that the circuit behaves purely resistively.

2. **Write the Condition for Resonance**:
The condition for resonance can be expressed as:
\[ X_L = X_C \]
This implies that the total impedance (Z) of the circuit is equal to the resistance (R) of the circuit.

3. **Calculate the Impedance at Resonance**:
At resonance, the impedance (Z) is given by:
\[ Z = R \]

4. **Define Power Factor**:
The power factor (cos φ) in an AC circuit is defined as:
\[ \text{Power Factor} = \cos φ = \frac{R}{Z} \]

5. **Substituting the Values**:
Since at resonance \( Z = R \), we can substitute this into the power factor formula:
\[ \text{Power Factor} = \frac{R}{R} = 1 \]

6. **Conclusion**:
Therefore, the value of the power factor in an LCR series circuit at resonance is:
\[ \text{Power Factor} = 1 \]

### Final Answer:
The value of the power factor in an LCR series circuit at resonance is **1**.

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