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 the Resonance Condition**:
- In an LCR series circuit, resonance occurs when the inductive reactance (XL) is equal to the capacitive reactance (XC).
- Mathematically, this is expressed as:
\[ XL = XC \]

2. **Determine the Impedance (Z)**:
- The total impedance (Z) in an LCR circuit is given by:
\[ Z = \sqrt{R^2 + (XL - XC)^2} \]
- At resonance, since \(XL = XC\), the reactance difference becomes zero:
\[ Z = \sqrt{R^2 + 0^2} = R \]

3. **Calculate the Power Factor (PF)**:
- The power factor (PF) is defined as the cosine of the phase angle (φ) between the total voltage and the current in the circuit:
\[ PF = \cos(\phi) = \frac{R}{Z} \]
- Substituting the values at resonance:
\[ PF = \frac{R}{R} = 1 \]

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

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

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