Power factor may be equal to 1 for:

Options

A. pure inductor
B. pure capacitor
C. pure resistor
D. An `LCR` circuit

Explanation

To determine when the power factor may be equal to 1, we need to analyze the conditions under which this occurs in an electrical circuit. The power factor (PF) is defined as the cosine of the phase angle (φ) between the voltage and current in an AC circuit. Mathematically, it can be expressed as:

\[ \text{Power Factor (PF)} = \cos(\phi) = \frac{R}{Z} \]

Where:
- \( R \) is the resistance,
- \( Z \) is the impedance of the circuit.

### Step-by-Step Solution:

1. **Understanding Power Factor**:
- The power factor is a measure of how effectively electrical power is being converted into useful work output. A power factor of 1 indicates that all the energy supplied by the source is being used effectively.

2. **Identifying Conditions for PF = 1**:
- The power factor is equal to 1 when the impedance \( Z \) is equal to the resistance \( R \). This occurs under specific conditions in AC circuits.

3. **Pure Resistor**:
- In a circuit with only a pure resistor, the impedance \( Z \) is equal to \( R \) (since there are no reactive components). Therefore:
\[ \text{PF} = \frac{R}{R} = 1 \]
- This means that the power factor is 1 for a pure resistor.

4. **LCR Circuit at Resonance**:
- In an LCR circuit (which includes inductance \( L \) and capacitance \( C \)), the power factor can also be equal to 1 at resonance. At resonance, the inductive reactance \( X_L \) equals the capacitive reactance \( X_C \):
\[ X_L = X_C \]
- Under this condition, the impedance \( Z \) is minimized and can be equal to \( R \), leading to:
\[ \text{PF} = \frac{R}{R} = 1 \]

5. **Conclusion**:
- Therefore, the power factor may be equal to 1 for:
- A pure resistor.
- An LCR circuit at resonance.

### Final Answer:
The power factor may be equal to 1 for a pure resistor and an LCR circuit at resonance.