For a series L - C - R circuit at resonance, the statement which is not true is

Options

A. Peak energy stored by a capacitor = peak energy stored by an inductor
B. Average power = apparent power
C. Wattles current is zero
D. Power factor is zero

Answer

To determine which statement regarding a series L-C-R circuit at resonance is not true, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Understanding Resonance in L-C-R Circuit**:
- In a series L-C-R circuit, resonance occurs when the inductive reactance (X_L) equals the capacitive reactance (X_C). This condition leads to maximum current flowing through the circuit.

2. **Analyzing the Statements**:
- **Statement 1**: "Peak energy stored in capacitor is equal to peak energy stored in inductor."
- At resonance, the energy stored in the capacitor (U_C) and the energy stored in the inductor (U_L) are indeed equal. This statement is **true**.

- **Statement 2**: "Average power becomes equal to apparent power."
- At resonance, the power factor (cos φ) is 1, which means that average power (P_avg) is equal to apparent power (P_apparent). This statement is also **true**.

- **Statement 3**: "Wattless current is zero."
- Wattless current refers to the component of current that does not contribute to power consumption, which is associated with reactive power. At resonance, the phase angle (φ) is 0°, leading to zero wattless current. This statement is **true**.

- **Statement 4**: "Power factor is zero."
- The power factor (cos φ) at resonance is 1, not 0. This statement is **not true**.

3. **Conclusion**:
- The statement that is not true is: "Power factor is zero."

### Final Answer:
The statement which is not true for a series L-C-R circuit at resonance is: **"Power factor is zero."**