Which of the following plots may represent is impedence of a series LCR combination?

Options

A.
B.
C.
D.

Answer

To determine which plot represents the impedance of a series LCR (Inductor-Capacitor-Resistor) combination, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Impedance Formula**:
The impedance \( Z \) of a series LCR circuit is given by the formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
where \( X_L = \omega L \) (inductive reactance) and \( X_C = \frac{1}{\omega C} \) (capacitive reactance).

2. **Identify the Conditions**:
- **Condition 1**: When \( X_L = X_C \) (resonance condition), then \( Z = R \).
- **Condition 2**: When \( X_L > X_C \) (inductive dominance), \( Z \) increases as frequency increases.
- **Condition 3**: When \( X_C > X_L \) (capacitive dominance), \( Z \) also increases but starts from a lower value.

3. **Plot the Impedance**:
- On the x-axis, we plot frequency \( \omega \).
- On the y-axis, we plot impedance \( Z \).
- The graph will show:
- A minimum point at resonance (\( Z = R \)).
- An increase in impedance as we move away from resonance in both directions (either \( X_L \) or \( X_C \) dominating).

4. **Analyze the Options**:
- Check each option to see which one reflects the behavior described:
- A curve that dips to a minimum at the resonance frequency and rises on either side indicates the correct representation of impedance in a series LCR circuit.

5. **Conclusion**:
- After analyzing the provided options, the correct plot that represents the impedance of a series LCR combination is identified.

### Final Answer:
The correct option is **Option C**.