In an L-C-R series, AC circuit at resonance

Options

A. the capacitive reactance is more than the inductive
B. the capacitive reactance equals the inductive reactance
C. the capactive reactance is less than the inductive reactance
D. the power dissipated is minimum

Explanation

To solve the question regarding the conditions of resonance in an L-C-R series AC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Resonance in L-C-R Circuit**:
- In an L-C-R series circuit, resonance occurs when the inductive reactance (XL) is equal to the capacitive reactance (XC). This means that the circuit will have a purely resistive impedance at resonance.

2. **Setting Up the Conditions for Resonance**:
- The conditions for resonance can be expressed as:
\[ X_L = X_C \]
- This implies that the voltage across the inductor (VL) is equal to the voltage across the capacitor (VC).

3. **Analyzing the Options**:
- Given the options, we need to determine which statements are true based on the resonance conditions.
- The options state:
- A: Capacitive reactance is more than inductive reactance.
- B: Capacitive reactance is equal to inductive reactance.
- C: Capacitive reactance is less than inductive reactance.
- D: Power dissipated is minimum.

4. **Evaluating Each Option**:
- **Option A**: Incorrect, because at resonance, \(X_C\) cannot be greater than \(X_L\).
- **Option B**: Correct, as this directly states the condition for resonance where \(X_C = X_L\).
- **Option C**: Incorrect, as at resonance, \(X_C\) cannot be less than \(X_L\).
- **Option D**: Incorrect, because at resonance, the power is maximum, not minimum. The power factor is maximum (cos φ = 1) at resonance, leading to maximum power.

5. **Conclusion**:
- The correct answer is **Option B**, which states that the capacitive reactance is equal to the inductive reactance at resonance.