At resonance frequency the impedance in series LCR circuit is

Options

A. maximum
B. minimum
C. zero
D. infinity

Explanation

To solve the question regarding the impedance of a series LCR circuit at resonance frequency, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the LCR Circuit**:
- An LCR circuit consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series with an AC source.

2. **Condition for Resonance**:
- At resonance frequency, the inductive reactance (XL) is equal to the capacitive reactance (XC). This can be mathematically expressed as:
\[ X_L = X_C \]

3. **Expression for Impedance**:
- The impedance (Z) of a series LCR circuit is given by the formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]

4. **Substituting the Resonance Condition**:
- Since at resonance, \( X_L = X_C \), we can substitute this into the impedance formula:
\[ Z = \sqrt{R^2 + (X_L - X_L)^2} \]
- This simplifies to:
\[ Z = \sqrt{R^2 + 0} = \sqrt{R^2} = R \]

5. **Conclusion**:
- Therefore, at resonance frequency, the impedance of the series LCR circuit is equal to the resistance (R) of the circuit.

### Final Answer:
At resonance frequency, the impedance in a series LCR circuit is equal to the resistance (Z = R).

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