At resonance frequency the impedance in series LCR circuit is

Options

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

Explanation

To solve the question about the impedance in a series LCR circuit at resonance frequency, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Resonance in LCR Circuit**:
At resonance frequency, the inductive reactance (X_L) is equal to the capacitive reactance (X_C). This condition can be expressed as:
\[ X_L = X_C \]

2. **Impedance Formula**:
The impedance (Z) in a series LCR circuit is given by the formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance.

3. **Substituting Resonance Condition**:
At resonance, since \(X_L = X_C\), we can substitute this into the impedance formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{R^2 + (0)^2} = \sqrt{R^2} \]

4. **Simplifying the Impedance**:
Therefore, the impedance at resonance simplifies to:
\[ Z = R \]
This means that at resonance, the impedance of the series LCR circuit is equal to the resistance (R) of the circuit.

5. **Conclusion**:
At resonance frequency, the impedance in a series LCR circuit is minimized and is equal to the resistance (R).

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

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