At resonant frequency the current amplitude in series LCR circuit is

Options

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

Answer

To solve the problem regarding the current amplitude in a series LCR circuit at resonant frequency, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Series LCR Circuit**:
In a series LCR circuit, the components are connected in series, and the total current flowing through the circuit is the same in all components.

2. **Identify the Resonant Frequency Condition**:
At resonant frequency, the inductive reactance (XL) is equal to the capacitive reactance (XC). This condition can be expressed as:
\[ X_L = X_C \]

3. **Impedance at Resonance**:
The total impedance (Z) of the circuit is given by the formula:
\[ Z = \sqrt{R^2 + (X_L - X_C)^2} \]
When \(X_L = X_C\), the term \((X_L - X_C)\) becomes zero, leading to:
\[ Z = R \]

4. **Current Amplitude Calculation**:
The current amplitude (I) in the circuit can be expressed as:
\[ I = \frac{V_m}{Z} \]
Substituting the impedance at resonance:
\[ I = \frac{V_m}{R} \]

5. **Conclusion**:
Since the impedance (Z) at resonance is equal to the resistance (R), the current amplitude reaches its maximum value. Therefore, at resonant frequency, the current amplitude in the series LCR circuit is maximum.

### Final Answer:
At resonant frequency, the current amplitude in a series LCR circuit is maximum.

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