Question

In an LCR circuit at resonance:

• A. Current is minimum
• B. Impedance is maximum
• C. Current is maximum
• D. Capacitive reactance is zero

Hint:

At resonance in LCR circuit: \[ X_L=X_C \] \[ Z=R\ (\text{minimum}) \] \[ I=\text{maximum} \]

Answer 1

The Correct Option is C

In a series LCR circuit, resonance occurs when: \[ X_L=X_C \] where:
• \(X_L\) = inductive reactance
• \(X_C\) = capacitive reactance
Step 1: Find impedance at resonance
Impedance is given by: \[ Z=\sqrt{R^2+(X_L-X_C)^2} \] At resonance: \[ X_L-X_C=0 \] Hence: \[ Z=R \] Thus impedance becomes: \[ \text{minimum} \]
Step 2: Find current
Current in AC circuit is: \[ I=\frac{V}{Z} \] Since impedance is minimum at resonance: \[ I=\text{maximum} \]
Step 3: Analyze other options
• Current is not minimum.
• Impedance is not maximum.
• Capacitive reactance is not zero; it becomes equal to inductive reactance. Therefore: \[ \boxed{ \text{Current is maximum} } \] Option analysis:
• Option (A): Incorrect
• Option (B): Incorrect
• Option (C): Correct
• Option (D): Incorrect Hence: \[ \boxed{\text{(C)}} \]