Question

Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C), and (D) as given below.
Assertion (A): A series LCR circuit behaves as a pure resistive circuit at resonance.
Reason (R): At resonance, \( X_L = X_C \) gives \( \omega = \frac{1}{\sqrt{LC}} \).

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Both Assertion (A) and Reason (R) are false.

Hint:

At resonance in a series LCR circuit, \( X_L = X_C \), cancelling out the reactive parts, so only resistance remains in the impedance.

Answer 1

The Correct Option is A

In a series LCR circuit: - Resonance occurs when the inductive reactance equals the capacitive reactance, i.e., \( X_L = X_C \).
- This implies: \[ \omega L = \frac{1}{\omega C} \Rightarrow \omega^2 = \frac{1}{LC} \Rightarrow \omega = \frac{1}{\sqrt{LC}} \] At this frequency: - The net reactance \( X = X_L - X_C = 0 \), so the impedance \( Z = R \) (purely resistive).
- Hence, the circuit behaves like a pure resistive circuit at resonance.
Therefore: - Assertion is true.
- Reason is also true.
- And Reason correctly explains the Assertion.
Final answer: Option (A)