Question

In LCR series resonant circuit, at resonance, voltage across \(L\) and \(C\) will cancel each other because they are

• A. 90° out of phase
• B. 90° in phase
• C. 180° in phase
• D. 180° out of phase

Hint:

In series LCR: \(V_L\) leads \(I\) by 90°, \(V_C\) lags \(I\) by 90°, so \(V_L\) and \(V_C\) are 180° out of phase. At resonance, \(X_L = X_C\) so they cancel.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
At resonance in series LCR circuit, voltages across inductor and capacitor cancel. We need the phase relationship.

Step 2: Key Formula or Approach:
In series LCR, current is same through all components. Voltage across inductor leads current by 90°, voltage across capacitor lags current by 90°.

Step 3: Detailed Explanation:
\(V_L\) leads \(I\) by \(90^\circ\). \(V_C\) lags \(I\) by \(90^\circ\). Therefore, \(V_L\) and \(V_C\) are \(180^\circ\) out of phase with each other. At resonance, \(V_L = V_C\) in magnitude, so they cancel exactly.

Step 4: Final Answer:
Option (D) is correct.