Question

In series LCR circuit at resonance, the phase difference between voltage and current is

• A. π
• B. \(\frac{\pi}{4}\)
• C. \(\frac{\pi}{2}\)
• D. zero

Answer 1

The Correct Option is D

Step 1: Resonance condition in an LCR circuit: 

At resonance, the inductive reactance (\(X_L\)) and capacitive reactance (\(X_C\)) become equal:

\[ X_L = X_C \]

Step 2: Implication for circuit impedance:

At resonance, the net reactance is zero. Hence, the impedance (\(Z\)) of the LCR circuit at resonance is purely resistive, equal to \(R\):

\[ Z = R \]

Step 3: Phase difference at resonance:

In a purely resistive circuit, voltage and current are in phase. Thus, the phase difference (\(\phi\)) between voltage and current at resonance is:

\[ \phi = 0 \]

Final Conclusion:
At resonance, the voltage and current in a series LCR circuit are in phase (phase difference = 0).

Answer 2

In a series LCR circuit at resonance, the inductive reactance (\( X_L \)) and capacitive reactance (\( X_C \)) are equal, i.e., \( X_L = X_C \). Therefore, the total reactance is zero, and the impedance of the circuit becomes purely resistive. At resonance, the current and voltage are in phase, meaning the phase difference between them is zero.
This is because the voltage and current reach their maximum values simultaneously, and there is no phase shift between them.

Thus, the phase difference is zero.