In alternating current circuit at resonance, the angle of lead or lag is?

1. Analyze the question You are asked for the phase angle between voltage and current in a series RLC circuit at resonance.

2. Explain the concept In a series RLC circuit, the phase angle φ is given by:

tan φ = (X_L − X_C) / R

where X_L = ωL (inductive reactance) and X_C = 1/(ωC) (capacitive reactance).

Resonance occurs when X_L = X_C, which happens at the frequency f₀ = 1/(2π√(LC)).

3. Solution At resonance:

• X_L = X_C, so X_L − X_C = 0
• tan φ = 0 / R = 0
• φ = 0°

The impedance Z = √[R² + (X_L − X_C)²] = R, which is its minimum value. The circuit behaves as a purely resistive circuit, so the current and voltage are in phase. There is no lead and no lag.

4. Answer The angle of lead or lag is 0°, which is option D.

5. Exam tip Remember this: resonance means X_L = X_C, so the circuit is purely resistive, and voltage and current are in phase (φ = 0). Other facts that follow from this:

• Impedance is minimum (Z = R).
• Current is maximum.
• Power factor = cos 0 = 1.

Note: a phase angle of π/2 (option B) applies to a purely inductive or purely capacitive circuit, not at resonance.