Which of the following conditions occur at resonance in a series RLC circuit? i. Impedance equals resistance…

Analyze the question: We need to decide which statements are true at resonance in a series RLC circuit.

Concept: At resonance, the inductive reactance equals the capacitive reactance (X_L = X_C), so ω₀ = 1/√(LC) and f₀ = 1/(2π√(LC)).

Checking each statement:

• i. Impedance equals resistance: TRUE. Z = √[R² + (X_L − X_C)²]. Since X_L = X_C, Z = R, which is the minimum impedance.
• ii. Current is maximum: TRUE. I = V/Z, and Z is at its minimum (R), so I = V/R is at its maximum.
• iii. Reactance is maximum: FALSE. The net reactance X = X_L − X_C = 0 at resonance. (The individual X_L and X_C are equal to each other, but they cancel, so the net reactance is zero, not maximum.)
• iv. Current and voltage are 90° out of phase: FALSE. The phase angle is φ = tan⁻¹[(X_L − X_C)/R] = 0°. Current and supply voltage are in phase, and the circuit behaves as purely resistive.

Conclusion: Only i and ii are correct, which matches option A.

Exam tip: Remember that at resonance, the circuit acts as if only the resistor is present: Z is minimum, I is maximum, phase angle is 0, and power factor is 1. Whenever you see "reactance is maximum" or "90° out of phase" in a resonance question, it is a trap.