A series RLC circuit is said to resonate, when

Analyze the question: We need the condition that defines resonance in a series RLC circuit.

Concept: In a series RLC circuit:

• Inductive reactance: X_L = 2πfL
• Capacitive reactance: X_C = 1/(2πfC)
• Impedance: Z = √(R² + (X_L − X_C)²)

Resonance happens at the frequency where X_L = X_C.

Solution:

1. At resonance, X_L = X_C, so (X_L − X_C) = 0.
2. The impedance becomes Z = √(R² + 0) = R.
3. This is the smallest value Z can take, since the reactive term can only add to R. So impedance is minimum.
4. Since I = V/Z, the current is then maximum, not minimum. This rules out C.
5. Resonant frequency: f₀ = 1/(2π√(LC)).

Checking the options:

• A. Capacitive reactance is zero: wrong. X_C equals X_L at resonance, and it is not zero.
• B. Conductance is maximum: this is a trap. Conductance (G = R/Z²) is also maximum at resonance, since Z is minimum, but it is not the standard defining statement. Also, "conductance" is loosely used, so it is ambiguous. The standard textbook answer is impedance.
• C. Current is minimum: wrong, current is maximum.
• D. Impedance is minimum: correct.
• E. Inductive reactance is zero: wrong, X_L equals X_C and is not zero.

Tip: Remember "Series resonance: Z minimum, I maximum." (For parallel resonance it's the opposite: impedance is maximum, current minimum.) The key phrase is X_L = X_C, so the reactances cancel and only R is left.