In an AC circuit, resonance occurs when the impedance of the circuit is:

Analyze the question: We're asked what happens to the impedance of an AC circuit at resonance. This is about the series RLC circuit, which is the standard case in JAMB.

Explain the concept: In a series RLC circuit, the impedance is:

Z = √[R² + (X_L − X_C)²]

where

• X_L = 2πfL (inductive reactance)
• X_C = 1/(2πfC) (capacitive reactance)
• R = resistance

Solution:

1. Resonance occurs when X_L = X_C.
2. Then (X_L − X_C) = 0, so the two reactances cancel each other.
3. The impedance becomes Z = √(R² + 0) = R.
4. Since the reactive part is zero, Z has its smallest possible value, which is R. At any other frequency, (X_L − X_C)² is positive, so Z is greater than R.
5. Because Z is minimum, the current I = V/Z is maximum at resonance.

The resonant frequency is f₀ = 1/(2π√(LC)).

Checking the options:

• A. Zero: Not correct. Z equals R, and a real circuit always has some resistance, so Z is never zero.
• B. Maximum: Wrong. It is the current that is maximum, not the impedance.
• C. Equal to the capacitive reactance: Wrong. At resonance Z = R, and X_C is generally not equal to R.
• D. Minimum: Correct. Z = R, its lowest possible value.

Exam tip: Remember "Resonance: Z minimum, I maximum." Impedance and current always move in opposite directions, since I = V/Z. If an option says "impedance is maximum", it is a trap. It is true for a parallel resonant circuit, but the standard JAMB question refers to the series circuit.