For a second-order RLC circuit, which statement best describes its dynamic behavior?

• A. It has a single energy storage element and a single pole.
• B. It cannot exhibit resonance.
• C. It has two energy storage elements and can exhibit resonance and damping.
• D. It requires passive components only and cannot be tuned.

Answer: (C)

In a second-order RLC circuit, the dynamics come from the exchange of energy between two storage elements: the magnetic energy in the inductor and the electric energy in the capacitor. The resistor provides energy dissipation, so the system can both store and lose energy over time. This combination makes the behavior second-order because the governing equation involves the second derivative of current or voltage with respect to time.

Two storage elements set the natural frequency, roughly determined by LC as ω0 ≈ 1/√(LC) in the ideal lossless case. The resistor introduces damping, so the actual response can be underdamped (oscillatory with exponential decay), critically damped (fastest non-oscillatory return), or overdamped (non-oscillatory and slower return). Because energy can slosh back and forth between the inductor and capacitor, the circuit can exhibit resonance when driven near its natural frequency, producing large responses under the right conditions.

So the statement that captures this dynamic best is: it has two energy storage elements and can exhibit resonance and damping. A single energy storage element would yield a first-order response; resonance requires energy exchange between L and C; and while RLC circuits are passive, they can be tuned by changing L or C values to shift the resonance.