Which type of circuit contains both an inductor and a capacitor?

• A. First-Order Circuit
• B. Second-Order Circuit
• C. RC Circuit
• D. RL Circuit

Answer: (B)

Having both an inductor and a capacitor means the circuit can store energy in two independent ways: in the magnetic field of the inductor and the electric field of the capacitor. Because there are two energy storage elements, the circuit’s dynamic equation involves two state variables and the second derivative appears in the relationship between voltage and current. This makes the circuit second-order. For example, a series LC circuit without resistance leads to a differential equation d^2q/dt^2 + (1/LC) q = 0, showing second-order behavior and potential oscillations at 1/√(LC). In contrast, circuits with only one energy storage element (just a capacitor with resistance, or just an inductor with resistance) are governed by first-order equations.