What is a second order circuit?

• A. A circuit described by first-order differential equations.
• B. An RLC circuit described by second-order differential equations.
• C. A circuit containing only a resistor.
• D. A circuit with two power sources.

Answer: (B)

A second-order circuit is one whose dynamic behavior is governed by a second-order differential equation, which happens when there are two energy storage elements that can exchange energy with the circuit. In practice, that usually means having both an inductor and a capacitor in the network. When you write the circuit equations for an RLC circuit, you end up with a differential equation that involves the second derivative of voltage or current, reflecting those two independent energy-storage channels.

That’s why an RLC circuit described by second-order differential equations is the textbook example. The presence of both L and C creates the second-order dynamics that yield natural responses (like ringing or exponential transients) and damping determined by the resistor.

The other descriptions don’t capture this dynamic order: a circuit described by first-order differential equations typically has only one energy storage element, so its response involves only the first derivative. A circuit with only a resistor has no energy storage at all, so it lacks the dynamic second-order behavior. Merely having two power sources doesn’t by itself determine the order; the order comes from how many energy storage elements you have.