What is a Second Order Differential Circuit?

A Second Order Differential Circuit (or, just simply, second order circuit) is a circuit with two energy storage elements, a capacitor and inductor. It is a called a second order differential circuit because in order to solve for the capacitor's and inductor's voltages and/or currents, a second order differential equation must be computed in order to find the results.

Shown above is a circuit in which, in order to solve, the second order differential equation of one of the storage elements must be computed in order to find the voltages or currents. The capacitor and inductor are the two energy storage elements of the circuit. In order to solve for their voltages in this circuit, Kirchhoff's current Law (KCL) is applied to the circuit. When doing KCL, a second order differential equation will result, which is why this is a second order circuit.

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