Analytic solution Parallel RLC Second Order Systems

The Sorder differential equation characterizes the RLC parallel cir- cuit, the circuit is classified as a second-order circuit. The two differential equations have the same form. In a parallel RLC circuit, the answer is the inductor current; in a series RLC circuit, the unknown is represented by the capacitor voltage A resistor, inductor, and capacitor are linked either serially or paral- lelly in second-order RLC circuits. The same method used to examine an RLC series circuit can also be used to study a second-order parallel circuit.Since the parts of the previously presented example parallel circuit are linked in parallel, you can use Kirchhoff’s current law (KCL) to set up the second-order differential equation. At a node, KCL states that the total of the incoming and outgoing currents is equal. The zero-state response can be obtained by setting the starting conditions (I0 and V0) to zero at Node A of the sampling circuit using KCL.