Introductory Electrical Engineering With Math Explained in Accessible Language

27RLC Circuits: Part 1: Voltage Analysis in Circuits Containing Resistors, Capacitors, and Inductors in Series

27.1 Introduction

Previously in this book, we have examined R_C and R_L series circuits and how capacitors and inductors react when subjected to voltage or current changes.

We saw that capacitors and inductors can store potential energy in the form of electric or magnetic fields.

R_C and R_L circuits are circuits that contain one element that can store energy, and for that reason, all equations we have found are first‐order differential equations.

However, RLC circuits contain two elements that can store energy, and at this point, the readers have realized that these circuits will produce second‐order differential equations.

Due to the complexity of this theme, we will divide the analysis of RLC series circuits into two parts. In this chapter we will make a voltage analysis and in the next chapter a current analysis.

27.2 A Basic RLC Series Circuit

Figure 27.1 shows a circuit with a voltage source, a switch, a resistor, an inductor, and a capacitor in series.

Figure 27.1 A basic RLC circuit.

The switch is open, there is no current flowing in the circuit, the inductor is completely de‐energized, and the capacitor is completely discharged.

At time t = 0 s, the switch is closed, and current flows and reaches the inductor.

The current that was zero before has now a nonzero ...