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28 RLC Circuits: Part 2: Current Analysis in Circuits Containing Resistors, Capacitors, and Inductors in Series
28.1 Introduction
In the last chapter, we have performed a voltage analysis in RLC series circuits, finding their voltage equations for various specific cases.
In this chapter we will continue to examine series RLC circuits in terms of current analysis.
28.2 The Circuit
Our analysis will focus on the same circuit we have used on the last chapter: a direct voltage source, a resistor, a capacitor, an inductor, and a switch in series, like shown in Figure 28.1.
Figure 28.1 A basic RLC circuit.
Like before, the switch is initially 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.
28.2.1 Current
As soon as the switch is closed, we can apply to the circuit. Kirchhoff’s voltage law (KVL) states that the sum of all voltages in a closed loop is 0.
Therefore, the power supply voltage (V1) is equal to the voltage drop on the resistor added to the voltage across the inductor and capacitor, or
Voltages across a capacitor, an inductor, and a resistor are defined as
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