Introductory Electrical Engineering With Math Explained in Accessible Language

26 RL Circuits: Voltage and Current Analysis in Circuits Containing Resistors and Inductors in Series

26.1 Introduction

In this chapter, we will examine RL series circuits formed by resistors and capacitors in series and what happens when these circuits are powered on or off.

26.2 Energizing

We have seen previously in this book that inductors hate current variations and will do everything to oppose the change by trying to block current increasing or pushing forward current decreasing.

Consider the circuit shown in Figure 26.1, composed of an inductor, a resistor, a voltage source, and a switch in series. The switch is initially open and the inductor is completely de‐energized.

Figure 26.1 RL circuit.

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

However, like we have learned before, inductors hate sudden variations in current and create an electromotive force to oppose this new current to flow. This electromotive force will make a voltage rise across inductor with a polarity inverted in relation to V₁. At the exact time the switch is closed, no current will flow across the inductor, and this component is seen by the circuit as an open circuit or as a resistor with a very large resistance.

As time passes, current gradually wins the battle against the electromotive force until the point where the electromotive force ...