Electricity and Magnetism

Chapter 38

RL Circuits

Consider the simplest RL circuit from Chapter 37, as recalled in Figure 38.1 [employing an

ideal battery with emf ε].

ε R

L

FIGURE 38.1 The Simplest RL Circuit

Analysis of the circuit’s dynamics begins with application of Kirchoff’s Rules.

K1 The junction rule applies trivially, as there is but one unique current.

K2 The loop rule gives rise to a dynamical equation for the current response,

0 = ε − I R − L

∂I

∂t

.

Several comments ought to be made. Since the current is confined to the wire, the partial

derivative in the above expression may be replaced by the ordinary derivative. The loop-

equation [expressing conservation of energy p