Electricity and Magnetism

Chapter 41

RCL Circuits

Consider the circuit pictured in Figure 41.1, which incorporates a switch, a fully charged

capacitor, C, a resistor, R, and an inductor, L. The switch is closed at the instant t = 0.

In this chapter, we shall perform the analysis of the circuit in terms of the charge on the

capacitor, q(t), which is equivalent [up to a factor] to the potential difference, V

C

, across

the capacitor. A current-based description of the circuit dynamics is presented in the

Addendum.

C

+q

−q

R

L

I

K1 =⇒ The current, I(t), is uniquely

defined at each instant.

K2 =⇒ 0 =

q

C

− I R − L

dI

dt

.

FIGURE 41.1 A Simple RCL Circuit without a Voltage Source

The flow of current ...