Electricity and Magnetism

Chapter 44

RCL AC Circuits

Having considered purely resistive, inductive, and capacitive AC circuits in turn, let’s go

all out and place an AC voltage source in series with resistive, capacitive, and inductive

elements characterised by R, C, and L.

∼

v

i

C

R

L

FIGURE 44.1 AC Source with Resistive, Capacitive, and Inductive Loads

Application of Kirchoff’s Loop Rule is straightforward. Moreover, we recognise that the

current is confined to the [thin] wires, and we exercise our freedom to choose t = 0 so that

the phase angle associated with the AC voltage source vanishes. Hence,

0 = v − i R −

q

C

− L

di

dt

and v(t) = V

0

sin(ω t) .

Taking the time derivative of this equation ...