phy1020.DVI

Chapter 40

AC Circuits

All of the electric circuits we have seen so far aredirect current(DC) circuits. This means that the current is
always traveling in the same direction at each point in the circuit. This is in contrast toalternating current
(AC) circuit, in which the direction of the current alternates back and forth between one direction and another.
Batteries provide direct current; the electric outlets in the walls of your house provide alternating current.
Capacitors and inductors are electrical components that are more typically seen in AC circuits than in DC
circuits. An AC circuit containing resistors, capacitors, and inductors can be analyzed using an interesting
mathematical trick: we simply treat all three components as if they werecomplex-valued resistors, then use
all the methods we used earlier to analyze DC circuits with resistors (but with complex arithmetic). This
complex-valued resistance is calledimpedance, and is given the symbolZ. Impedance has the same units as
resistance, ohms ().
The value of the complex impedance for a resistor, capacitor, and inductor is shown in the table below. In
the table, the symboljstands for the imaginary unit,^1 i.e.jD

p
 1. The variablefin the table refers to
the frequency of the voltage source attached to the component.

Component Impedance

ResistanceRZRDR

CapacitanceCZCDj2fC^1

InductanceLZLDj2fL

We interpret the final results of the analysis (complex numbers) as giving information about both the
amplitude and phase of the signal at any point in the circuit.

(^1) In most areas of science, mathematics, and engineering, the symboliis used forp 1. But in electrical engineering,iis used for
current; so to avoid confusion, electrical engineers writejinstead ofifor
p
 1.