35 AC Circuits
Recommended class days: 2
Background Information
AC circuits are an important application of electricity and magnetism, but no new physics is
required. This is an extension of the study of DC circuits in Chapter 31, and the same misunder
standings about current and voltage will continue to haunt students unless those misunderstandings
were successfully dealt with in Chapter 31.
The title of this chapter, although conventional, is somewhat of a misnomer. Rather than
being about “household electricity,” as most students would surmise, the phasor analysis and the
majority of topics (e.g., resonance circuits) are more relevant to radiofrequency circuits.
Phasor analysis will be a new idea for nearly all students, and many find the idea rather difficult.
Students don’t readily distinguish between instantaneous values (v and i), peak values (V and I ) and
rms values (V and I ), and they’re often not sure which to use.
rms rms
Student Learning Objectives
To use a phasor analysis to analyze AC circuits.
To understand RC filter circuits.
To understand the series RLC circuit and resonance.
To calculate power loss in an AC circuit using the power factor.
Pedagogical Approach
All results in this chapter are derived from the geometry of a phasor diagram. Complex impedances
are not introduced. Students need to see careful explanations of phasors, the distinction between
peak and instantaneous values, and the idea of phase leads and lags.
AC circuits are much harder to demonstrate than DC circuits, but it’s well worth using a dual
trace oscilloscope to show simultaneously both the voltage across and current through a circuit
element (using voltage through a series resistor as the current trace). In an RC circuit, for example,
you can show that changing the amplitude does not change the ratio V /V , but changing the fre
R C
quency does. Frequency is usually the most important parameter for understanding AC circuits.
Using Class Time
DAY 1: This is a chapter easily covered in two days. Day 1 should concentrate on what a phasor is,
distinguish between peak and instantaneous values, and use phasors to understand resistor, capa
citor, and RC filter circuits. The 90° phase difference between position and velocity in simple
harmonic motion is a good analogy for explaining the phase difference between voltage and
351352 Instructor’s Guide
current in a capacitor. It’s important to emphasize that the reactance of a capacitor relates only the
peak voltage and current. Although reactance is much like resistance, resistance applies to both
peak and instantaneous values, whereas reactance applies only to peak value. Students easily lose
sight of the distinction.
An RC filter circuit is easily demonstrated with the dualtrace oscilloscope. Students find this
quite interesting if you relate it to the bass and treble knobs on their stereo. You could even have
students design a midrange filter that passes frequencies between 100 Hz and 1000 Hz by cascading
a highpass filter and a lowpass filter, then build one and test it.
DAY 2: Day 2 can then focus mostly on inductor circuits and the RLC series circuit. Students like
the idea of resonance circuits because of their importance in telecommunications. A dramatic
demonstration is to watch the current of a highQ circuit on the oscilloscope while sweeping the
frequency back and forth through resonance. Although the textbook derives the phase angle
and shows graphs, the fact that the current switches from leading to lagging as you go through
resonance is a fairly minor point. The resonance in the current amplitude is the most important
feature.
Power and the power factor are treated conventionally. The main point to get across is that no
net power is dissipated in an ideal capacitor or inductor. They alternately store and release energy as
the fields build and then collapse, but the average over a cycle is zero. All the power dissipation is
in the resistor, but the dissipation is less than a DC analysis would lead you to expect, due to the
fact that the current and voltage are usually not in phase. Hence the idea of the power factor.
Sample Reading Quiz Questions
1. The analysis of AC circuits uses a rotating vector called a .
2. In a capacitor, the peak current and peak voltage are related by the
a. capacitive resistance. c. capacitive impedance.
b. capacitive reactance. d. capacitive inductance.
3. In a series RLC circuit, what quantity is maximum at resonance?
a. The voltage. c. The impedance.
b. The current. d. The phase.Chapter 35: AC Circuits 353
Sample Exam Questions
These questions cover the material of Chapters 34–35.
1. Reference frame S′ moves along one of the coordinate axes of reference frame S.
Experimenters in frames S and S′ measure the electric and magnetic fields shown. Along
which axis does S′ move, and in which direction?
yy′
r
E
r
E′
r r
B B′
x x′
S S′
z z′
2
2. A 100 MHz radio wave with intensity 500 W/m is traveling in the positive ydirection.
a. Draw the magnetic field vector at the point shown.
b. What is the amplitude of the wave’s magnetic field?
y
x
r
E
z
3. A circuit with two elements, 1 and 2, has the phasor diagram shown in the figure. Each
element could be a resistor, a capacitor, or an inductor. Draw the circuit diagram.
0
I
V
1
V
2
4. Your supervisor asks you to build a lowpass filter with a crossover frequency of 500 rad/s.
You have two 50 Ω resistors, a 25 µF capacitor, and a 100 µF capacitor. Can you build the
circuit? If so, show the circuit diagram. If not, why not?
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