Name: ______________________________
Chapter 8 - AC circuits
page 1
Alternating Voltage is a voltage that:
1. Continuously varies in
___________________
2. Periodically _______________ in
polarity
Symbol for a _______________________________ source.
The sinusoidal waveform _______ __________ is the fundamental alternating
current (ac) and alternating voltage waveform.
____________ _______ ________ are named from the mathematical function with
the same shape.
Sinusoidal voltage sources
Sinusoidal voltages are produced by ___ ___________ and
electronic oscillators.
When a conductor rotates in a constant magnetic field, a
sinusoidal wave is generated.
Fill in chart as we talk about it:
N
Motion of conductor
S
Conduc tor
When the conductor is moving _______________ with the lines of flux, no voltage is induced.
When the loop is moving __________________ to the lines of flux, the maximum voltage is induced.
Sine waves are characterized by the __________________ and _____________.
Page 2
1. The ______________ is the maximum value of a voltage or current.
2. The period is the ___________________________
____________.
20 V
15 V
The amplitude (A) of this sine wave is _________.
10 V
0V
The period is :_________.
t (s)
0
25
37.5
50.0
-10 V
-15 V
-20 V
The period (T) of a sine wave can be measured between any
___________________________on the waveform.
By contrast, the ______________ of a sine wave is only
measured from the center to the maximum point.
Frequency ( f ) is the _________________________ that a sine wave completes in one ___________.
Frequency is measured in______________. If 3 cycles of a wave occur in one second, the frequency
______________.
The smaller amount of cycles per second the ____________
frequency.
The larger amount of cycles per second the _________
Frequency.
The ___________ and ________________ are reciprocals of each other.
Period and Frequency:
f
1
T
T 
1
f
If the period is 50 s, the frequency is
(The 1/x key on your calculator is handy for converting between f and T.)
Page 3
Period and Frequency problems:
1
f
T
T 
1
f
1. Calculate the frequency for each of the following periods:
a.) 4 s
b.) 300 µs
c.) 0.5 s
d.) 2 ms
2. Calculate the period for each of the following frequencies:
a.) 40 Hz
b.) 3 kHz
c.) 7 MHz
d.) 300 MHz
3.
How long does it take a 20 kHz sine wave to complete 200 cycles?
4. A sine wave has a frequency of 30 kHz. How many cycles does it complete in 6 ms?
5. A sine wave goes through 4 cycles in 8µs. What is its period?
Page 4
Sine wave voltage and current values
• Instantaneous value____ : __________ __ ___________at any point on the curve.
•
• Peak value (______ for voltage): The ____________of a sine wave.
20 V
15 V
The peak voltage of the wave form is ______.
10 V
0V
t (s)
25
0
37.5
50.0
t= micro seconds
Below are the equations to find:
Peak to peak value: Value from positive peak to negative
peak.
pp = peak to peak
p = peak value
-10 V
-15 V
-20 V
V  2V
PP
Vpp = 2 (20v) = 40 Voltage
I  2I
P
PP
P
RMS(Root mean square): Most ac voltmeters display rms voltage. The 120V at your wall outlet is an rms value.
RMS (root mean square) value: Is the sinusoidal wave with the same heat value as a DC voltage source (known
as the effective value)
V  0.707V
rm s
P
V  1.414V
p
vms
I  0.707 I
rm s
P
I  1.414 I
p
15 V
vms
10 V
Vavg = 0.637Vp
V = ______
0V
Vp = _____________
30
Vpp = ___________
Vavg = ________________
Use the graph below to answer these questions.
What is Vp =
What is Vrms = ____________
__________________
What is Vpp = __________
Voltage (V)
10
0
What is Vavg = ___________
-20
-30
- 40
50.0
-20 V
20
-10
37.5
-15 V
The rms voltage is =______
40
t (s)
25
0
-10 V
The peak-to-peak voltage is = _______
P
1.
20 V
What is the period = ____________
What is the frequency = _____________
2. Try this one yourself.
Page 5
What is Vrms = ____________
What is Vpp = __________
What is Vavg = ___________
What is the period = ____________
What is the frequency = _____________
60 V
45 V
30 V
0V
t (s)
0
25
37.5
50.0
-30 V
-45 V
-60 V
Homework p. 377 selftest 1-9 in complete sentences or if equations show your work! Also
p. 378 2,6,9,10,15 all parts and show your work.
Phase of a sine wave:
Phase:
Angular measurement that specifies the position on the sine wave relative to a reference point
Phase Shift:
Page 6
Occurs when a sine wave is shifted right or left in relation to the base/reference sine wave.
Phase Shift: Lead and Lag
Occurs when a sine wave is shifted right or left in relation to the base/reference sine wave.
Add comments to graphs
Poly Phase Power
An important application of phase-shifted sine waves is in electrical power systems.
o
•
Electrical utilities generate ac with three phases that are separated by 120 .
•
3-phase power is delivered to the user with three hot lines plus neutral. The voltage of each phase,
with respect to neutral is 120 V.
Add Current to graph
Sine Wave equation:
page 7
Instantaneous values of a wave are shown as____________.
The equation for the ___________________ voltage (v) of a sine wave is
v  V p sin 
Where Vp = Peak Voltage
Θ(theta) = Angle in Radians or degrees.
If the peak voltage is 25 V, the instantaneous voltage at 50 degrees is
A certain sine wave has a positive-going zero crossing at 0° and an peak value of 40V.
Calculate its instantaneous voltage for the degrees listed below for the sine wave below.
45°, 125°, 180°, 220°,325°
Show your work!
Homework problem 16 all parts, pay close attention to the Voltage. Can you use Vrms to calculate
Instantaneous voltage!
Page 8
Phasor (aka Phase Vector):
Representation of a ______ _______ whose amplitude (A) and __________ frequency (ω - omega)
are a ___________ rate.
Power in resistive AC circuits:
A sinusoidal voltage produces a
Kirchhoff’s _________ _____applies to AC circuits just like DC
circuits
_______________ current.
Power in AC circuits is calculated using RMS values for ___________ and ____________. Finish picture!
The formula’s are:
The dc and the ac sources produce the same power to the bulb:
P  Vrms I rms
2
Vrms
P
R
2
P  I rms
R
ac or dc
source
Bulb
WHY?
Page 9
Assume a sine wave with a peak value of 40 V is applied to a 100  resistive load. What power is dissipated?
40
V
30
Voltage (V)
20
10
rms
= 0.707 x V =
p
0
-1 0
-2 0
-3 0
- 40
Homework Page 379 #21 all parts
AC Generators (alternators)
• Generators convert rotational energy to_____________ _____________.
•
• The __________ has an induced voltage, which is connected through ______ _____ and brushes to a
______.
•
• The armature loops are wound on a __________ _______.(not shown for simplicity).
•
Small alternators may use a ____________ magnet. Others use
Use ______ coils to produce ____________ _______.
•
Increasing the number of________ increases the number
of _________ per revolution.
•
A _________ ________ generator will produce _______
complete cycles in each revolution.
An output Frequency of an AC Generator
f 
Ns
120
f – frequency (Hz)
N – number of poles
s - speed in RPM
Alternators:
page 10
• In vehicles, alternators_________ ___, which is converted to dc for operating _____________
_______and charging the battery.
•
• AC is more ____________ to produce and can be easily____________, hence it is generated and
converted to DC by____________.
Housing
The _________ is taken from the
________ through the ______ rings.
Stator coils
Rotor
Diode plate
AC Motors
There are two major classifications of ac motors.
1. _____________ motor.
Diodes
Slip rings
2. _________________ motor.
Both types use a _____________ field in the __________ windings.
Induction motors work because __________ is induced in the rotor by the changing _________ in the
________. This current creates a ______________ ________ that reacts with the __________ field of the stator,
which develops a __________ and causes the __________ to turn.
Synchronous motors have a ___________ for the rotor. In small motors, this can be a _______________
magnet, which keeps up with the ___________ field of the stator. Large motors use an _________________ in
the rotor, with external dc supplied to generate the magnetic field.
Induction verses Stator
p. 358
Pulse Definitions
p. 11
Ideal Pulses
Leading (rising) edge
Leading (falling) edge
Trailing (falling) edge
Trailing (rising) edge
Baseline
Am plitude
Am plitude
Baseline
Pulse
width
(a) Positive-going pulse
Pulse
width
(b) Negative-going pulse
Repetitive pulse Waveforms
•
•
•
•
•
•
•
Periodic waveforms repeat at __________ intervals.
Pulse repetition frequency: _______ at which the pulses _________.
_________________ – Ratio of pulse width (t ) to the period (T).
w
Add formulas to picture below.
Define these terms on page 359,
Rise time:
Fall time:
Pulse Width:
Voltage Ramp:
page 12
Ramp – Linear increase or decrease in voltage or current.
Slope =
Yaxis  V  I

or
Xaxis
t
t
Triangular and Sawtooth waves
Triangular and sawtooth waveforms are formed by __________ or ____________ current ramps (linear
increase/decrease).
____________waveforms have
T
T
T
positive-going and negative-going
ramps of ______ duration (same slope
either increasing or decreasing).
T
The sawtooth waveform consists of ____
ramps, _____ of much longer duration than the
other. (_________ slopes in either direction).
Find the T, Vp, Vpp, Vrms for each graph
A.)
B.)
C.)
D.)