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9-1
Electricity
Principles & Applications
Eighth Edition
Richard J. Fowler
Chapter 9
Power in AC Circuits
(student version)
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9-2
INTRODUCTION
• Phase Shift
• True Power
• Apparent Power
• Angle Theta
• Power Factor
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9-3
Dear Student:
This presentation is arranged in segments. Each segment
is preceded by a Concept Preview slide and is followed by a
Concept Review slide. When you reach a Concept Review
slide, you can return to the beginning of that segment by
clicking on the Repeat Segment button. This will allow you
to view that segment again, if you want to.
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9-4
Concept Preview
(Page 231)
• In pure resistance ac circuits, there
are only two power pulses per cycle.
• In pure resistance ac circuits, both
power pulses are positive.
• In pure resistance ac circuits, current
and voltage are in-phase.
• In pure resistance ac circuits, use the
the power formula used for dc circuits.
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9-5
Ac- Power Facts
• Resistance doesn’t cause phase shift.
• Reactance causes 90 of phase shift.
• Theta is the angle by which the current leads
or lags the voltage.
• Trigonometric functions can be used to find
the resistive and reactive parts of a phasor.
• Apparent power calculations ignore phase shift.
• It is advantageous for a system to operate with
a power factor close to one.
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9-6
Power In A Resistive Ac Circuit (Page 232)
P
5V
2A
Note that both
power pulses
are positive.
There are only
two pulses per
cycle. Voltage
and current are
in-phase.
V
I
P = IV in an ac circuit containing only resistance.
P = 2 A x 0.707 x 5V x 0.707 = 5 W
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9-7
Resistive-Power Quiz
Power equals current times voltage in an ac
circuit when the only load is ____.
resistance
Use ____ values of current and voltage when
calculating power.
rms
Without phase shift, there are ____ power
pulses for each cycle.
two
There are no ____ power pulses when current
and voltage are in phase.
negative
An ac circuit with a 30-VP-P source and a 10-W
resistor load uses ____ watts of power.
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11.25
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9-8
Concept Review
• In pure resistance ac circuits, there
are only two power pulses.
• In pure resistance ac circuits, both
power pulses are positive.
• In pure resistance ac circuits, current
and voltage are in-phase.
• In pure resistance ac circuits, use the
the power formula used for dc circuits.
Repeat Segment
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9-9
Concept Preview
• Capacitance causes I to lead V.
• Inductance causes V to lead I.
(Page 232)
(Page 233)
• Circuits with both R and X (reactance)
cause theta to be >0 and <90. (Page 233)
• It (or Vt) can be divided into its
resistive and reactive parts. (Page 235)
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9 - 10
Reactance Causes Phase Shift
(Page 232)
V
I
50
A combination circuit with capacitance causes I to lead V.
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9 - 11
Reactance Causes Phase Shift
(Page 232)
60
V
I
A combination circuit with inductance causes V to lead I.
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9 - 12
Working With Right Triangles
(Page 236)
opposite
tan q =
adjacent
q
hypotenuse
adjacent side
Ireactive
adjacent
cos q = hypotenuse
Ireactive
sin q =
opposite
=
q
q
Iresistive
Vsource
Iresistive
The hypotenuse can be either the total voltage or the total current.
Of course, the sides must be the same quantity as the hypotenuse.
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9 - 13
Combination-Loads Quiz
Capacitance causes current to ____ voltage.
lead
Inductance causes current to ____ voltage.
lag
The ____ of a triangle of current phasors
represents the total current.
hypotenuse
The resistive current is ____ amperes when
9.2
theta is 40 and the total current is 12 amperes.
The total voltage is ____ volts when theta is
25 and the reactive voltage is 40 volts.
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94.6
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9 - 14
Concept Review
• Capacitance causes I to lead V.
• Inductance causes V to lead I.
• Circuits with both resistance and
reactance cause theta to be >0 and <90.
• It (or Vt) can be divided into its
resistive and reactive parts.
Repeat Segment
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9 - 15
Concept Preview
(Page 240)
• Phase-shifted circuits produce two
positive and two negative power pulses.
• In pure reactance circuits the negative
and positive pulses are equal.
• Wattmeters measure true power.
• Apparent power ignores angle theta.
• Power factor = power  apparent power.
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9 - 16
Power In A Phase-Shifted Circuit (Page 241)
P
cos 30° = 0.866
30°
3V
2A
I
V
The power pulse is negative when I and V have opposite signs.
P = I V cos q = 2 A x 0.707 x 3V x 0.707 x 0.866 = 2.6 W
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9 - 17
Power in a Pure
Reactance
Circuit
(Page 231)
The
negative
power
pulses
cancel
the
positive
power
pulses.
There is
no true
power.
P
I
V
90
This circuit has capacitance because I leads V.
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9 - 18
Two Types Of(PagePower
In
Ac
Circuits
240)
80 W
W
4A
A
25 V
V
Combination
of
resistance
and
reactance
Power (true power) is measured with a wattmeter or calculated
using the formula P = IV cos q. Measured P = 80 W.
Apparent power is determined by measuring current and voltage
and then using the formula Papp = IV. Papp = 4 A x 25 V = 100 VA
When the load is all resistance, power (P) = apparent power (Papp).
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9 - 19
Determining Power Factor (PF) and Angle Theta (q)
(Page 241)
75.5 W
W
3A
A
30 V
V
Combination
of
resistance
and
reactance
The measured power, current, and voltage can be used to
determine power factor and angle theta. Papp = 3 A x 30 V = 90 VA
PF = cos q = P / Papp = 75.5 W / 90 VA = 0.839
q = arccos 0.839 = 33 ( Arccos means the angle that has this cos.)
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9 - 20
Calculating Currents
(Page 238)
Determine the resistive and reactive currents when the
source current is 43 A and the power factor is 0.92.
cos q = Iresistive / IT
Therefore,
Iresistive = IT x cos q
Iresistive = 43 A x 0.92 = 39.56 A
arccos 0.92 = 23.1 ( Arccos means the angle that has this cos.)
And, tan 23.1 = 0.426
tan q = Ireactive / Iresistive
Therefore, Ireactive = Iresistive x tan q
Ireactive = 39.56 A x 0.426 = 16.85 A
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9 - 21
Combination-Load-Power Quiz
There are ____ negative power pulses per cycle
when current and voltage are out of phase.
two
With combination loads, P = IV cos q will
yield the ____ power.
true
With combination loads, P = IV will
yield the ____ power.
apparent
The unit for apparent power is the _____.
VA
The power is ____ watts when I = 16 A,
V = 240 V, and q = 20.
3608.4
The power factor is ____ when P = 860 W,
I = 10 A, and V = 120 V.
0.717
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9 - 22
Concept Review
• Phase-shifted circuits produce two
positive and two negative power pulses.
• In pure reactance circuits the negative
and positive pulses are equal.
• Wattmeters measure true power.
• Apparent power ignores angle theta.
• Power factor = power  apparent power.
Repeat Segment
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9 - 23
REVIEW
• Phase Shift
• True Power
• Apparent Power
• Angle Theta
• Power Factor
McGraw-Hill
© 2013 The McGraw-Hill Companies Inc. All rights reserved.