Transcript Document

Chapter
23
Alternating Current Circuits
Topics Covered in Chapter 23
23-1: AC Circuits with Resistance but No Reactance
23-2: Circuits with XL Alone
23-3: Circuits with XC Alone
23-4: Opposite Reactances Cancel
23-5: Series Reactance and Resistance
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
Topics Covered in Chapter 23
 23-6: Parallel Reactance and Resistance
 23-7: Series-Parallel Reactance and Resistance
 23-8: Real Power
 23-9: AC Meters
 23-10: Wattmeters
 23-11: Summary of Types of Ohms in AC Circuits
 23-12: Summary of Types of Phasors in AC Circuits
McGraw-Hill
© 2007 The McGraw-Hill Companies, Inc. All rights reserved.
23-1: AC Circuits with Resistance
but No Reactance
Fig. 23-1
 In this figure, combinations of series and parallel resistances are shown.
 All voltages and currents throughout the resistive circuits are in phase.
 There is no reactance to cause a lead or lag in either current or voltage.
23-2: Circuits with XL Alone
Fig. 23-2
 A series inductive circuit is shown in Fig. 23-2.
The ohms of XL are just as effective as ohms of R in limiting the current or
producing a voltage drop.
 XL has a phasor quantity with a 90° phase angle.
23-2: Circuits with XL Alone

Fig. 23-3
 A parallel inductive circuit is shown in Fig. 23-3.
 The ohms of XL are just as effective as ohms of R in limiting the current
or producing a voltage drop.
 XL has a phasor quantity with a 90° phase angle.
23-3: Circuits with XC Alone
Fig. 23-4
Series XC
 Capacitive reactances are shown in Fig. 23-4
 Since there is no R or XL, the series ohms of XC can be combined directly.
23-3: Circuits with XC Alone
Fig. 23-5
Parallel XC
 Capacitive reactances are shown in Fig. 23-5.
 Since there is no R or XL, parallel IC currents can be added.
23-3: Circuits with XC Alone
XC and XL are phasor opposites.
R
XL
XC
R
When analyzing series circuits:
Opposite reactances in series must be subtracted.
 If XL is larger, the net reactance is inductive.
 If XC is larger, the net reactance is capacitive.
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23-4: Opposite Reactances Cancel
 In a circuit with both XL and XC, the opposite phase
angles enable one to offset the effect of the other.
 For XL and XC in series, the net reactance is the
difference between the two series reactances.
 In parallel circuits, the net reactive current is the
difference between the IL and IC branch currents.
23-4: Opposite Reactances Cancel
Fig. 23-6:
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23-4: Opposite Reactances Cancel
Fig. 23-7:
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23-5: Series Reactance
and Resistance
 The resistive and reactive effects of series reactance




and resistance must be combined by phasors.
For series circuits, all the ohms of opposition are
added to find ZT.
First, add all series resistances for one total R.
Combine all series reactances, adding all XLs and all
XCs and finding X by subtraction.
The total R and net X can be added by phasors to find
the total ohms of opposition in the entire series circuit.
23-5: Series Reactance
and Resistance
Magnitude of ZT
 After the total R and net reactance X are found, they
can be combined by the formula
ZT =
R2 + X2
23-6: Parallel Reactance
and Resistance
 In parallel circuits, the branch currents for resistance
and reactance are added by phasors.
 Then the total line current is found by
IT =
IR2 + IX2
23-6: Parallel Reactance
and Resistance
Parallel IC and IL are phasor opposites.
IC
IR
IR
IL
 Opposite currents in parallel branches are subtracted.
 If IL is larger, the circuit is inductive.
 If IC is larger, the circuit is capacitive.
23-6: Parallel Reactance
and Resistance
Parallel RCL Circuit Analysis
VA = 120
R = 30 Ω
XC = 60 Ω
XL = 24 Ω
IT = 5 A
IT = IR2 + IX2 = 42 + 32 = 5A
2A
4A
The circuit
is inductive.
5A
4A
3A
IT = 5 A
23-6: Parallel Reactance
and Resistance
Parallel RCL Circuit Impedance
R = 30 W
VA = 120
XC = 60 W
XL = 24 W
IT = 5 A
4A
ZEQ =
3A
IT = 5 A
VA
IT
=
120
5
= 24 Ω
23-6: Parallel Reactance
and Resistance
Parallel RCL Circuit Phase Angle
VA = 120
R = 30 W
XC = 60 W
XL = 24 W
IT = 5 A
Θ=
Tan-1
−
IX
=
Tan−1
−
IR
−37°
3A
3
4
4A
IT = 5 A
= −37°
23-7: Series-Parallel Reactance
and Resistance
Figure 23-12 shows how
a series-parallel circuit
can be reduced to a
series circuit with just
one reactance and one
resistance.
The triangle diagram in
(d) shows total
impedance Z (141 Ω).
Fig. 23-12:
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23-7: Series-Parallel Reactance
and Resistance
Waveforms and Phasors for a Series RCL Circuit
Θ = 0
VR
I
L
Θ = −90
I
VR
R
C
I
VC
VC
VL
Θ = 90
VL
I
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23-7: Series-Parallel Reactance
and Resistance
Series RCL Circuit Analysis
R=4W
4A
20 V
XC = 12 W
L
XL = 9 W
Z=
R
XNET
3W
The net reactance is 3 W, capacitive.
R2 + X2 =
42 + 32 = 5Ω
4W
Z=5W
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I=
V
Z
=
20
5
=4A
23-7: Series-Parallel Reactance
and Resistance
Series RCL Circuit Phase Angle
I
20 V
L
XL = 9 W
ΘZ= Tan-1 −
XNET
3W
R
−37°
4W
5W
R=4W
Z = 5Ω
XC = 12 W
ΘZ= Tan-1 ± X / R
The net reactance is 3 W, capacitive.
X
= Tan−1 −
R
3
= −37
4
Note: Since the circuit is capacitive,
the source voltage lags the source
current by 37 degrees.
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23-7: Series-Parallel Reactance
and Resistance
Series RCL Voltage Drops
20 V
4A
L
R=4Ω
VR = IR = 4 × 4 = 16 V
XC = 12 Ω
VC = IXC = 4 × 12 = 48 V
VL = IXL = 4 × 9 = 36 V
XL = 9 Ω
VC and VL are phasor opposites, so the net reactive
voltage is the difference between the two or 12 V.
R
16 V
XNET
12 V
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VT = 162 + 122 = 20 V
23-8: Real Power
 In an ac circuit with reactance, the current I supplied
by the generator either leads or lags the generator
voltage V.
 The product VI is not the real power produced by the
generator, since the instantaneous voltage may have
a high value while at the same time the current is near
zero, or vice versa.
23-8: Real Power
 The real power in watts can always be calculated as
I2R, where R is the total resistive component of the
circuit.
 To find the corresponding value of power as VI, this
product must be multiplied by the cosine of the phase
angle Θ. Then
Real power = P = I2R
or
Real power = P = VI cos Θ
23-8: Real Power
Series RCL Circuit Power Dissipation
R=4W
4A
20 V
XC = 12 W
L
XL = 9 W
Note: the power dissipation is zero in
ideal capacitors and ideal inductors.
All of the dissipation takes place in
the circuit’s resistance.
P = V × I × Cos Θ = 20 × 4 × 0.8 = 64 W
P = I2R = 42× 4 = 64 W
−37
4A
20 V
The source voltage and source current are not in
phase and the true power is not equal to VI. It is
equal to VI × power factor.
23-8: Real Power
Parallel RCL Circuit Power Dissipation
VA = 120
R = 30 W
XC = 60 W
XL = 24 W
IT = 5 A
P = V × I × Cos Θ = 120 × 5 × 0.8 = 480 W
P=
−37°
3A
4A
IT = 5 A
V2
R
=
1202
30
= 480 W
The source voltage and source current are not in
phase and the true power is not equal to VI. It is
equal to VI × power factor.
23-9: AC Meters
 An ac meter must produce deflection of the meter
pointer up-scale regardless of polarity.
 This deflection is accomplished by one of the following
methods for nonelectronic ac meters.
 Thermal type
 Electromagnetic type
 Rectifier type
 All analog ac meters (meters with scales and pointers)
have scales calibrated in rms values, unless noted
otherwise on the meter.
23-10: Wattmeters
 The wattmeter shown in Fig.
23-14, uses fixed coils to
measure current in a circuit,
and the moving coil measures
voltage.
 The deflection is proportional
to power.
 Either dc power or real ac
power can be read directly by
the wattmeter.
Fig. 23-14:
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23-11: Summary of Types of
Ohms in AC Circuits
 Ohms of opposition limit the amount of current in dc




circuits or ac circuits.
Resistance is the same for either case.
Ac circuits can have ohms of reactance because of
the variations in alternating current or voltage.
Reactance XL is the reactance of an inductor with
sine-wave changes in current.
Reactance XC is the reactance of a capacitor with
sine-wave changes in voltage.
23-12: Summary of Types of
Phasors in AC Circuits
Fig. 23-15
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