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22 Alternating Current
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What is the phase?
Examples: RC & RL circuits
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Phasors & Alternating-Current (AC)
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Root-mean-square (rms)
2
)(
cos)(
02
0
ItII
tItI
rms
avg
Example : Average powerP = I2R
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Resistance and Reactance
)2cos()cos()(
)2cos()(
)(
coscos)()(
cos)(
00
0
00
0
tC
Itt
C
ItV
tLIt
tILtV
tVtRIRtItV
tItI
C
L
RR
RXC
XLX RCL
1
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Reactance & Phase
Low-pass High-pass
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Series R-L-C Circuit: Impedance
reactance) called
Impedance
CL
CL
CL
CL
CLR
XXX
XRXXRZ
XXRI
IXIXIR
VVVV
(
)(
)(
)()(
)(
2222
22
22
22
VL
VR
VC
V
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Series R-L-C Circuit: Phase
VL
VR
VC
V
R
CLR
X
R
XXIR
XXI
V
VV
CL
CL
R
CL
/1tan
)(
tan
1
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Power in AC: Pure Resistor
power) peak of half (one
0000
2
1
22VI
VIVIP rmsrms
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Power in AC: General Case
inductors) pure and capacitors purefor (Zero
factorpower :cos
cos2
1
22cos 00
00
VIVI
VIP rmsrms
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Series Resonance: Frequency
22
2222
1
)(
series C-L-R ain Impedance
CLR
XRXXRZ CL
When XL = XC , Z = Zmin = R, which occurs at
LCCL
110
00
i.e. (resonance frequency)
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Resonance & Tuning
Z
VI
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Summary: Phasor & AC
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Summary: Resistance & Reactance
RXC
XLX RCL
1
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Summary: R-L-C Circuit (series)
LCC
L
CLRXXRZ CL
11
1)(
0
2222
resonance ,R
tan
-1
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Summary: Power in AC
cos2
1cos 00VIVIP rmsrmsavg
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HomeworkProblems: 3, 8, 10, 16, 21, and 22
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P3-Resitance & Reactance
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P 7&8 Voltage & Current in C & L
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P 10-RLC in Series
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P 16-Power in AC
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P 21&22-Series Resonance
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Schedule (MWF)
WednesdayMar 3
FridayMar 5
MondayMar 8
WednesdayMar 10
FridayMar 12
Review Test 2
Lab DemoRC-const
Test 2Ch19~21
Lab MidtermLabs done so far
LabInduction
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Schedule (ThTr)
ThursdayMarch 4
TuesdayMarch 9
ThursdayMarch 11
Review T2Test 2
Lab DemoRC-const
Test 2Ch19~21
Lab MidtermLabs done so far
LabInduction