Lecture March 23
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Transcript of Lecture March 23
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8/9/2019 Lecture March 23
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51 ectr c rcu ts nter 1
Instructor: Dr. Karthi Umapathy
1EES 512, Winter 2010, KU
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Previous Lecture
- Series and Parallel - C and L
- AC circuits
- Generation of AC voltage
- Parameters of AC waveforms
- Phasor representation
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EES 512, Winter 2010, KU 2
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AC Waveforms
T
Amplitude = mV
Phase Shift 1
Angular Freq. =
Period = T
zT Frequency = 1/T
EES 512, Winter 2010, KU 3
12 21
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Phasor representation
mm ttv cos
(Time domain) (Phasor or frequency domain)
tjte
sincos
jtjVeVetv VVRe
Eulers Identity
mm
j Im 1
T
TTTT
t ,3
,,,0
A rotating phasor
1-1Re
424
EES 512, Winter 2010, KU 4- j
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Phasor representation
mm VtVtv V)cos()(
t,, mmeev
Phasor diagram
mag nary x s
V
m
II Real Axis
mLeadingdirection
mI
Laggingdirection
EES 512, Winter 2010, KU 5I
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Examples
Express these sinusoids as phasors:
a v t = 7 cos 2t + 40 V
b) i(t) = - 4 sin ( 10t + 10) A
EES 512, Winter 2010, KU 6
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EES 512, Winter 2010, KU 7
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Find the sinusoids corres ondin to these hasors:
a V = -10 30 V
b) I = j(5 j12) A
EES 512, Winter 2010, KU 8
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EES 512, Winter 2010, KU 9
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Phasor relationship for circuit elementsResistor Inductor Capacitor
EES 512, Winter 2010, KU 10
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Phasor relationship for circuit elements
Summary of voltage-current relationship
emen
R
L diLv IV L
C dvCi
IV
dvVj
EES 512, Winter 2010, KU 11vdt jV
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Examples:
EES 512, Winter 2010, KU 12
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EES 512, Winter 2010, KU 14
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EES 512, Winter 2010, KU 15
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Impedance and Admittance
Resistor Inductor Capacitor
IV R IV LjC
Vj
I
CjLjR
1,,
IV
IV
IV
V I
,Impedance
Im edance of a circuit is the ratio of the hasor volta e V and the hasor
EES 512, Winter 2010, KU 16
current I, measure in Ohms
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1Y
Admittance of a circuit is the reciprocal of Impedance
Impedances and admittances of passive elements
Element Im edance Admittance
R 1
YRZ
L
L
1YLjZ
CCjY
C
1Z
EES 512, Winter 2010, KU 17
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j
LR
1
,,
VVV
CCj III
V,
I
1
CCL
,
Inductive Capacitiveeactance eactance
ZZ jXR)( InductiveXvejXR Z
)( CL XXjR ZZ
EES 512, Winter 2010, KU 18)
1
( CLjR Z
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ZZ jXR
R
XXR
122tan,
Z
s n,cos
Admittance
V
I
Z
1Y jBG Y
Susceptance2222
,XR
XB
XR
RG
EES 512, Winter 2010, KU 19
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Series and Parallel Impedances
Volta eDivision
ZZZZ .... VZ
VVZ
V 21 eq ZZZZ 2121
Current
1....
111 ZZ 12
EES 512, Winter 2010, KU 20
N21eq ZZ,
ZZ 212
21
1
N21eq YYYY ....