§ 8-3 Phasor diagrams
The phasor diagram is a name given to a sketch in
the complex plane of the phasor voltages and currents
throughout a specific circuit.
VjV ?1.5310861 ?????
VjV ?1.535432 ??????
VjVV ?2485.94921 ????? ??
VjVVVV ?764.12123)( 2121 ???????? ????
j?
1?
21
?? ?VV
2
?V
1
?V
21
?? ?VV
The series RLC circuit--The phasor diagram is constructed most
easily by employing the single current as the reference phasor.
?? ? IRV R
?? ? ILjV
L ?
?? ?? I
CjV C ?
1
CV?sV
?
?
?I
RV?
LV?
?I
RV?
LV?
CV?sV?
?
XV?
CLRs VVVV ???? ??? CLX VVV
??? ??XRs VVV ??? ??
The parallel circuit--employing the voltage as the reference
phasor.
RI?
LI?
CI?
sI?
?V
AI R 2.05/1 ???
AjjI L 25.04/1 ????
AjjI C 1.0)10/(1 ????
A
j
jj
IIII CLRs
?
9.3625.0
15.02.0
1.025.02.0
???
??
???
???
????
VVL e t ?01 ???
The first circuit complete response when sinusoidal input.
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t
fnf Aetftftftf
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Aff f ?? ?? )0()0(
)0()0( ?? ?? fffA
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t
ff efftftf
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???? ?? ??????
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m
mm I
LjR
VI
)co s ()( ??? ? ??? tIti mf
CI?
LI? RI?
? 250
1000o V
sI?
H2,0F 8?
xI?
=1000rad/s?
3.04.0
8.0
5.04.0
5.04.0
jIII
jI
jIII
jII
CXS
C
LRX
LR
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??
?
RI
?
LI
?
CI
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XI
??? ??
CXS III
8-15
???? 044V 85 jV ???
843 jV ???
124 842 jj jI ???????
22 ??V 861 jV ???
11 jI ??
???? 044V
85 jV ?? ?
?
3V
22 ??V
861 jV ???
8-16
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1I
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2I
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3I
)co s ()( ??? ? ??? tIti mf RL /??0)0()0( ?? ?? ii
tLR
mm eItIti
??????? )]c o s (0[)c o s ()( ?????
??
tLR
mm eItI
?????? )c o s ()c o s ( ?????
??
2
???
? ??w h e n tItIti mm ??? s i n)2/c o s ()( ????
0?? ?? ?w h en t
L
R
mm eItIti
??? ?c o s)(
tIm ?co s
tLR
meI
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tLR
mm eItIti
??? ?c o s)(
i
2/T T
t
)2( mm Ii ?