§ 7-7 Impedance
We define the ratio of the phasor voltage
to the phasor current as impedance.
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I
V
Z
RZR
I
V
orIRVR ???? ?
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:
LjXLjZLj
I
V
orILjVL ????? ?
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CjXCjCjZCj
I
V
orI
Cj
VC ??????? ?
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1111
:
)CX( C ?1??
)LX( L ??
Impedance may be combined in series and parallel by the
same rules we have already established for resistance.
4?RZ
5jZ L ?
2jZ C ??
????????? ?9.36534254 jjjZ eq
2jZ C ??
????????? 33.331025 )2(5 jjjj jjZZ ZZZ
CL
CL
eq
s/110 3??
mH5?4 F?500
mH5
F?500
s/110 3??
5jZ L ?
Example:
?????? ZZjXRZ
Rectangular form Polar form
Z
R
C
L
XXX CL
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1
??
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R--resistance
X--reactance
am pl i t u dei m pe da n c eXRZ ???? 22
a n g l ei m p e d a n c eRX ??? ? 1t a n?
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r es i s t i ve
ca p a ci t i ve
i n d u ct i v e
0
0
0
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Example,Find i,Solution:
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211
211
51
.k.k.jk
kjkkj
)kjk(kj
k.Z eq
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9.1261016
9.362500
9040
3 ????
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eq
s
Z
V
I
Attior )9.363 0 0 0s i n (21016)( 3 ???? ?
Atti )9.1 2 63 0 0 0c o s (21016)( 3 ???? ?