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REVIEW OF FUNDAMENTALS OF ELECTRICITY WITH TELECOMMUNICATION APPLICATIONS
A.8.3
Calculating Impedance
When we calculate impedance (
Z), we must take into account resistance. All circuits are
resistive, even though in some cases there is only a minuscule amount of resistance. We
first examine the two reactive possibilities; that is, a circuit with inductive reactance and
then a circuit with capacitive reactance. For the case with inductive reactance, we have
Z = (R
2
+ X
2
L
)
1
/2
.
(A.35a)
Substituting, we obtain
Z = [R
2
+ (2fL)
2
]
1
/2
.
(A.35b)
For the case with capacitive reactance, we have
Z = (R
2
+ X
2
C
)
1
/2
.
(A.36a)
Substituting, we obtain
Z = [R
2
+ (1,000,000/2f C)
2
]
1
/2
.
(A.36b)
We can also state the impedance:
Z = (R
2
+ X
2
).
Substituting, we obtain
Z = [R
2
+ (2f L - 1,000,000/2f C)
2
]
1
/2
.
(A.37)
Example. Figure A.24 illustrates a simple ac circuit consisting of resistance
(100 ),
capacitance (2
.16 µF), and inductance (400 mH) in series. The frequency is 1020 Hz and
Figure A.24
A simple ac circuit with resistance, capacitance, and inductance in series.
Summary :
(A.35b) For the case with capacitive reactance, we have Z = (R 2 + X 2 C ) 1 /2 . Substituting, we obtain Z = [R 2 + (2f L - 1,000,000/2f C) 2 ] 1 /2 .
Tags :
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