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51
Vp
Ip
t
Vp
Ip
t
Vp
Ip
t
Resistor Capacitor Inductor
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Impedance
52
Series Parallel
Zeq =Z1+Z2+Z3+…+Zn 1/Z eq =1/Z1+1/Z2+1/Z3+...+1/Zn
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Impedance
53
The impedance, Z, of a circuit relates peakcurrent to peak voltage:
I V
Z p
p
(Units: Ohms)
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Example 4.3.2
54
A practical capacitor can be modeled by an ideal
capacitor in parallel with a resistor. Theresistance represents leakage losses in thecapacitor and is usually quite large. Find theimpedance of a practical capacitor at the radianfrequency ω =377 rad/s (60 Hz). C
1=10 -9 F, R
1=1M Ω
Impedance
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55
Z1=R 1||X C;R1=10 6 XC=1/jωC1=1/(377)(10 -9)=2.65 x 10 6 / jΩ
Z1= Write in polar form:
A= 10 6/√(12+0.377 2)=9.36 x 10 5
θ=tan -1(0.377/1) =-20.66 ° =-0.36 radZ(j377)= 9.36 10 ∠ − 0.36 Ω @
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Example 4.3.3
56
A Voltage Source V=100 ∠0° is supplied to 3
impedances in series; Z 1=5 ∠53° , Z 2=3 ∠90° ,Z3=1∠ − 90° .
Calculate Z eq , currents supplied and voltage at Z 2
element.
Impedance
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Example 4.3.4
58
A parallel circuit of several circuit elements contain
Z1=5.6 ∠30° , Z2=2.2 ∠ − 20° , Z3=3.3 ∠45° withV=120 V. Calculate Zeq and currents.
Impedance
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59
Zeq=(1/z1+1/z2+1/z3) -1
Zeq=[(1/5.6 ∠30°)+(1/2.2 ∠ − 20° )+(1/3.3 ∠45°)]-1
Zeq=[(0.18 ∠ − 30°) + (0.45 ∠20°)+(0.3 ∠ − 45° )]-1
Zeq=[(0.16-0.09j)+(0.42+0.15j)+(0.21-0.21j)] -1
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