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https://texercises.raemilab.ch/exercise/maximum-and-asymptotic-behaviour-of-parallel-impedance/
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Exercise:
Qualitatively graph the impedance for an ac circuit with a resistor resistance R a capacitor capacitance C and a coil inductance L in parallel. Discuss the maximum and the asymptotic behaviour.

Solution:
The impedance is given by Zomega fracsqrtfracR^+leftfracomega L-omega Cright^ The expression reaches the maximum value when the expression in parenthesis is equal to zero i.e. for an angular frequency omega_ with fracomega_ L omega_ C omega_ fracsqrtL C The impedance at omega_ is sscZmax Zomega_ fracsqrtfracR^ R For omegato the term with the inductance ist the dominant term: Zomega &propto fracsqrtfracleftomega Lright^ omega L quad textrmfor omegato For omegato infty the term with the capacitance ist the dominant term: Zomega &propto fracsqrtleftomega Cright^ fracomega C quad textrmfor omegato infty A typical graph for two different values of R is displayed in the figure below. center includegraphicswidthtextwidth#image_path:parallel-impedance# center
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Exercise:
Qualitatively graph the impedance for an ac circuit with a resistor resistance R a capacitor capacitance C and a coil inductance L in parallel. Discuss the maximum and the asymptotic behaviour.

Solution:
The impedance is given by Zomega fracsqrtfracR^+leftfracomega L-omega Cright^ The expression reaches the maximum value when the expression in parenthesis is equal to zero i.e. for an angular frequency omega_ with fracomega_ L omega_ C omega_ fracsqrtL C The impedance at omega_ is sscZmax Zomega_ fracsqrtfracR^ R For omegato the term with the inductance ist the dominant term: Zomega &propto fracsqrtfracleftomega Lright^ omega L quad textrmfor omegato For omegato infty the term with the capacitance ist the dominant term: Zomega &propto fracsqrtleftomega Cright^ fracomega C quad textrmfor omegato infty A typical graph for two different values of R is displayed in the figure below. center includegraphicswidthtextwidth#image_path:parallel-impedance# center
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Attributes & Decorations
Branches
Circuits
Tags
ac circuit, impedance
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Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Descriptive / Quality
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