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Exercise:
A resistor is connected in series to a capacitor and an inductor in parallel. Derive the formal expressions impedance and phase shift. Visualize how the impedance and the phase shift dep on the angular frequency. center includegraphicswidthcm#image_path:r-lc-# center

Solution:
Using the complex reactances for the inductor and the capacitor the complex impedance can be calculated as follows: tildeZ R + leftfractilde X_L + fractilde X_C right^- R + leftfracj omega L + j omega C right^- R + leftfrac+j^ omega^ L Cj omega L right^- R + fracj omega L - omega^ L C The impedance corresponds to the modulus: Z abstilde Z sqrtR^ + fracomega ^ L^left-omega^ L Cright^ The phase shift is given by the argument: tanDeltaphi argtilde Z fracomega LR -omega^ L Cd The graphs for Zomega and Deltaphiomega are displayed below. center includegraphicswidthcm#image_path:r-lc-impedanc# center center includegraphicswidthcm#image_path:r-lc-phasshift-# center
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Exercise:
A resistor is connected in series to a capacitor and an inductor in parallel. Derive the formal expressions impedance and phase shift. Visualize how the impedance and the phase shift dep on the angular frequency. center includegraphicswidthcm#image_path:r-lc-# center

Solution:
Using the complex reactances for the inductor and the capacitor the complex impedance can be calculated as follows: tildeZ R + leftfractilde X_L + fractilde X_C right^- R + leftfracj omega L + j omega C right^- R + leftfrac+j^ omega^ L Cj omega L right^- R + fracj omega L - omega^ L C The impedance corresponds to the modulus: Z abstilde Z sqrtR^ + fracomega ^ L^left-omega^ L Cright^ The phase shift is given by the argument: tanDeltaphi argtilde Z fracomega LR -omega^ L Cd The graphs for Zomega and Deltaphiomega are displayed below. center includegraphicswidthcm#image_path:r-lc-impedanc# center center includegraphicswidthcm#image_path:r-lc-phasshift-# center
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Attributes & Decorations
Branches
Electrodynamics
Tags
ac circuit, complex impedance, impedance, phaseshift
Content image
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration