AC Circuit Analysis- Find Impedance

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SUMMARY

The discussion focuses on AC circuit analysis, specifically finding impedance using voltage division and phasors. The participant suggests that starting with the impedance formula Z = R + jX complicates the problem by introducing unnecessary variables. Instead, they recommend using Nodal Analysis to derive the impedance more efficiently, leveraging the given output voltage (V_o) to simplify calculations. The approach emphasizes breaking down complex impedance into its real (R) and imaginary (X) components for clarity.

PREREQUISITES
  • Understanding of AC circuit analysis principles
  • Familiarity with phasor representation of voltages and currents
  • Knowledge of Nodal Analysis techniques
  • Ability to manipulate complex numbers in electrical engineering contexts
NEXT STEPS
  • Study Nodal Analysis in-depth for AC circuits
  • Learn about complex impedance and its applications in circuit design
  • Explore voltage division in AC circuits with phasors
  • Review techniques for converting between rectangular and polar forms of complex numbers
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Electrical engineering students, circuit designers, and professionals involved in AC circuit analysis and impedance calculations.

Valour549
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Homework Statement



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2. The attempt at a solution

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Am I doing something wrong? I know it's just voltage division with AC phasors and we have to equate the real parts and imaginary parts to find the unknown, but I feel like the question shouldn't be this hard.
 

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How you feel is usually irrelevant. Are you satisfied with the answer? Did you check all your work?
 
I think you're making it more difficult than it has to be by starting with Z = R + jX, which essentially doubles the number of variables to deal with.

Instead, I would suggest writing Nodal Analysis equations and solving for Z.

upload_2018-3-28_20-21-0.png


Since ##V_o## is already given, you can take advantage of that as that node is "solved" already.

Once you have complex Z you can split it into its R and X components.
 

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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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