Calculating Impedance and Drawing a Basic Phasor Diagram

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SUMMARY

This discussion focuses on calculating impedance and drawing a basic phasor diagram in electrical engineering. The user successfully completed part a by expressing the reactance of the capacitor in the form a+jb but needed clarification on plotting reciprocal reactances in part b. For part c, the user struggled with rearranging the equation to the form a+ib before calculating the magnitude. Key corrections include ensuring units are included and properly handling complex numbers.

PREREQUISITES
  • Understanding of complex numbers and their representation in electrical engineering.
  • Familiarity with impedance calculations, specifically reactance of capacitors and resistors.
  • Knowledge of phasor diagrams and their construction on the complex plane.
  • Ability to manipulate equations in the form a+ib for magnitude calculations.
NEXT STEPS
  • Learn how to express reactance in the form a+jb for various circuit components.
  • Study the principles of phasor diagrams and how to plot them accurately.
  • Research the concept of reciprocal reactances and their implications in circuit analysis.
  • Practice calculating magnitudes of complex numbers using the formula sqrt(a^2+b^2).
USEFUL FOR

Students and professionals in electrical engineering, particularly those studying circuit analysis and phasor representation of impedances.

maherelharake
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Homework Statement


I have attached the problem and all my work. If someone can check my work for part a, that would be great. As far as part b, I need the most help here. Finally for part c, I think my work so far is correct, but I need help to graph it. Thank you in advance.


Homework Equations





The Attempt at a Solution

 

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The numbers for part a) look correct, though you should express the reactance of the capacitor in the form a+jb by multiplying top and bottom by j. Also, don't forget units (ohms).

The phasor diagram is straightforward, simply plot the three reactances as vectors on the complex plane.

For part c), you have made an error on the fourth line of working (taking magnitudes). You cannot take the magnitude of each individual term on the RHS as you have done. You need to rearrange the RHS in the form a+ib first, then take the magnitude as sqrt(a^2+b^2).

Claude.
 
Ok I think I took care of part a.

As far as b, it says to plot the reciprocal reactances. Does that mean that the Resistor Reactance is along the x-axis (Real axis) and the other two are plotted along the y axes (imaginary axis)?

For c, I am struggling to get it in that form. For the form a+ib, I can't collect the imaginary terms and get it in that form. Any pointers?

Thanks again.
 

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