Solving Complex Impedance Calculations: Step-by-Step Guide

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Discussion Overview

The discussion revolves around solving complex impedance calculations, specifically focusing on the conversion between rectangular and polar forms of impedance. Participants seek clarification on the step-by-step process for calculating both the modulus and phase angle of the impedance.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a series of equations from their textbook regarding complex impedance, including both rectangular and polar forms.
  • Participants express confusion about how to derive the phase angle of 60.8 degrees from the given values of resistance and reactance.
  • Another participant explains that the modulus of impedance is calculated using the formula \(\sqrt{R^2 + X_L^2}\) and that the phase angle can be found using \(\tan^{-1}(X_L/R)\).
  • Some participants inquire about the meaning and calculation of \(\tan^{-1}\), indicating a lack of understanding of the inverse tangent function.
  • There are requests for step-by-step examples to clarify the calculations involved.
  • One participant questions whether others have studied trigonometry, suggesting a potential gap in foundational knowledge related to the topic.

Areas of Agreement / Disagreement

Participants generally agree on the formulas for calculating impedance but express differing levels of understanding regarding the application of these formulas, particularly concerning the phase angle calculation. The discussion remains unresolved as participants seek further clarification and examples.

Contextual Notes

Some participants appear to lack familiarity with trigonometric functions, which may affect their ability to follow the calculations presented. There is also uncertainty about the specific steps required to arrive at the correct phase angle.

Who May Find This Useful

This discussion may be useful for students studying electrical engineering or physics, particularly those grappling with complex impedance and trigonometric functions.

maddyfan811
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I have trouble figuring out how my textbook came up with the totals and am looking for step by step help. Here is what the text shows.

Z = R + j0 = R = 56 Ohm (in rectangular form [XL = 0])
Z = R < 0 degrees = 56 < 0 degrees Ohm (in polar form)

Z = 0 + jXL = j100 Ohm (in rectangular form [R = 0])
Z = XL < 90 degrees = 100 < 90 degrees Ohm (in polar form)

Z = R + jXL = 56 Ohm + j100 Ohm

Z = square root(R^2 + X^2L)<tan^-1(100 Ohm/56 Ohm) = 115<60.8 degrees Ohm

I think I figured out how to get the first number 115 but I'm having trouble on how the 60.8 degrees was determined. But a step by step explanation on how to get both numbers would be really helpful.
 
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maddyfan811 said:
I have trouble figuring out how my textbook came up with the totals and am looking for step by step help. Here is what the text shows.

Z = R + j0 = R = 56 Ohm (in rectangular form [XL = 0])
Z = R < 0 degrees = 56 < 0 degrees Ohm (in polar form)

Z = 0 + jXL = j100 Ohm (in rectangular form [R = 0])
Z = XL < 90 degrees = 100 < 90 degrees Ohm (in polar form)

Z = R + jXL = 56 Ohm + j100 Ohm

Z = square root(R^2 + X^2L)<tan^-1(100 Ohm/56 Ohm) = 115<60.8 degrees Ohm

I think I figured out how to get the first number 115 but I'm having trouble on how the 60.8 degrees was determined. But a step by step explanation on how to get both numbers would be really helpful.

R and jXL form the orthogonal sides of a rectangle triangle. Z is the hypotenuse. It's modulus is [tex]\sqrt{R^2 + X_L^2}[/tex] and the phase is the angle between the hypotenuse and the side R: [tex]tan^{-1}\frac{X_L}{R}[/tex]
 
I think I figured out where I went wrong. I know I need to divide XL/R and then multiply it by tan^-1. Only problem is I don't know what tan^-1 is. What does tan^-1 equal?
 
maddyfan811 said:
I think I figured out where I went wrong. I know I need to divide XL/R and then multiply it by tan^-1. Only problem is I don't know what tan^-1 is. What does tan^-1 equal?

You don't have to multiply for anything. [tex]tan^{-1}[/tex] is the trigonometric function inverse of the tangent. It means the arc whose tangent is...
 
I'm sorry I don't understand. Can you give a step by step example?
 
Have you ever studied trigonometry? Are you familiar with the functions sine, cosine and tangent?
 

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