Optimizing Accuracy: Complex Number Calculations for RL Circuit

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Discussion Overview

The discussion revolves around the accuracy of calculation methods for complex numbers in the context of RL circuits. Participants explore whether converting complex numbers to polar form before calculations or performing calculations in rectangular form until the final result is more accurate. The scope includes mathematical reasoning and homework-related inquiries.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant questions the accuracy of different calculation methods for complex numbers, specifically whether to convert to polar form first or to calculate in rectangular form until the end.
  • Another participant argues that both methods can achieve the desired accuracy if sufficient significant figures are maintained, suggesting that neither method is inherently more accurate.
  • A different participant notes that converting to polar form increases the number of steps in calculations, which may introduce more opportunities for error, especially given the precision of the initial values.
  • One participant emphasizes that calculations in rectangular form can be exact when using whole numbers, but acknowledges that practical scenarios often involve uncertainties in values.
  • There is a caution raised about angle conversions, highlighting that they can amplify small errors and recommending that more digits be kept in intermediate angle values to avoid significant rounding errors.

Areas of Agreement / Disagreement

Participants express differing views on the accuracy of calculation methods, with no consensus reached on which method is superior. The discussion remains unresolved regarding the best approach for optimizing accuracy in complex number calculations.

Contextual Notes

Participants note that the precision of initial values and the presence of uncertainties in practical work can affect the accuracy of results. There is also mention of the non-linear nature of angle conversions, which may complicate calculations.

shaltera
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Homework Statement


Calculate
Z1=5+j10
Z2=10+j8
Z3=10+J5
RL=40
V=100

VTH=VX(Z2/Z1+Z2)
ZTH=Z3+(Z1Z2/Z1+Z2)
I=VTH/(ZTH+RL)

IL=?

Homework Equations


My question is what calculation method is more accurate:

First to convert complex numbers in polar forms, and then calculate or calculate complex number until final result and then convert in polar form?

The Attempt at a Solution

 
Last edited by a moderator:
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You carry along sufficient significant figures so that either gives the answer to the desired accuracy. So neither can be said to be "more accurate".
 
Ya got a little happy with the HW template.
 
I removed the additional copies of the homework template.

As you have to add complex numbers, I would not convert them to polar form. This increases the number of steps a lot, probably also increasing the error. I would not worry about that, however, your initial values are given with a precision of 2-3 digits, every reasonable system will calculate that with much more than 3 digits precision.
 
Staying in rectangular form it's possible to carry through the calculations exactly when the given values are all expressed with whole numbers. Here, for example, ##I_L = \frac{12176}{13121} - j\frac{4888}{13121}##.

For practical work, though, this rarely happens, and in general all values have some uncertainty associated with them. Keep enough guard digits in all intermediate values though the calculation so that rounding and truncation doesn't introduce errors larger than your uncertainties!

Angle conversions, in particular can be troublesome since the conversions are not linear functions: plot the tan and arctan functions and see. In some parts of the curves small errors can be magnified while in other places the conversion is practically insensitive to small changes in the function argument. My advice is to keep more digits in angles than you think is necessary and never round intermediate angle values. Round only for final result presentation.
 

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