AC Circuits: Phasors/Polar to rectangular transformation

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Discussion Overview

The discussion revolves around the conversion between polar and rectangular forms in AC circuits, specifically focusing on phasors. Participants explore methods for transforming complex numbers and multiplying them, as well as addressing difficulties encountered in these processes.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about converting a sum of phasors from rectangular to polar form, noting their own calculation and seeking clarification on the process.
  • Another participant provides a formula for calculating the magnitude and angle of a complex number, suggesting the use of a phasor diagram for better understanding.
  • Participants discuss the multiplication of complex numbers, with one suggesting the FOIL method and another providing a detailed breakdown of the multiplication process, including the treatment of the imaginary unit.
  • There is mention of calculators that can assist in converting between forms, indicating that some participants may prefer computational tools over manual calculations.

Areas of Agreement / Disagreement

Participants generally agree on the methods for converting between forms and multiplying complex numbers, but there is no consensus on the best approach to tackle these problems, as different methods are proposed and discussed.

Contextual Notes

Some participants rely on specific formulas and methods without fully addressing the assumptions behind them, such as the conditions under which certain techniques are applicable. There is also a lack of clarity on the effectiveness of the FOIL method in all cases of complex multiplication.

Who May Find This Useful

This discussion may be useful for students learning about AC circuits, phasors, and complex number operations, particularly those seeking help with homework or conceptual understanding in these areas.

sgonzalez90
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40<50degrees + 20<-30 degrees,
I get how to convert to rectangular,

I got 43.03 + j20.64, but converting it back to polar... how exactly do you do so? The answer is 47.72<25.63degrees... my book doesn't explain it.

Also with
(2+j4)(3-j5)... how exactly do you tackle this sort of problem? I tried the FOIL method and it didn't exactly work.


Thank you!
 
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Homework Statement



40<50degrees + 20<-30 degrees,
I get how to convert to rectangular,

I got 43.03 + j20.64, but converting it back to polar... how exactly do you do so? The answer is 47.72<25.63degrees... my book doesn't explain it.

Also with
(2+j4)(3-j5)... how exactly do you tackle this sort of problem? I tried the FOIL method and it didn't exactly work.


Thank you!
 
Length: |I|= sqrt(Re2+Im2)

sqrt(432+212)=48

Angle: < = arctan (Im/Re)

arctan (21/43) = 26 (deg)

Draw a phasor diagram and you see it easily. Simple geo/trig.

Part 2:
Either convert to polar form and multiply the length and add the angles, or just multiply out the two parenthesis inn a normal fashion. Remember j*j=-1
 
Rectangular \rightarrow Polar

x + jy \rightarrow \sqrt{x^{2} + y^{2}} \angle tan^{-1}(\frac{y}{x})

There are a lot of calculators which can do this for you too!


(2+j4)(3-j5) ... FOIL is the way, expand the brackets first

2*3 + 2*-j5 + j4*3 + j4*-j5 ... simplify

6 - 10j + 12j - 20j*j ... keep in mind j = \sqrt{-1}, so j^{2} = -1

6 +2j + 20

26 + 2j
 

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