AC Circuit Analysis (Nodal RMS)

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Discussion Overview

The discussion revolves around the use of RMS (Root Mean Square) versus peak values in nodal analysis for AC circuit analysis. Participants explore whether using peak voltage and current would yield similar results to using RMS values, particularly in the context of calculating power.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the validity of using Vpeak and Ipeak instead of Vrms and Irms for nodal analysis, specifically asking if dividing Va(peak) by sqrt(2) would yield Va(rms).
  • Another participant asserts that using peak or average values is acceptable as long as the results are converted back to RMS when necessary, particularly for power calculations, provided the sources are sinusoidal and the circuit is linear.
  • A third participant confirms the relationship V = √2Vrms, suggesting that either method would lead to correct answers.
  • A later reply reflects on a previous attempt using V_max that did not match the expected answers, indicating a mistake was made in that calculation, and expresses satisfaction with the resolution of the confusion.

Areas of Agreement / Disagreement

Participants generally agree that both RMS and peak values can be used in the analysis, provided that conversions are made appropriately. However, there is no consensus on the specific reasons for discrepancies in earlier calculations.

Contextual Notes

The discussion does not resolve the specific mathematical errors encountered by the participant who initially used V_max, leaving the exact nature of those errors unclear.

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Homework Statement


The question is:
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The given answer is:
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Homework Equations


The Attempt at a Solution


I already got the "correct" answers.
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My question is, I used Vrms voltage and Irms current to solve the nodal analysis. Would it be incorrect to use Vpeak and Ipeam to solve the circuit. Would it yield a similar result? I mean, would I be able to divide Va(peak) by sqrt(2) and get Va(rms)?

I understand that the author's intent was to use Vrms and Irms since the second part of the question requires to calculate Power, which is usually done using RMS values to avoid dividing by 2.
 
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Sure, you can use peak or average or any other scaled version of the voltages and currents so long as you "revert" to rms when required (such as determining average power). This works so long as all the sources are sinusoidal and the circuit is linear.
 
Yes, V =√2Vrms for all your voltages so either way you'd get the right answers.

In general, the phasor for V0sin(ωt + θ) is [V0/√2]e.
 
The reason why I asked this question was when I originally did the question with V_max, it did not match the given answers (even after dividing by sqrt(2) to the given rms). I knew it did not make since I was just multiplying all the currents by a factor. When I did the question again using V_max, it turned out that I had originally made a mistake some where. Math makes sense and the universe is in order!
The algebra gets tedious when solving systems of linear equation with complex values.

Thank you both for the confirmation.
 

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