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AC Circuit Analysis (Nodal RMS)

  1. Dec 7, 2012 #1
    1. The problem statement, all variables and given/known data
    The question is: wlpXm.png
    The given answer is: kbFkP.png

    2. Relevant equations
    3. The attempt at a solution
    I already got the "correct" answers.
    n1X9Z.png


    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.
     
  2. jcsd
  3. Dec 7, 2012 #2

    gneill

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    Staff: Mentor

    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.
     
  4. Dec 7, 2012 #3

    rude man

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    Homework Helper
    Gold Member

    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.
     
  5. Dec 7, 2012 #4
    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 When I did the question again using V_max, it turned out that I had originally made a mistake some where.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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