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What is the variable theta of omega in a series RL cct?

  1. May 20, 2013 #1
    What is the variable "theta of omega" in a series RL cct?

    1. The problem statement, all variables and given/known data

    Hi

    I'm not looking for a complete solution to this problem. My question concerns just one specific part of the solution to part A:
    why is tan θ(ω) = ωL/R?

    and what θ(ω) represent? how does it relate to the current? I took the introductory EC course almost two years ago so I need a refresher. Which section should I review? (I am using Electric Circuits 9ed by Nilsson)

    I was able to complete the entirety of part A except for that part.

    Also, is it true that tan [-θ(ω)+90°] = R/Lω? If so, then my answer is correct because I got that answer, but in cosine form. So the +90 would validate my answer.

    2. Relevant equations
    PROBLEM
    13_35.jpg

    13_35_2.jpg
    SOLUTION
    13_35_S.jpg

    3. The attempt at a solution
     
    Last edited: May 20, 2013
  2. jcsd
  3. May 21, 2013 #2

    tiny-tim

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    welcome to pf!

    hi kl055! welcome to pf! :smile:
    it's simple trig …

    Acosφ + Bsinφ = A(cosφ + (B/A)sinφ)

    and cos(φ+θ) = cosφcosθ - sinφsinθ = cosθ(cosφ - tanθsinφ)

    so if we define θ so that tanθ = -B/A,

    then Acosφ + Bsinφ = (A/cosθ)cos(φ+θ) :wink:

    (and tan(90°- θ) = cotθ = 1/tanθ)
     
  4. May 21, 2013 #3

    rude man

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    Show us your computation of K1.

    That way I can show you why θ(ω) = tan-1(ωL/R).
    θ(ω) is part of the phase angle between voltage and current. It's the part that's a function of frequency wheras phi and -90 deg. are constant angles, independent of frequency.
     
  5. May 21, 2013 #4
    IMG_20130520_225200.jpg

    IMG_20130520_225235.jpg

    IMG_20130520_225433.jpg

    IMG_20130520_225510.jpg


    I did a partial fraction expansion, solved the system of equations, then rewrote K1 using trig laws.
     
  6. May 21, 2013 #5

    rude man

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    So you're happy with what you did, no more questions?
     
  7. May 21, 2013 #6
    Yes. I don't have a problem with the math but I was wondering how to conceptually interpret the theta angle. You mentioned the "phase angle between voltage and current" which indicates that I need to review the phasor section of the textbook. Thanks for the help.
    I've got quite a bit of reading to do =/
    I'll post here again if I have trouble with the textbook's explanation.
     
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