1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    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


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


    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Homework Helper
    Gold Member

    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




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

    rude man

    User Avatar
    Homework Helper
    Gold Member

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted