Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Kirchoff laws for phasors

  1. Nov 23, 2004 #1


    User Avatar
    Homework Helper

    Something's bugging me. Suppose we take kvl around a loop in a circuit, we have:


    Suppose v1, v2, v3(t) are all sinusoidal (they can be written as Acos(wt+s)).

    So we have

    Suppose we replace all of them by their phasors, this should also equal zero but why? I'll write it out here (without suppressing e^jwt, but just adding the imaginary parts)

    (A1cos(wt+s1)+A2cos(wt+s2)+....) + j(A1sin(wt+s1) + A2sin(wt+s2)+....)

    If I know the group of real terms add to zero, does that necessary imply that the group of imaginary terms add to zero? Is there a proof of this?
  2. jcsd
  3. Nov 23, 2004 #2


    User Avatar
    Homework Helper


    I just saw a very unsatisfying derivation of kvl for phasors here. How do you just remove the "R", and assume kvl holds for the entire phasor (not just the real part). I saw a similar technique elsewhere. They write kvl for the reals, and then R {V1+V2+...}=0 (where V1, V2 are phasors), then just remove the R. This removing of the R is bothering me. I don't see how it is justified.
  4. Nov 24, 2004 #3


    User Avatar
    Homework Helper

    Figured out the answer. It's simple. I wish they just put it in the proof in my book:

    If we know

    then take the derivative of both sides


    divide by -w on both sides:


    so the imaginary parts in phasor notation add to zero.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Kirchoff laws for phasors
  1. Kirchoff 's law in A/C (Replies: 3)

  2. Kirchoffs Current Law (Replies: 6)

  3. Kirchoff Laws Help (Replies: 5)