1. Not finding help here? Sign up for a free 30min 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!

LCR circuits and phase angle

  1. May 29, 2012 #1
    1. The problem statement, all variables and given/known data
    A resistor (R), capacitor (C), and inductor (L) are connected in series. What is the complex impedance, Z,
    of this LCR series combination?

    An AC supply of voltage V(t)=V0eiωt is applied across an LCR series combination.
    Derive an expression for the current I(t) in the circuit. From your expression for I(t)
    write down expressions for both the magnitude of the current and the tangent of the
    phase angle between current and applied voltage.


    2. Relevant equations

    ZL=iωL

    ZC=-i/(ωC)

    ZR=R

    I(t)=V(t)/Z.​

    where; ω=Angular frequency of the voltage and i=√(-1).

    3. The attempt at a solution
    For the total impedance I got:

    Z=R+i(ωL-[itex]\frac{1}{ωC}[/itex]),​

    and for the current:

    I=(V0eiωt)/(R+i(ωL-[itex]\frac{1}{ωC}[/itex])).​

    For the tangent of the phase angle it would just be the tangent of the argument of the above equation for the current? If so, I can't get it into a "nice" equation without a trig function of another trig function. Thank you for any help.
     
    Last edited: May 29, 2012
  2. jcsd
  3. May 30, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Sleepy_time! Welcome to PF! :smile:
    tan of the phase angle of a + ib is simply b/a

    for (a+ib)/(c+id), use the tan(θ-ψ) formula :wink:
     
  4. May 30, 2012 #3
    Hi tiny-tim, thanks for the help. So what I got is shown in the attachment. Have I got it right?
     

    Attached Files:

  5. May 30, 2012 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Sleepy_time! :smile:

    erm :redface:
    An AC supply of voltage V(t)=V0eiωt

    the tangent of the phase angle between current and applied voltage.​

    apart from that, fine! :smile:

    (remember, impedance, complex current, etc are all constants! :wink:)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: LCR circuits and phase angle
  1. Phase angle RC circuit (Replies: 5)

  2. Phase in LCR circuits (Replies: 1)

  3. LCR circuit. (Replies: 18)

Loading...