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Multiple RLC problems

  1. Feb 26, 2015 #1
    1. The problem statement, all variables and given/known data
    a)
    For the following circuit, if Vrms= 40V, write the current and the voltage equations.
    http://www.imageupload.co.uk/images/2015/02/26/Captureaa814.png [Broken]

    b) For the following circuit, if i=0.8 sin(1000t-30), write the voltage equation and determine the average value of current.
    http://www.imageupload.co.uk/images/2015/02/26/Capture2.png [Broken]

    2. Relevant equations
    Ohm law for AC network.

    3. The attempt at a solution

    a)
    Vmax=Vrms/0.707=56.57 V
    ZT=sqrt(R^2+XL^2)=12.72 ohms
    Imax=Vmax/Z=4.44 A

    So the equations would be:
    i=Imax sin(wt) = 4.44 sin (wt)
    v=Vmax sin(wt) = 56.57 sin(wt)

    Should I write -90 or +90 since I'm dealing with inductor?

    b) Since Imax=0.8 A, Vmax=Imax*ZT =0.8*5=4 (ZT=sqrt(R^2+(XL-XC)^2) =5)
    v=4 sin(1000t-30)

    Iavg=2*Imax/pi = 0.5 A (Or is it zero since we are dealing with sine wave?)
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Feb 27, 2015 #2

    BvU

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    Hello Jason,

    a) Neither -90 nor +90: it isn't a purely inductive load. Can you handle complex impedance ?

    b) Again: there is a phase difference between V and I . Non-zero, because not resonant: XL not equal to XC
    Average I zero ? true but corny.
     
  4. Feb 27, 2015 #3
    I meant the equation for the voltage source itself.

    Also, I mean the equation for the source itself.
    For the average value, should I dismiss 2*Imax/pi?
     
  5. Feb 27, 2015 #4
    Are you asking if the number you plug in for Vmax in problem "a" should have a phase angle associated with it? I would assume no. It would be explicitly stated in the problem.
     
  6. Feb 28, 2015 #5
    OK. And for problem b)?
     
  7. Feb 28, 2015 #6

    BvU

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    I maintain that the wording
    constitutes asking for amplitude and phase angle. The angle is pretty easy to solve with these values for ##|Z_R|## and ##|Z_L|## and you want to pay attention that you get the correct sign. b) idem.
     
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