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Finding Phase Difference in an RC circuit

  1. Apr 16, 2017 #1
    1. The problem statement, all variables and given/known data
    2f81f751582010247d94b5e5d9a53c5a.png

    2. Relevant equations
    ##V = ZI##
    ##Z_R = R##
    ##Z_C = -\frac{j}{\omega C}##
    ##Z = \sqrt{R^2 + (\frac{1}{\omega C})^2}##
    ##P_{av} = \frac{1}{2}V_m I_m cos(\phi)##
    ##\phi = arctan(\frac{-1/\omega C}{R})##
    ##\Delta \phi = \phi _1 -\phi _2##

    3. The attempt at a solution
    I've found what I believe to be the solution to the first part ##Z_{in} = Z_R + Z_C = 5\Omega - 3.97j \Omega## and the admittance which is ##Y = \frac{1}{Z}##

    For part b, I calculated the magnitude of Z and got ##Z = 6.83 \Omega ## and then found the current using ##I_m = \frac{V_m}{Z}## = 1.57A. I calculated ##\phi = -38.4^o## and got a power of ##6.15W##.

    For part c, I'm stuck on finding the phase difference (##\Delta \phi##) because I'm not sure how to find another value of ##\phi## and there is none specified in the question. Any help would be appreciated.
     
  2. jcsd
  3. Apr 16, 2017 #2

    Hesch

    User Avatar
    Gold Member

    Ii = Io = Vi/(R - j/ωC)

    Vo = Io * ( -j/ωC )

    Phase shift = Φ , where Φ is calculated from Vo/Vi = xxxx∠Φ ( result in polar notation )

    You may find an easier way, but this is the "basic" method.
     
    Last edited: Apr 16, 2017
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