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RLC AC Circuit Question

  1. Jan 21, 2012 #1
    Voltage V(t)=V1 Re{eiwt} produces a current I(t)=I1 Re{e(iwt+θ). Determine I1 and θ.

    The circuit is AC so do I treat it the same as an SHM question? Is π/2? And what do I need to do to find I1? I don't know where to start.
     
  2. jcsd
  3. Jan 21, 2012 #2

    ehild

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    What is the circuit? You need its complex impedance to find I1 and θ.

    ehild
     
  4. Jan 21, 2012 #3
    Ohh. The circuit is like this one:

    pic012.png

    with no values given.
     
  5. Jan 21, 2012 #4

    ehild

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    What is the impedance in terms of R, L, and C?

    ehild
     
  6. Jan 21, 2012 #5
    z = R + iωL +1/iωC ?

     
    Last edited: Jan 21, 2012
  7. Jan 21, 2012 #6

    ehild

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    OK, collecting the imaginary terms, it is Z=R+i(ωL -1/ωC ). This is a complex number. You can write it in exponential form:

    Z=|Z|e (How?).

    The complex voltage is V=V1eiωt

    Use the equation I=V/Z to find the complex current.

    ehild
     
    Last edited: Jan 21, 2012
  8. Jan 21, 2012 #7
    I=V0/|Z| ?

    But that gives me I0= V0/|Z|ei(ωt+θ).
     
    Last edited: Jan 21, 2012
  9. Jan 21, 2012 #8

    ehild

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    You used I1 and V1 for the amplitudes in the original post.

    I=V/Z . Z=|Z|e

    That means

    I0ei(ωt+θ)=V0ei(ωt)/[|Z|e]

    Simplify with ei(ωt).

    I0e=V0/[|Z|e]=[V0/|Z|]e-iψ

    The magnitudes and phases have to be the same on both sides.

    ehild
     
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