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RLC Circuit

  1. Nov 11, 2015 #1
    Vs6FXYA.png

    The question is:

    The voltage source in the above circuit is a sinusoidal AC source with constant amplitude and constant phase shift but an adjustable frequency.
    Calculate the frequency ω at which the phasor current I will have zero phase shift relative to the
    voltage source. In other words, the equivalent impedance across the voltage source behaves like a
    pure resistance with zero reactance at the required frequency.
    (HINT: Given two complex numbers such that A + jB = C + jD, then A = C and B = D by inspection,
    i.e. the real portion must equal the real portion and the imaginary portion must equal the
    imaginary portion.)

    Attempt:

    Since it stated that the reactance is zero, that means Z = R. So Req = (1/100+1/100)^-1 = 50. I converted the v(t) into V (phasors) which become 100. Then I = V/R, so I get 100/50 = 2. I don't know what to do next. Am I even doing it correctly?
     
  2. jcsd
  3. Nov 11, 2015 #2

    sophiecentaur

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    Suggestion: when will the two reactances be equal and opposite? (giving zero sum)
     
    Last edited by a moderator: Nov 11, 2015
  4. Nov 11, 2015 #3

    BvU

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    Hello trying, welcome to PF :smile: !

    You are doing fine. What about the hint in the exercise ? You have ## {1\over Z_{\rm total} } = {1\over Z_1 } + {1\over Z_2 } ## with 1 for branch 1 and 2 for branch 2, and all ## Z ## complex, but the imaginary part of ## {Z_{\rm total} }## equal to 0 ...
     
  5. Nov 11, 2015 #4
    During resonance?
     
  6. Nov 11, 2015 #5

    BvU

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    At the frequency the exercise is asking for Z = R, a real quantity.
     
  7. Nov 11, 2015 #6

    donpacino

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    building off what BvU said, why don't you start by getting an algebraic expression for Z
     
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