Simplifying circuit

Discussion in 'Homework Help' started by jobu180, Nov 1, 2008.

  1. jobu180

    Thread Starter New Member

    Nov 1, 2008
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    I'm trying simplify the following circuit:

    ( R1 in series with C1) || C2

    I'm looking for Z .

    Thanks.
     
  2. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    HINT:

    Assign the series RC leg the reference Z1 and assign the C2 leg the reference Z2.

    Then write the expression for Z1||Z2.

    With the expression Z1||Z2 figured out, you can then plug in the impedances for each of the elements and solve.

    hgmjr
     
  3. jobu180

    Thread Starter New Member

    Nov 1, 2008
    7
    0
    Z1||Z2

    Z1 = R1+C1
    Z2 = C2

    Z = Z1*Z2/(Z1+Z2)

    Z = (R1*C2+C1*C2)/(R1+C1+C2)

    Correct?
     
  4. hgmjr

    Moderator

    Jan 28, 2005
    9,030
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    Sorry, No.

    Remember:

    \Large Z_{\small 1}=R_{\small 1}+X_{c\small 1}

    \Large X_{c} = \frac{1}{sC}

    hgmjr
     
    Last edited: Nov 1, 2008
  5. jobu180

    Thread Starter New Member

    Nov 1, 2008
    7
    0
    That's right, so ...

    Z1 = R1 +1/sC1
    Z2 = 1/sC2

    Z = (R1/sC2 + 1/s^2C1C2) / (R1 +1/sC1+1/sC2)

    Hope that's right.

    Thanks.
     
  6. hgmjr

    Moderator

    Jan 28, 2005
    9,030
    214
    You have the the equation correct. You probably need to simplify the expression to be totally complete.

    hgmjr
     
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