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Impedance of a Capacitor

  1. Jun 9, 2007 #1
    I know the impedance of a capacitor is,

    [tex]
    \frac {1}{j \omega C}
    [/tex]

    so in an audio circuit it lets more high frequency energy through, which is obvious looking at the equation. When a capacitor is in parallel with a fixed resistor, I worked out the magnitude of the impedance of the pair to be

    [tex]
    \frac{R \omega C}{\sqrt{R^2 + (\omega C)^2}}
    [/tex]

    and this pair should still have lower impedance at higher frequencies, right?
    So my question is, how does this expression reflect this? I just can't see it.
     
    Last edited: Jun 9, 2007
  2. jcsd
  3. Jun 9, 2007 #2
    first caps and inductors have reactance, the resistance plus reactance is the impedance of the circuit. just correcting a nomenclature mistake.

    second i have no idea how you got that for the total impedance of the circuit

    [tex]
    V=I|Z|[/tex]

    [tex]
    |Z|= \sqrt{R^2 + (\chi _c)^2}}[/tex]
    [tex]
    |Z|= \sqrt{R^2 + (\frac{1}{j \omega C})^2}}
    [/tex]

    as you see with omega in the denominator as freq goes down impedance goes to infinity
     
    Last edited: Jun 9, 2007
  4. Jun 9, 2007 #3
    ahhh i meant parallel, sorry

    I got it like this:
    [tex]
    \frac {1}{Z_eq} = \frac {1}{R} + \frac {1}{j \omega C}
    [/tex]

    [tex]
    Z_eq = \frac {R \omega C}{R + j \omega C}
    [/tex]

    [tex]
    |Z_eq| = \frac {R \omega C}{\sqrt{R^2 + ( \omega C )^2}}
    [/tex]

    Thanks for your help with this.

    edit: should the second term in the first equation be jwC, not 1 on? could be my problem :confused:
     
    Last edited: Jun 9, 2007
  5. Jun 9, 2007 #4
    a high pass filter is a cap and a resistor in series though
     
  6. Jun 9, 2007 #5
    The circuit I'm working on has a number of capacitors that can be switched in parallel with a resistor to give different frequency response depending on which one you select.

    I reworked the above as:
    [tex]
    \frac {1}{z_{eq}} = \frac {1}{R} + j \omega C
    [/tex]

    which gives
    [tex]
    |z_{eq}| = \frac {R}{\sqrt{1 + ( \omega CR)^2}}
    [/tex]
     
    Last edited: Jun 9, 2007
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