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How can capacitive reactance be zero for no capacitor?

  1. Jun 20, 2009 #1
    I have a quick question about a problem requiring calculating impedance of a circuit where there is no capacitor. The formula for impedance Z is
    Z=sqrt(R^2 + (Xl - Xc)^2).
    I am told capacitive reactance Xc = 0 because C = 0 (there is no capacitor in the circuit). But the formula for Xc is Xc = 1/2(pi)fC. So if C = 0, then Xc must be huge or infinite, not zero!
    I'm confused. Can someone please explain this contradiction to me. Thank you!

    P.S.: Maybe I should visualize replacing the nonexistent capacitor with a "short". A short has infinite capacitance, right???
     
    Last edited: Jun 20, 2009
  2. jcsd
  3. Jun 20, 2009 #2

    LowlyPion

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    Homework Helper

    Welcome to PF.

    Capacitance of 0 is like an infinite insulator right? An open circuit. No current flows.

    If Xc is ∞, then no current flows for any ω.
     
  4. Jun 20, 2009 #3
    Th impedance Z is a complex value. Z = R + jX
     
  5. Jun 20, 2009 #4
    Thanks for the insight. I was thinking C varies inversely with the capacitor gap d, so if there is no capacitor, then there is no gap, d goes to zero, which means C is infinite... Is this goofy thinking?
     
  6. Jun 21, 2009 #5
    You give the formula for reactance in a series circuit.

    The term "no capacitor" would typically be interpreted to mean a short in a series circuit and an open in a parallel circuit. So i think its meant that there is no capacitor in the series circuit.

    The statement "capacitive reactance Xc = 0 because C = 0" is certainly flawed (i.e. not true in the general sense!). I suspect it should have been "capacitive reactance Xc = 0 because there is no capacitor in this series circuit".

    Finally, yes, a short can be thought of as having infinite capacitance, but I wouldn't say that in front of a class since it would make the students think they have to look at wires as devices of infinite capacitance, resulting in long queues outside the instructor's office after the class.
     
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