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Electric impedance

  1. Feb 17, 2015 #1
    1. The problem statement, all variables and given/known data
    Consider a circuit with a capacitor C in series an inductor of inductance L. Explain what happens when ω2LC=1, without calculations, using your knowledge and intuition.

    2. Relevant equations
    1/Z = 1/impedance = 1/(iωL) +1/(iωC)
    i is pure imaginary.

    3. The attempt at a solution
    Well, unfortunately I have no intuition. I don't know what the quantity ω2LC represents, but it appears in the equation when you rearrange to find Z. So when I worked out Z, it was -1/(iωC+iωL) when the set condition is met. Which is a bit weird, because -ve resistance makes no sense...?
    I've obviously gone wrong somewhere!
     
  2. jcsd
  3. Feb 17, 2015 #2

    BvU

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    Yes, a capacitor has impedance $$1\over j\omega C$$
    Look here for some ideas
     
  4. Feb 17, 2015 #3
    So when ω2LC=1 then the inductive and capacitive reactances are equal. The current is oscillating at the resonant frequency of the circuit?
     
  5. Feb 17, 2015 #4

    BvU

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    That's right. Nothing wrong with your intuition.
    Reactances are equal and opposite. So together they are 'zero'. ##\bf V = Z I## (bold face to mark them as complex): there can be huge currents shooting back and forth with 'no' voltage needed to whip them up. In reality you can't have a lossless system, so characteristics of an RLC circuit sneak in.
     
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