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Open circuit with capacitor

  1. Feb 24, 2013 #1
    The problem asks to find the steady state voltage across the capacitor. i attached the circuit (sorry for the poorly drawn and yes, that open part of the branch is supposed to be there) This is a multiple choice question where the answers are:
    a) 0V
    b) V_dc/2
    c) V_dc/3
    d) V_dc
    e) 2*V_dc

    In steady state, a capacitor behaves as an open.
    If the capacitor was placed before the resistors, I think its voltage would be V_dc.
    However, this capacitor is placed after the resistor.
    In steady state, no current will flow through these 2 branches due to the open circuit, thus the voltage drop across the 2 resistors are 0.
    This means that the ends of the capacitor are at the same voltage (V_dc). Thus the voltage difference is V_dc-V_dc=0.
    So the answer is a. Am I right?
     

    Attached Files:

  2. jcsd
  3. Feb 24, 2013 #2

    NascentOxygen

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    Staff: Mentor

    I expect that gap is supposed to be bridged by a switch, otherwise the circuit is rather pointless.
     
  4. Feb 24, 2013 #3
    The diode used to be where the gap is. But the orientation of the voltage source implies that the diode will become a gap because it will be reverse biased.
     
  5. Feb 24, 2013 #4

    NascentOxygen

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    Staff: Mentor

    The capacitor (if it carries any charge) will discharge via the resistor path, until the capacitor voltage reaches zero.
     
  6. Feb 24, 2013 #5
    Yes. So I think my proof in my first post was correct.

    Just for practice, if this was not steady state and the capacitor just began to charge, would its voltage be 0 still? I think that because initially when (time is just greater than 0) a capacitor behaves as a short branch.
     
  7. Feb 24, 2013 #6

    NascentOxygen

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    Staff: Mentor

    Yes, but not for that reason. To change the voltage on a capacitor you have to add charge to it. Adding charge takes time. Immediately after t=0 there has been no time to add much charge, so the voltage across the capacitor plates hasn't changed.
     
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