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Homework Help: Increase dielectric strength of a cylindrical capacitor

  1. Jun 21, 2011 #1
    1. The problem statement, all variables and given/known data
    You have a co-axial cylindrical capacitor placed in vacuum. The two co-axial cylinder tubes are made of copper. The outside tube radius a1 and inside tube radius a2, with overlapping length L; both tubes have a thickness of t. Say, the capacitor was designed to withstand 5 kV voltage at 10 kHz. Now you are applying 10 kV at same 10 kHz, and you see a breakdown. Assume a1, a2 and L are fixed. The question is: How can you make the capacitor work for 10 kV at 10 kHz?

    2. Relevant equations

    3. The attempt at a solution
    (1) dip the capacitor tubes in sodium hydroxide, then oven-heat it, to turn surface copper into a thin layer of copper oxide (CuO). CuO has larger dielectric strength, so it can withstand higher voltage. Issue: CuO has larger permittivity and will this affect the frequency transmission?
    (2) dip the capacitor tubes in nitric acid, to remove a thin layer of the copper, so the gap distance between two cylinders increased a little, affording a larger voltage.
    (3) coat the tubes with a thin layer of zinc. Similar idea as in attempt (1).
  2. jcsd
  3. Jun 21, 2011 #2


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    Staff: Mentor

    I think you are on the right track with the coatings.

    Also, the use of the term "vacuum" in the problem statement is a bit vague. Think about how the Paschen Curve can have an effect...


  4. Jun 21, 2011 #3
    Thanks Berkeman,

    You are right about the Paschen curve. I should say that the vacuum is at the lower end of the curve. (say, an other attempt could be to adjust the vacuum to either a small tor or a higher pressure with an inert gas, if the original vacuum was not at the optional level)

    I have another thought. How about change the material from copper to zinc: repalce the copper tubes with zinc tubes?


  5. Jun 22, 2011 #4


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    Staff: Mentor

    The idea of oxide growth is analogous to the electrolytic capacitor, though in the electrolytic the oxide insulator/dielectric is continually maintained by electrolytic action.

    It seems to me that this self-maintenance function would be absent with the CuO layer, though beyond that I offer no opinion.

    Is an oil or plastic or porcelain dielectric not feasible?

    How would changing the conductor change things?
  6. Jun 22, 2011 #5
    Do you have an oil in your mind?

    Basically, the capacitor, which was designed for 5 kV 10 kHz, is expect to work for 10 kV 10 kHz.

    Another question, if add/change material (oil dielectric or zinc coating or CuO coating or zinc tube), will the signal/frequency transmission be affected (e.g. out of phase)? What else will change?


  7. Jun 23, 2011 #6


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    Staff: Mentor

    I don't have a particular oil or synthetic fluid in mind, so with no better leads to go on, if I had to I'd look at transformer oil and see what its properties are, then proceed from there. Whatever you add will increase the capacitance, though this is probably inconsequential.

    10 kHz is audio frequency. What property would you hope may change were you to provide a different metal either side of the gap? Do you have any equations relevant to the task that reflect a different value for different metals?

    As it stands, the air gap is withstanding 5kV and you need something else to withstand the other 5kV. I can't see a thin oxide/chemical layer withstanding even a few hundred volts.

    I've been out of electrical power for many years, so take what I say as not even worth the paper it's written on. :shy: Have you googled for liquid dielectrics? It makes it easy when all you are concerned with is dielectric strength, as here, with no concern for permittivity.

    I'd be interested in knowing how many uF a practical 5kV concentric cylinder capacitor like this can be expected to have, and to what use it would be put. Is the "attempted solution" something you came up with, or is it integral to the problem?

    Have you worked out how wide the gap would be in a vacuum to just withstand 5kV? This would give you a feel for the dimensions you are dealing with.
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