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Homework Help: Formula for delta star in capacitors

  1. May 15, 2014 #1
    1. The problem statement, all variables and given/known data

    How to find out the equivalent capacitance using delta star conversion?

    2. Relevant equations

    Delta star conversion formula of capacitors

    3. The attempt at a solution

    Using the formula of resistors but not coming.What is the formula of delta star in capacitors?
  2. jcsd
  3. May 15, 2014 #2


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    Homework Helper

    The slow way to do it is from first principles.

    The quick way is to use the AC impedance of a capacitor, which is ##\displaystyle \frac{1}{j\omega C}##, which can be treated like a resistance, then apply the delta-star conversion formula to it and see what you end up with. Remember to convert the final impedance you get back to a capacitance by reversing the formula.
  4. May 15, 2014 #3


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    Science Advisor
    Gold Member

    The delta-star transformations work for more than simple resistance - they work for any impedance.

    So just convert the capacitances to impedances ... and use the formulas for resistors.

    Then convert the impedances back into capacitances.
  5. Apr 19, 2017 #4
    Hi Curious3141,
    quick run down.... C1 across b and c, C2 across c and a, C3 across a and b.
    I'm trying to derive the formula for Ca in terms of C1, C2 and C3.
    If these capacitors were resistances the formula would be Ra=(R2R3/R1+R2+R3) (I think ?)
    there for if capacitors.. 1/ωCa=(1/ωC2*1/ωC3)/(1/ωC1+1/ωC2+1/ωC3). (??)
    How do I convert this back to capacitance so I just have Ca=.......???
  6. Apr 19, 2017 #5


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    Staff: Mentor

    Looks like it's just a bit of algebra. Logically, you know that ω should ultimately play no role in the capacitance values you obtain, so it should cancel out along the way. Might as well just eliminate it from the start (or choose a convenient working frequency such as ω = 1). That may make things less cluttered looking.
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