Y-Delta conversion for Capacitors

  1. This was a ques in my book ... (Pic)

    After thinking a while, i realized that it can be solved using Y-Delta (by converting Y to delta form) conversion. But i couldn't get the answer ... i dont know why ...

    I used this equation

    It is given for resistors ... i guess its same for resistors and capacitors ... Right???

    Please tell me if the eqn used is wrong or something else!!!

    Attached Files:

  2. jcsd
  3. gneill

    Staff: Mentor

    Remember how capacitors combined differently in series and parallel than do resistors?

    What you can do is convert all your capacitances to their equivalent impedance, then use those formulae. Impedances mix and match like resistances.
  4. How do i find impedance of a capacitor?
  5. gneill

    Staff: Mentor

    [tex]Zc = 1/(j\omega C[/tex])

    [tex]\omega[/tex] is the operating frequency. The result is in Ohms, and will be an imaginary value.

    Don't panic! You don't need to know the frequency for the math to work out; it's a constant for the given Y to Delta situation. If you do the algebra, a pretty simple result obtains. If the resistor version is:

    Ra = (R1*R2 + R2*R3 + R3*R1)/R2
    Rb = (R1*R2 + R2*R3 + R3*R1)/R3
    Rc = (R1*R2 + R2*R3 + R3*R1)/R1

    Then the capacitor version looks like:

    Ca = C1*C3/(C1 + C2 + C3)
    Cb = C1*C2/(C1 + C2 + C3)
    Cc = C2*C3/(C1 + C2 + C3)
  6. And to find Y form,

    C1 = (CaCb + CbCc + CcCa) / Cc

    Thanks for the help gneill !!!!!!!!!!!!!!!!!!!!!
    Thanks a lot !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
  7. gneill

    Staff: Mentor


    You're welcome.
  8. SammyS

    SammyS 9,299
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member


    The three capacitors enclosed in red form a Y. So does the other set of 1, 3, and 4 μF capacitors. Converting each of these sets to Δ configuration, as shown by gneill above, will allow you analyze the circuit as a combination of parallel and series capacitors.
  9. Thanks for the help!!!!
  10. Is there a simple result for delta to Y as well?
  11. gneill

    Staff: Mentor

    Sure. Just substitute the appropriate capacitor impedances into the formulas for resistance, stir and serve. Note that a capacitor impedance is of the form [itex] 1/(j \omega C) [/itex].


    So for example, given that for resistors
    [tex] R_1 = \frac{R_a R_b}{R_a + R_b + R_c} [/tex]
    [tex] \frac{1}{C_1} = \frac{C_c}{C_b C_c + C_a C_c + C_a C_b} [/tex]

    and so on.

    EDIT: Fixed up the expression. Should have been 1/C1 on the LHS.

    Attached Files:

    • Fig1.gif
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    Last edited: May 1, 2015
  12. Thank you! :)
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