Y-Delta conversion for Capacitors

  • #1
1,137
0
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 http://en.wikipedia.org/wiki/Y-%CE%94_transform" [Broken]

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!!!
 

Attachments

Last edited by a moderator:

Answers and Replies

  • #2
gneill
Mentor
20,901
2,854
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 http://en.wikipedia.org/wiki/Y-%CE%94_transform" [Broken]

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!!!
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.
 
Last edited by a moderator:
  • #3
1,137
0
How do i find impedance of a capacitor?
 
  • #4
gneill
Mentor
20,901
2,854
How do i find impedance of a capacitor?
[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)
 
  • #5
1,137
0
And to find Y form,

C1 = (CaCb + CbCc + CcCa) / Cc
Right?

Thanks for the help gneill !!!!!!!!!!!!!!!!!!!!!
Thanks a lot !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 
  • #6
gneill
Mentor
20,901
2,854
And to find Y form,

C1 = (CaCb + CbCc + CcCa) / Cc
Right?

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

You're welcome.
 
  • #7
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,347
1,022
... 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)
attachment.php?attachmentid=31194&d=1294597370.jpg


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.
 
  • #8
1,137
0
Thanks for the help!!!!
 
  • #9
12
0
Is there a simple result for delta to Y as well?
 
  • #10
gneill
Mentor
20,901
2,854
Is there a simple result for delta to Y as well?
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].

attachment.php?attachmentid=38864&stc=1&d=1316032546.gif


So for example, given that for resistors
[tex] R_1 = \frac{R_a R_b}{R_a + R_b + R_c} [/tex]
then
[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.
 

Attachments

Last edited:
  • #11
12
0
Thank you! :)
 

Related Threads on Y-Delta conversion for Capacitors

Replies
4
Views
13K
  • Last Post
Replies
4
Views
4K
Replies
3
Views
4K
  • Last Post
Replies
4
Views
2K
Replies
9
Views
5K
  • Last Post
Replies
2
Views
1K
Replies
6
Views
495
Replies
5
Views
181
Replies
2
Views
22K
Top