Homework Help: Formula for delta star in capacitors

1. May 15, 2014

avistein

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. May 15, 2014

Curious3141

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.

3. May 15, 2014

UltrafastPED

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.

4. Apr 19, 2017

Greg Arnald

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=.......???

5. Apr 19, 2017

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.