Formula for delta star in capacitors

[avistein]

Homework Statement

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

Homework Equations

Delta star conversion formula of capacitors

The Attempt at a Solution

Using the formula of resistors but not coming.What is the formula of delta star in capacitors?

 

[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.

 

[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.

 

[Greg Arnald]

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.

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=...?

 

[gneill]

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=...?

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.