Equivalent capacitor in the circuit

[nik jain]

Find the equivalent capacitance of the combinations shown in the fig.
(refer to the file attached)

Is there any easier method to solve instead of this method by assuming a constant potiential difference is applied across the circuit and a total charge Q flown in it.

 

[sirisha kotik]

this can be dne by charge distribution . and applying kirchhoffs loop law.

 

[CWatters]

Transforms...

http://en.wikipedia.org/wiki/Y-Δ_transform

 

[Saitama]

Transforms...

http://en.wikipedia.org/wiki/Y-Δ_transform

Would that work for capacitors?

 

[NascentOxygen]

Find the equivalent capacitance of the combinations shown in the fig.
(refer to the file attached)

Is there any easier method to solve instead of this method by assuming a constant potiential difference is applied across the circuit and a total charge Q flown in it.

No easier. Let current in top 2F cap be I₁, and in top 4F cap be I₂.
And current down through vertical 4F cap is I₁ - I₂.
etc

Solve for I´s in terms of applied voltage V and ω.

Does the textbook give the answer?

 

[sirisha kotik]

the ans is 20/7 F i think...is tht correct?

 

[Saitama]

No easier. Let current in top 2F cap be I₁, and in top 4F cap be I₂.
And current down through vertical 4F cap is I₁ - I₂.
etc

Solve for I´s in terms of applied voltage V and ω.

Does the textbook give the answer?

So, the star delta transformation isn't applicable here?
I had a quick search on google about this. The first link directed me to this thread. Check this post by gneill in that thread, he mentioned a formula which could be of use here. Can you explain that formula NascentOxygen?

 

[sirisha kotik]

tht is nt a wheatstone bridge homework cn u apply the star delta thn?

 

[nik jain]

Yes the ans. is 20/7 F and I also get it by using krichoff's law

 

[nik jain]

I also want to know that can we use star to delta formation here as in this case applying of
krichoff's law is easy , but what if all the value of capacitance is different ?

 

[NascentOxygen]

I also want to know that can we use star to delta formation here as in this case applying of krichoff's law is easy , but what if all the value of capacitance is different ?

The formulae given in the wikipedia article are general formulae, so their transform is applicable where the three branches are all different. On this page http://en.wikipedia.org/wiki/Y-Δ_transform under the heading Equations for the transformation from Y-load to Δ-load 3-phase circuit you are shown how to relate the impedance of each arm of Δ to that of the Y.

https://www.physicsforums.com/images/icons/icon2.gif In their formula, instead of resistances, you will use impedances, remembering that the impedance of a capacitor C = (ωC)⁻¹

I tried it on your capacitor network, transforming the upside-down Y shape of the vertical capacitor and the two lower ones into a delta. This changes the network to an uncomplicated arrangement of capacitors in parallel, and in series. I got the same answer, 20/7 F