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.

Attached Thumbnails

 

sirisha kotik

this can be dne by charge distribution . and applying kirchoff's loop law.

CWatters

Transforms...

http://en.wikipedia.org/wiki/Y-%CE%94_transform

Pranav-Arora

Would that work for capacitors?

NascentOxygen

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?

Pranav-Arora

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 hw 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

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-%CE%94_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.

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