PLEASE, HELP ME OUT WITH THIS PROBLEM ON CAPACITANCE

[Mozart]

PLEASE, Help me out with this capacitance problem!!! I have been trying all my best to solve this question, most times, i end up in a dead lock and I leave it! I have just made a resolution to find the solution today.

 

 

this is the original question;

 

I redrew it and I had this;

 

 

My problem is that there is a certain principle i think I should know in order to tackle that question, but i dont! any links to search??

We did the course last semester!

how do I solve it? The question says I should find the effective capacitance. Thank You.

Edited November 22, 2013 by Mozart

[studiot]

This looks like homework,

 

So what do you know about 2 capacitors in series and 2 capacitors in parallel ?

[Mozart]

It's not a home work. I know that if two capacitors are in series, sum of each inverse of the capacitance is equivalent to the inverse of the effective capacitance. also, if they are parallel, that's simpler, just sum up the values. please, Just help me do this one! it's not an assignment. Infact, I already passed the course long ago. I just feel sad I can't solve it.

[Enthalpy]

This network cannot be computed as series and parallel combinations. You need a more general method, with several unknwon voltages or currents, which you solve as a linear set of equations.

 

Many methods apply, choose the one you're familiar with. Examples:

 

- Take zero volt at node b, arbitrary Va at node a, name Vc and Vd the potentials at the middle nodes of your redrawn circuit.

Express the five currents resulting from the potentials, write two equations telling that the (signed) sum of currents at nodes C and D is zero.

Solve Vc and Vd as a function of Va. Deduce the currents in the two left capacitors. Compare with Va, deduce the equivalent capacitance.

 

- Or take three loop currents, the third closing through the (not drawn) external part of the circuit. Write that loop voltages are zero. Solve two loop currents as a function of the external one, deduce the voltages, etc etc.

 

- Some shortpaths exist to write the set of linear equations directly, or even write the solutions, with fluence graphs or others. Need a significant time investment, exaggerated for this case alone. Someone doing that all the day would learn them; uncommon with digital electronics.

 

Few real-life circuits need the general methods, that's why most engineers forget them quickly. A ladder filter doesn't need them. A bridged T does, a double T as well - or use Y parameters (admittance matrices) for these two.

[Mozart]

Thank You Enthalpy! From what you have said so far, Sincerely speaking, I didn't quite understand you. I gather that the knowledge required to tackle that question is above my reach. Unless you are just referring me to Kirchhoff's Voltage and current rule! That will be very tedious! I just need a link with a similar question solved. If there is none, I'll be lift with no other alternative than to brain storm the question. I already have the answer. So there isn't a shortcut! ?

[Externet]

Would it help knowing the voltage at the left voltmeter is 42.857 % of the voltage applied to the network;

and at the right voltmeter is 57.143 % of the voltage applied to the network ?

 

Which means C3 has 14.286 % of the voltage applied to the network.

 

 

(Ignoring C3 the equivalent capacitance is 1uF, (but cannot be ignored as it is active; there is current trough it)

Edited November 22, 2013 by Externet

[studiot]

Ok, I agree with your first transformation, and does the term delta - star (the americans call it wye -mesh) transformation mean anything?

It is the next step on in network theory from series and parallel, but still does not require any voltages or current to be considered.

 

I have developed your diagram further to show the delta to the right of the wiggly line and labelled the vertices to keep track in the transformation to a star.

You require the capacitance between D and C. C is one vertex of the delta, A and B are the others.

Finally I have redrawn the transformed circuit to show a parallel combination of two pairs of series capacitors, in series with another capacitor.

 

You can therefore analyse this network purely by formule involving capacitor combinations.

 

Incidentally since it is possible to derive the transformation solely from consideration of series and parallel combinations it is not true to say that

 

This network cannot be computed as series and parallel combinations.

 

 

http://www.electronics-tutorials.ws/dccircuits/dcp_10.html

 

 

Edited November 22, 2013 by studiot

[Externet]

Error in my post:

The left vertical series C1, C4 = 2uF in parallel with the right vertical series C2, C5 = 2uF makes 4 uF; not 1 as I wrote as if they where series also.

[Enthalpy]

[...] delta - star (the americans call it wye -mesh) transformation. [...] You can therefore analyse this network purely by formule involving capacitor combinations.

Agreed now.

[studiot]

If we label the star point as S and compute the capacitances from the delta nodes A, B and C to S using the formulae

[math]{C_{AS}} = \frac{{{C_{AB}}{C_{AC}} + {C_{AB}}{C_{BC}} + {C_{AC}}{C_{BC}}}}{{{C_{BC}}}}[/math]

etc

 

We can easily reduce and compute the equivalent capacitance of the network.

 

I have amended my sketch to show that the star capacitance from A to S C_AS is 12 microfarads.

 

 

You should be able to complete the job from here.

Edited November 23, 2013 by studiot

[Mozart]

Thank You very much Studiot! I'm very happy! please. thank you once more! I'll get back to you with the Answer I'm very glad!!! you really tried for me!

[Mozart]

Please studiot, the "DELTA STAR TRANSFORMATION" and the "STAR DELTA TRANSFORMATION" processes as explained by the link you provided are not yet clear to me. I played around with that formular you used to solve for Z₁ , I wanted solve for C_BS so i thought that this might be the formular. Am I correct? are there any other known links that can explain this thing more clearly? Thank you all for your replies!!!

[studiot]

Since the transformation is usually reported in terms of resistance or impedance, and others might be interested in capacitance (or admittance) I have written these transformations out in full.

 

 

The notation is that the capacitance between the nodes is given by the subscript

 

eg the capacitance between B and C is C_BC which only appears in the Delta configuration

 

In the star configuration all the capacitances are between an individual node and the star point (S).

So the star has one more node than the delta.

Edited November 24, 2013 by studiot

[ASG]

when i charge, i use the term capacitance to explain the ability of a conductor to respond to emf. when i discharge, i allow the normal static forces to return my electrons to their usual states.

 

during this transfer, the medium i use offers some resistance to my charging and discharging. in vacuum, we call this epsilon nought. why is it that my medium does not participate in this process.

 

am i craftily choosing my apparatus to put forth scientific principles. am i working my math before my experiment. i like semi conductors.