dc capacitor divider?

[zorro]

Hi all,

The simplest form of the "dilemma" of no single solution is what we get with Vdc=0 in the original post and merging the two capacitors into a single one. It is a "circuit" consisting of a single capacitor; the terminal connected to ground is the reference node.
If we consider an ideal (lossless) capacitor, it can hold any voltage indefinitely.
The circuit has only one node (other than the reference).
Lossless means in this case that parallel conductance from the single node (to the reference) is zero.

The dual of this "circuit" is an ideal (lossless) short circuited inductor.
The current across it continues to circulate indefinitely.
The circuit has only one mesh.
Lossless means in this case that series resistance in the single mesh is zero.

A useful point of view is that these "circuits" have an "initial" condition that does not evolve in time towards a steady state of zero stored energy because there are no losses able to dissipate it.

The single-C circuit holds a nonzero voltage if (and only if) there is a nonzero net electric charge in its single node.
Analogously, In the original circuit (with Vdc and 2 identical ideal capacitors) the solution with Vdc/2 on each of the capacitors assumes that there is no net charge in the node connecting them.
For all other solutions (see LvW's post #8 and FvM's post #16), there is a net charge in that node.

Regards

Z

 

[Ratch]

zorro,

The simplest form of the "dilemma" of no single solution is what we get with Vdc=0 in the original post and merging the two capacitors into a single one.

Just one "simple" question. What is the dilemma, and how can it be said that there is not a solution? I thought that I did present a single finite solution for the conditions given. Perhaps you can a submit a simple example where the solution is indeterminate.

Ratch

 

[zorro]

Hi Ratch,

What is the dilemma,...

The dilemma:

Can in be said that there is a unique solution to the problem?
or
Can in be said that there are many solutions?

...and how can it be said that there is not a solution?
...
Perhaps you can a submit a simple example where the solution is indeterminate.

I didn't say that that there is not a solution.
I didn't say that that the solution can be indeterminate.

Of course, there is a solution (at least one).
Recall that we are considering ideal capacitors, like in the original post.

My answer:

There is a unique solution with no net charge at the node.
There are many solutions if net charge at the node is allowed.

In the above sentences, "the node" is the "middle node" in the problem with two capacitors (original post), or the non-grounded terminal of the capacitor in the simplest form of the problem that I presented.

Regards

Z

 

[Ratch]

zorro,

Can in be said that there is a unique solution to the problem?
or
Can in be said that there are many solutions?

I didn't say that that there is not a solution.
I didn't say that that the solution can be indeterminate.

Of course, there is a solution (at least one).
Recall that we are considering ideal capacitors, like in the original post.

My answer:

There is a unique solution with no net charge at the node.
There are many solutions if net charge at the node is allowed.

OK, let me say that for any combination of capacitance, initial capacitor voltage, voltage source, or resistance across each two capacitors in series, there is a only one unique steady state solution. Is that statement unambiguous enough?

Ratch

 

[LvW]

OK, let me say that for any combination of capacitance, initial capacitor voltage, voltage source, or resistance across each two capacitors in series, there is a only one unique steady state solution. Is that statement unambiguous enough?
Ratch

Ratch, I think I can agree to this statement without any restrictions.
LvW