Re: [Phys-L] imperfect transformers and/or multi-terminal capacitors

[John Denker <jsd@av8n.com>]

On 04/01/2014 01:49 PM, Bernard Cleyet wrote:
> This is something that has puzzled me since I first noticed a v. long
> time ago.
>
> The drop from OC E/q  to loaded w/ a rather high resistance is not
> explained by the internal resistance and the external resistance
> load.  i.e. the E/q is > predicted by the input E/q and the turns
> ratio.

Yeah, that's a good question.  I noticed the same thing,
and it had me mystified for quite a while, longer than 
I care to admit.  However, there exists a reeeeeally 
good answer.

Possibly helpful pedagogical suggestion:  Start with multi-
terminal capacitors.  This can be formalized in terms of
the capacitance matrix:
 -- self-capacitances on the diagonal
 -- mutual capacitances elsewhere

I mention this because most people have a better intuition
about electric fields and charges than about magnetic fields
and currents.

As a second stage, you can map the capacitance matrix
formalism onto the inductance matrix formalism:
 *) An /ideal/ transformer will have the mutual inductances
  equal to the self-inductances.  This leads to some weird
  cancellations and singularities.
 *) In contrast, a non-ideal transformer will have some
  "extra" self-inductance.  I reckon this is a big piece
  of the answer to the question that was asked.  You can
  develop any voltage you like across the "extra" self-
  inductance on the primary;  it's not locked to whatever
  is going on with the secondary.

The formalism is trickier than you might have expected,
especially when it comes to /inverting/ the capacitance
matrix ... but it's not too bad once you know the tricks.
  http://www.av8n.com/physics/capacitance.htm