Re: [Phys-L] circuit analysis : a simpler approach?

[John Denker <jsd@av8n.com>]

On 09/01/2015 06:48 PM, Lulai, Paul wrote:

> Wouldnt we get the same result for most dc circuits with resistors and
> capacitors in steady state if we worked  things by:
> A) determining equivalent resistances or capacitances
> B) using kirchoffs laws

Here's how I see it:

a) The method of series/parallel reduction is a subset of
 Kirchhoff's «laws».  In any case where series/parallel
 reduction works, direct application of Kirchhoff's «laws»
 would have worked also.

b) The converse does not necessarily hold.  You can "usually"
 do fine with series/parallel reduction, but not always.
 Notable exceptions include certain 2D and 3D mesh structures.

c) A mesh of /linear/ elements can be solved fairly
 easily, but a mesh with diodes here and there is a mess.

d) There are situations where neither series/parallel
 reduction nor Kirchhoff's «laws» make sense.  An obvious
 example is a big chunk of metal with a current source
 at one point and a current sink at another.  I suppose
 you could model it approximately using Kirchhoff's «laws»
 applied to a fine mesh, but I wouldn't recommend it.

e) In cases where series/parallel reduction is a viable
 option, I recommend it over other methods.  It's quick,
 easy, intuitive, and easy to visualize.

 Most simple circuits you are likely to encounter fit
 into this category, if only because designers don't
 like to design stuff that can't be analyzed this way.

 As Diego Saravia pointed out, if a solution has been
 found by whatever method, you can use Kirchhoff's
 «laws» to check it.  Verifying a solution is usually
 very much easier than deriving it from scratch.

f) What you really need to watch out for are situations
 where Kirchhoff's «laws» get the wrong answer (and
 series/parallel reduction gets the same wrong answer 
 for the same reasons).  That's because Kirchhoff's «laws»
 are predicated on a whole bunch of assumptions that are
 not always true in real life.  Ground loops are the
 canonical example of this.

https://www.av8n.com/physics/kirchhoff-circuit-laws.htm