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



On 08/27/2015 09:24 AM, andre adler wrote:

What about the Wheatstone Bridge? (And I'm taking about the general
situation where you have a non-zero current through the bridge.)
The Wheatstone bridge is in introductory texts.

I introduce this circuit to show students circuits do not have to have
parallel nor series connections.

That's a good question ... for which I have a couple of
good answers.

1) In real life, such bridge structures are almost always
operated at /or near/ zero current across the middle.
In particular, there is usually a voltmeter or other
high-impedance element spanning the middle.

In that case, any engineer on earth would analyze it by
computing the Thévenin equivalent of the left half and
the Thévenin equivalent of the right half, and use that
to figure out the current across the middle, valid to
first order.

2) If you want the exact answer, any halfway clever engineer
would open up the diamond-shaped bridge to form an H-shaped
bridge, with two inputs (at the tops of the H) instead of
just one. Then you zero one of the inputs and analyze the
remaining circuit using series/parallel reduction. Ditto
for the other input. Then, since it's a linear circuit,
you add the two solutions, to cover the original case where
the two inputs were tied together.

If you know the trick, you can carry out this analysis in
less time than it takes to tell about it. Note that the
same trick works for a tremendous number of other circuits.