hi all,
i'm not an EE, i'm only a lowly physicist, so forgive me a very
simple-minded approach to what seems to be a problem to some
subscribers on this reflector.
i'd like to find the resistance (Re, where "e" stands for
equivalent, so we don't get into whether it's parallel or series,
nichrome or carbon, etc.) of a simple network. i want to know the
value(Re) of the ONE resistor which will replace threethat are hooked
up as follows:
there are two resistors in parallel, both of resistance R, and
another of the value R in series with the parallel combination. OK?
first, i would find the equivalent of the parallel combination:
that means i could replace the parallel combination with a single
resistor of this value:
Rparallelcombo = R*R/(R+R) = R/2; correct? or, if i want, i can work
in "admittance space"
1/Rparallelcombo=1/R + 1/R = 2/R; correct? solve for
Rparallelcombo = R/2; correct? [same answer both ways!]
so far, my equivalent circuit is the original series resistor with
value R (remember it?) in series with a new resistor (R/2) replacing
the original parallel combination. what resistor would i use to
replace the new series pair?...
Re = R + R/2 = 3R/2 = 1.5 R, correct? these aren't apples and
oranges, they are all resistors. i took a foray into "admittance"
(ok, conductance) just as an optional, but not necessary, detour.
however i arrived at the equivalent resistance of the parallel
combination, i can simply treat it as a series resistor, and
combine it (by simple addition) with the other original series
resistor.
total Re = 1.5 R
now the EXACT same reasoning (i.e. current is the same through
series elements, potential is the same across parallel elements;
... these are physical principles) can be used with resistors and
reactances. the math is more of a pain, what with complex numbers
requiring "rationalization of the denominator" and stuff like that,
but i don't have to return to first principles every time, because
the equations have been solved, and they are in books!
this stuff works! if it didn't, i couldn't "design" (with a paper
and pencil ... or even a computer program) any circuits.
finally, i don't recall anyone ever saying that rich's nichrome wire
supressors didn't work. they have resistance, they have
inductance, they even have a bit of lurking capacitance.
depending on the frequency, they can look just right for the job!
the question in my mind is whether they are always NECESSARY.
i didn't get to go to dayton, so i had time to spend on this!
73,
George T. Daughters, K6GT
--
FAQ on WWW: http://www.contesting.com/ampfaq.html
Submissions: amps@contesting.com
Administrative requests: amps-REQUEST@contesting.com
Problems: owner-amps@contesting.com
Search: http://www.contesting.com/km9p/search.htm
|