Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Series, Parallel, and Resistivity Equations



I've always done both. I also have the students 'derive' the resistance
equation. I will use an analogy of running--on different surfaces, through
the woods versus in the open, a short run versus a long run. As with all
analogies it isn't perfect, but it does get them to recognize the
geometrical and material dependencies. One can even include temperature and
the effect does go in the same direction--to a point.

I've used texts that make the geometrical connections to series and
parallel--although sometimes only in the problems.

Rick

**********************************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556
rtarara@saintmarys.edu

FREE PHYSICS INSTRUCTIONAL SOFTWARE
www.saintmarys.edu/~rtarara/software.html
PC and MAC software
NEW! SIMLAB2001--DYNAMIC CARTS now available.
CD-ROMs now available
******************************************************
----- Original Message -----
From: "Tim Folkerts" <tfolkert@FHSU.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, February 18, 2002 4:03 PM
Subject: Series, Parallel, and Resistivity Equations


I don't know why it had never occurred to me before, but the equations for
the series an parallel resistors are contained within the equation for
resistivity. The texts I just checked all do the traditional derivation
using either equal currents or equal voltage differences, but none seem to
appeal to this simple argument.

Consider a resistor of uniform composition and diameter, with length L.
Cut it into two pieces of length L1+L2=L, which will have resistances of
R1 = (rho/A)L1 and R2 = (rho/A)L2.
So R1+R2 = (rho/A)(L1+L2) = (rho/A)L = R

Consider a resistor of uniform composition and diameter, with length L.
Slice it lengthwise into two pieces of area A1+A2=A, which will have
resistances of R1 = (rhoL)/A1 and R2 = (rhoL)/A2.
So 1/R1 +1/R2 = A1 /(rhoL) + A2 / (rhoL) = (A1+A2) / (rhoL) = 1/R

But the circuit doesn't care about the geometry of individual resistors,
so
any other resistors with R1 & R2 would behave the same.

Surely this isn't a new idea, and it's not surprising, but it was new to
me. Does this seem like a reasonable way to introduce series & parallel
resistance? Or perhaps just use it as a way to reinforce the traditional
derivation?

Tim Folkerts