Re: Series, Parallel, and Resistivity Equations

[Larry Woolf <Larry.Woolf@GAT.COM>]

I also came to this insight about 5 years ago, never having seen it in any
physics texts. I use it in quite a bit in a module I wrote:
The Line of Resistance: Using a Graphite Pencil to Explore the Electrical
Properties of Materials and Circuits
http://www.sci-ed-ga.org/modules/materialscience/lor/index.html

Drawing graphite lines on a piece of paper and measuring their resistance
shows the correlation in an obvious way.

1. Draw 2 consecutive pencil (use graphite pencil from an art store or
mechanical pencil) lines and measure their resistance (make the lines about
a 1/4 inch wide:

----------R1----------   -------------R2-----------

Now connect them up by adding a little pencil spot


------------------------R3------------------------

You find R1 + R2 = R3

Two resistors in series is nothing more than a long resistor.


2. Draw two parallel pencil lines very near each other and measure their
resistance:

----------------------------
--------------R1-----------
----------------------------

-----------------------------
---------------R2-----------
-----------------------------

Now connect them up using a using your pencil:

-------------------------------
-------------------------------
-------------------------------
--------------R3---------------
--------------------------------
--------------------------------
---------------------------------

You find 1/R1 + 1/R2 = 1/R3
and 2 resistors in parallel is nothing more than a wide resistor.
(Note: the above diagram is not to scale - the width should be at least a
factor of 5 less than the length.


I'll be presenting a workshop on this and 3 other units at NSTA in San
Diego if anyone's interested.


At 2:03 PM -0700 2/18/2002, Tim Folkerts wrote:
> 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.

Dr. Lawrence D. Woolf; General Atomics, 3550 General Atomics Court, Mail
Stop 15-242, San Diego, CA 92121