From darwin@laser.nip.upd.edu.ph Sun May 7 09:01:02 2000
Date: Sun, 7 May 2000 01:02:07 +0800 (PHT)
From: Mr. Darwin Z. Palima <darwin@laser.nip.upd.edu.ph>
To: "phys-l@lists.nau.edu: Forum for Physics Educators" <PHYS-L@lists.nau.edu>
Subject: Re: R=V/I
The problem with using R=V/I as an operational definition for resistance
arises from the students' (mis)understanding of (inverse) proportionality.
Seeing a relation such as R=V/I, many students are quick to conclude that
R is proportional to V and inversely proportional to I.
But that is not how we understand (inverse) proportionality:
R is proportional to V if I remains a constant with variations in V.
R is inversely proportional to I if V remains a constant with variations
in I.
I usually ask my students whether the power P associated with a resistor
is proportional or inversely proportional to resistance R, after
discussing the equations:
P = I*I R and P = V*V/R
When (as usual) i encounter blank stares, i recognize that they might have
a problem with (inverse)proportionality.
I would then go about reviewing the concept:
A proportional to B
is represented in an equation as
A = k*B
where k is a CONSTANT.
Therefore, we don't say that P is proportional to R unless I is held
constant. The same goes for the inverse proportionality.
Clarifying the idea of proportionality can eliminate similar confusions in
using C =Q/V as operational definition of capacitance.
It's not a surprise that students have difficulty with proportionality. As
a listmember claims, their math difficulties/problems start with
fractions.
I don't find anything wrong with operational definitions. When properly
understood, they help the student think of a situation on how they will be
able to measure the physical quantity in question.