Re: [Phys-l] Thermal heating in a resistor?

["John Clement" <clement@hal-pc.org>]

The choice of formulas is certainly dependent on the textbook author's bias,
and often the reasoning behind it is opaque.  So yes.  I think this answers
the questions, but it does not answer why?

There have been other suggestions, some of which are very good.  I would say
that the primary formula should be P=IV or VI.  This is because students
have to understand that it is analogous to working which is force x
distance.  (Ok divide by delta t to get power)

What are some other possible rationales?  The P=I^2V certainly brings out
that it is a quadratic, and it also brings out the idea that it is current
that causes electrical energy to be transferred to thermal energy.  A simple
microscopic model of electrons bouncing off of atoms and transferring
kinetic energy can be visualized.  This simple model is well within the
grasp of beginning students and is used in Workshop Physics.

Unfortunately this formula has problems with non-ohmic resistors, while
P=V^2/R does not.  So this third formula can be used as part of an
explanation of why light bulbs flash brightly before burning out.  It also
might be preferred if you are using the model that a battery produces a
constant voltage output.  This formula also suffers from the problem that it
has a division, which throws students for a loop.  Many HS and some college
students do not have a good understanding of compensation reasoning so a
division sign in a formula makes is harder to understand.  I contend that
many HS students use division for hard problems, and addition for easy ones
because they use the difficulty as an indicator for the type of math to use.

The idea that the 3 formulas should be treated as equivalent and used
according to the information given is a poor idea because it results in
equation hunting rather than doing concept based problem solving.  They are
certainly equivalent as long as variations in R can be ignored.  This same
problem happens with the 4 SVT equations of motion, so research based books
do not introduce them in the beginning, but students are required to use a
smaller set of equations and reasoning.  Often this requires graphs to
figure out what is going on.  Indeed there is evidence from Modeling that
learning to use graphs first without specialized equations results in better
understanding and problem solving.

The big battle is getting students to first think in terms of models as to
what is going on, and then to use equations as appropriate.  Unfortunately
most textbooks are poor at motivating this.

A curious point of view came to my attention in college.  My E&M instructor
told a story about a friend who was applying to the army to be an engineer.
So he took the test and it asked the following:  Give the 3 fundamental
equations of electromagnetism.  Well he was nonplussed.  There are 4 Maxwell
equations, so he picked the two that he considered the most basic, and then
thought "maybe these are practical men".  So he added V=IR.  That was the
only item he got right.  I don't think I need to give the other 2 equivalent
fundamental equations.

Actually I prefer I=V/R and a=F/m_net because then students can build a
mental model that force produces acceleration and voltage produces current.
They also may be part of an effort to build compensation reasoning.  Yes I
know that causality is not implied by these equations, we have been around
that many times.  But I also know that student thinking proceeds through
various stages (with detours of course).  This is one thing Piaget showed
with his seminal experiments.  So you can't jump to a purely abstract view
of equations without first going through certain natural stages, one of
which is the idea that force produces acceleration.  Similarly conservation
reasoning is generally acquired before proportional or compensation.  And
formal reasoning is much later and even much rarer.

John M. Clement
Houston, TX

> Why is the formula P=I^2V used to describe thermal power loss in resistor
> instead of P=IV or P=V^2/R? Is this just the textbook author's choice of
> formula?