Re: brightness vrs. power

[Robert A Cohen <bbq@ESU.EDU>]

Back in May, this list had a discussion regarding Ohm's Law and the
resistance of light bulbs.  I posted a question on the following series
parallel configuration:
            /-----X------X-----\
       -----                    -------
            \-----X------X-----/
vs. a single configuration:
       ---------------X----------------

I wrote that I thought beginning students would guess (assuming constant
resistance) that the total current in each case would be the same and so
each light bulb in the second circuit would be half as bright as the lone
light bulb in the first circuit.

In response to that post, Brian Whatcott wrote:

> If Robert believes that beginners expect twice the illumination from the
> same electrical power input to a series parallel arrangement of four
> bulbs as to a single bulb, does he give them too little credit, or do we
> give him too much? :-)

In response to Brian I reaffirmed my belief that beginning students (who
assume R is constant) will guess that the four lights *together* will be
brighter than the one alone (but that each individual light will be dimmer
than the one alone).

John Mallinckrodt then posted a message which implied that he disagreed
with me and suggested that rather than underestimating my students I was
making the same mistake I assert my students would make:

> I think brian was alluding to an apparent error in your own reasoning:
> Under the naive assumptions 1) that the resistance is independent of
> current and 2) that the illumination from each bulb is proportional to
> the electrical power consumed by each bulb, the students should predict
> that the total illumination is the *same* in both cases.

Well, I happen to be teaching a 6-week non-calculus physics II course this
summer to 4 students (via a somewhat personalized system of instruction
method).  I just gave the above problem to the students.  One was unable
to answer the question.  The other three all assumed the light bulbs would
have a constant resistance (as I asserted they would) and said the total
current would be the same (as I asserted they would).  While one said the
*total* brightness would be the same as before, the other two said each
light bulb would have the *same* brightness (I was wrong - I thought they
would say the brightness would decrease to 1/2).

Let me also say a word about the preparation of the students.  Although
the pace of the course is pretty quick, I think the course is pretty
normal otherwise.  All four students are pretty average (which corresponds
to a C).  The students have finished a unit on Electric Forces, Fields and
Potentials, and are currently in the midst of a unit on DC circuits.  They
have already covered Ohm's Law.  They measured the dependence of
resistance on material, length, area, temperature and potential
difference.  (note: they found the relationships before reading from the
book what the "correct" relationships should be).  The difficulty in
measuring a value for the resistance of a light bulb was also covered.

They then do a lab in which they investigate the equivalent resistance of
resistors in series and parallel.  As part of this they investigate
internal resistance as well.  In the last part of the lab, they come up
with a relationship for resistors in series (R = R1+R2+...) and parallel
(1/R = 1/R1 + 1/R2...) and test it by extending their measurements to
three resistors.  They then test their relationship by applying it to
lightbulbs.  Of course, they find the relationship does not hold.  After
much mind probing, I finally reminded them that the resistance of each
light bulb depends upon temperature and that the temperature changes with
current.  Note: I did *not* mention the relationship between brightness
and current (neither the naive assumption that illumination is
proportional to current nor the "real" relationship that was discussed in
the list).

It was *right* after this lab that I asked them to complete the "quiz" on
the series-parallel configuration.

I am alone in the quality of students I get?  Do people still think I
underestimate them?  Am I guilty of poor understanding of the concepts
myself?

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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