Re: [Phys-L] widget rate puzzle ... reasoning, scaling, et cetera

[Philip Keller <pkeller@holmdelschools.org>]

I would start at the other end of the process.  After we define 
resistance, I give my students a two-part question:

1. We apply 1 volt across a device and measure a current of .2 A. Find 
the resistance.

That usually goes fine.

2.  We increase the applied voltage to 3 volts.  Find whatever you can.

I let them work on that for a while, arguing in groups.  Then we discuss 
what answers they have come up with.  There are usually some who guess 
that resistance stays constant.  Others guess that current stays 
constant.  And some just give up, feeling (correctly, as it turns out) 
that they don't have enough information.

By this time of the year, they know that I would LIKE for them to think 
about proportions and ratios, but they don't know what stays constant.  
To settle the question, we do an experiment.  First I use a resistor, 
but then I use a little light bulb.  The resistor behaves nicely -- the 
current triples.  The light bulb not so much. So on the first day that 
they hear the word "ohmic" they discover that it is a property that some 
devices have and others don't.  I don't even like to call it "Ohm's 
Law".  I call it  "the Ohmic property".

But once it is given that something is ohmic, then yes, this is another 
setting to practice with ratio thinking.



On 1/2/2015 5:39 PM, Richard Tarara wrote:
> On 1/2/2015 4:21 PM, Robert Cohen wrote:
>
> It is quite likely that students having problems with this are too 
> focused on the algebraic equation...Ohm's Law...without much 
> understanding of what the three quantities in that equation actually are.
>
> I'd be careful to introduce and discuss current, resistance, and 
> voltage thoroughly before introducing Ohm's Law.  I will have my 
> classes come up with an equation for the resistance of an object 
> through analogy and simple reasoning.   They will even come up with 
> the idea of temperature dependency (which we then say we usually 
> ignore!)  But at this point, sans the temperature component, the 
> resistance of a given object (yes, between two specified points) is 
> fixed by its geometry and material.
>
> With that idea firmly in place, students may be less likely to try and 
> solve for the resistance as V/I and then be befuddled because they 
> don't know that the current is.
>
> To be honest though, I've never actually used the question below in 
> quizzing, so not sure how my groups would have fared.
>
> rwt
>
> > How about the following? Students frequently have trouble with it. An 
> > ohmic resistor of resistance 10 ohms allows 1 A of current to flow 
> > when a voltage of 10 V is applied across it. What is the resistance 
> > of the SAME resistor when a voltage of 100 V is applied across it? 
> > How would you help students who have difficulty with this question? 
> > Philip Keller wrote:
> > > They are already functioning at the edge, not completely convinced 
> > > that thinking is a way to find things out.
> > When formulating your answer, keep PK's quote in mind.
> >
> > _______________________________________________