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22 February 2017

Rank the voltages: experimental evidence

 The question: 

The three circuits above are all connected to the same battery. Each resistor represents an identical light bulb.  Rank the circuits from greatest to least by the potential difference across bulb A. If more than one circuit has the same potential difference across bulb A, indicate so in your ranking.

The (very much in-depth paragraph-style) answer: Since all bulbs are identical, they have the same resistance.  By Ohm's law with the same R for each, whichever bulb takes the largest current also has the largest voltage (i.e. potential difference) across it.  

The equivalent resistance of the parallel combinations gets smaller the more parallel resistors are added.  So circuit 1 has the largest equivalent resistance, with circuit 3 the smallest -- consider each resistor to be 100 ohms, and you get 200 ohms in circuit 1, 150 ohms in circuit 2, and 130 ohms in circuit 3.  

Bulb A takes the total current in each circuit, so consider Ohm's law for the circuits as a whole.  In that case, the voltage of the battery is the same for each; the circuit with the smallest equivalent resistance takes the largest total current.  So rank the circuits 3 > 2 > 1.

The common misconceptions: I gave this to my class as a quiz, and most got it wrong.  I saw four typical categories of wrong answers:

* Since the batteries are the same, each bulb in each circuit takes the same voltage.  (No, just each circuit as a whole takes the same voltage.)

** Since the batteries are the same, they each provide the same current.  (No, batteries provide voltage, not current.)

*** Since bulb A is closest to the battery, it must take the greatest voltage.  (No, "closeness" to the battery has no bearing on a circuit problem.)

So far, this is standard fare misconception-bustin' physics teaching.  Because I posed this problem as a quiz, the class waited expectantly for me to reveal The Answer.  Ho hum... those who got it right reflexively pumped their fists, those who got it wrong either made sad eyes, or used some sour-grapes reasoning to convince themselves why they could have gotten it right.  And then they forgot the whole thing.

Or did they?

"Okay, there are the light bulbs.  You know where the wires and power supplies are kept.  Go set up the three circuits and show me which bulb A has the largest current.  Take a picture of your circuits to show me."

Ah, sh*t just got real.  

The photos are by my student Clay Tydings.  He conveniently labeled bulb A in each picture.  Now we can all see that bulb A is brightest in circuit 3.  

To address the misconceptions above, you can have the students measure voltage across the battery, and across each bulb, with the voltmeter.  If you're brave, you can even have them measure current from the battery.  They'll see The Answer, that bulb A carries the largest current in circuit 3.

But they also see that (*) the bulbs take different voltages, (**) the battery takes the same voltage every time but different currents, and (***) the voltages across each bulb don't change even when we place bulb A "last" rather than "first" by switching the leads from the battery.  

I find myself asking the class to set up the experiment proposed by a quiz problem all the time in AP Physics 1.  We've established the class's lab skills; we have introduced and practiced all topics at a basic level; we have 90 minute class periods with which to work.  So why not make the students verify an answer experimentally?  The AP exam will certainly ask them how to design experiments!

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