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03 March 2009

Test - Correction - Recall Quiz

There's only one assignment you can give on which you can be sure of the class's full attention:

A test.

Thus, it's useful to sqeeze every last bit of usefulness you can out of a test. The cycle I try to use on every test all year is test - correction - recall quiz.

Consider the exam I gave last week. One of the questions was #3 from the 2007 AP Physics B exam. I can't post the question itself here, but you can get it at the College Board's archive of AP physics B exam questions. The problem shows a simple circuit and asks for a ranking of resistors in order of their current and voltage. Then, a capacitor replaces a resistor; students are asked to calculate current through the resistors and voltage across the capacitor.

The Test
On the test itself, most of my students get the ranking task and the calculation. The difficulty comes when the capacitor is added. Still, my class averaged 10.9 out of 15 points. That's 73%, or well into the range for an AP score of 5. (That's also a full standard deviation above the national average of 6.0 points. Statistics for many exam questions can be found at the archive page linked above.)



The Correction
In a test correction, students earn back half the points they originally missed by redoing the lettered parts they got wrong. Of course, I sometimes ask an additional question, or change the given values, so that they can't just parrot, they have to think about what they did wrong.

The most common mistake on the voltage ranking task is to assume that the first resistor takes the most voltage simply because it's first in line; or, to assume that the first resistor takes all 12 volts of the battery. Thus, for part (b) I ask the additional question:

First, draw me an example of a circuit in which the FIRST resistor does NOT experience the largest voltage across it. Explain your answer.

Now, justify the ranking you gave to the three voltages.


For the calculations in part (c) and (d), I simply change the R value from 100 ohms to 200 ohms so that they'll have to pay attention when they redo the circuit problem.
The most extensive part of the correction is for part (e), calculating the charge on the capacitor -- because that's the part that most people missed. I use the original question, but I add the following parts:
i. Diagram the new circuit.

ii. What does a capacitor do in a circuit?

iii. Explain how to figure out the voltage across the capacitor.

iv. Now calculate the charge on the capacitor.


The Recall Quiz
You might well be familiar with my "fundamentals quizzes," which test the basic facts that must be memorized before higher-level physics problem solving can happen. The third step in my testing process is to remind my class of the fundamental physcis facts behind each question. The questions on these recall quizzes are a bit too involved to ask on my regular fundamentals quizzes, because I assume familarity with the problem. The recall quizzes usually only ask about the most-missed issues on the original test -- there's no use beating a dead horse. Thus, the the recall quiz dealing with AP Physics B 2007 #3 only discusses the capacitor:


A capacitor is in parallel with RC in the circuit shown above.

i. Check one and explain briefly: After a long time, the voltage across the capacitor is

☐ Greater than e
☐ Less than e
☐ Equal to e

ii. Rank the current through the three items RA, RC, and C from greatest to least, with number 1 being greatest. If two items have the same current, give them the same ranking. Justify your ranking briefly.
____ RA ____ RC _____ C

iii. Rank the voltage across the three items RA, RC, and C from greatest to least, with number 1 being greatest. If two items have the same voltage, give them the same ranking. Justify your ranking briefly.
____ RA ____ RC _____ C

GCJ

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