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Solution to the AP-Style Question
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by Greg Jacobs
Woodberry Forest School
Woodberry, Virginia
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| | Consider three commercially available, standard incandescent lightbulbs, each rated for use on a standard 120 V wall outlet. Bulbs A and C are rated at 100 W; bulb B is rated at 60 W. (For the questions below, ignore any effects of temperature on resistance.)
a. Determine the resistance of each of the three bulbs.
Answer:
b. Consider that bulbs A and B are connected in series with each other and with a 120 V wall outlet.
i. Fill in the chart above for each bulb in the series circuit.
Answer: Start with the total circuit. Resistances in series add algebraically, giving an equivalent resistance of 380 
. The voltage of the battery is 120 V. Use Ohm's law to get the current flowing from the battery:
Since the bulbs are in series, this current flows through both bulbs. Find the voltage across each bulb by applying Ohm's law to each bulb individually:
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(the sum is not precisely 120 V because of rounding). |
Now calculate power for each bulb from P = IV:
The chart looks like this:
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Voltage |
Current |
Power |
| Bulb A |
45 V |
0.32 A |
14 W |
| Bulb B |
77 V |
0.32 A |
25 W |
ii. Indicate which bulb is brighter. Justify your answer.
Answer: Bulb B is brighter. According to the chart, bulb B dissipates more power.
c. If, separately, bulb C is connected directly to a 50 V source, how will its brightness compare with that of bulbs A and B in part (b) of this question? Explain.
Bulb C has 140 W of resistance. The power it dissipates when connected to 50 V is 
. So bulb C will be brighter than bulb A and dimmer than bulb B.
d. Now bulbs A and B are connected in parallel with each other and with a 120 V wall outlet. Determine the total power dissipated by this circuit.
Answer: 120 V is the rated voltage for each bulb, so each bulb will dissipate its rated power. Bulbs A and C dissipate 100 W; bulb B dissipates 60 W. The total power is the sum of the power dissipated by each bulb, 260 W.
Commentary
- A similar problem about the brightness of lightbulbs appeared on the 2002 AP Physics B Exam. If you want evidence that AP Physics B is far more about conceptual understanding than about mathematical virtuosity, this problem is as good as it gets. The actual math necessary for the solution might charitably be called eighth-grade level, yet this is a tough question. On the 2002 exam question, students averaged 6.7 out of 15 points, putting it in the category of "above average" difficulty.
- By far the most common mistake is to assume that power, not resistance, is an unchanging property of the bulb, leading to incorrect answers in part (b) and beyond.
- Interestingly, a number of students who get part (b)(i) and recognize that power correlates with brightness are still hesitant to state that the bulb rated at 60 W is brighter than the one rated at 100 W.
- A less common but more worrying mistake is to forget that the current through series bulbs must be the same through each, and that series resistors add algebraically to get the equivalent resistance. Teachers cannot drill in this point enough: parallel resistors take the same voltage but split current; series resistors take the same current but split voltage.
- Some students see the word "parallel" in part (d) and interpret that to mean that the power of the bulbs must add inversely (like the equivalent resistance of parallel resistors). But this betrays a misconception of the meaning of power. Whether in electricity or mechanics, power is a measure of energy per time. A bulb dissipating 100 W converts 100 joules (J) of electrical energy to heat energy every second. Another bulb dissipating 100 W does the same thing. So two bulbs, each dissipating 100 W, must convert 200 J of energy each second, regardless of how these bulbs are connected to one another.
- When I assign this and similar questions, I see some students covering the page with intense calculations. They are wasting their time. I want my students to develop an instinct for the level of calculation necessary in a typical AP question. It is very rare that a circuit problem requires any kind of intense algebra.
- How do I prepare my students for AP-style circuit questions? I try to avoid the temptation to assign calculation-intensive homework questions. Certainly texts include some very interesting problems involving the simplification of a horrendously complex circuit; some circuit situations can be elegantly approached with a three- to five-variable system of equations and matrix mechanics. But no matter how good the question may be, no matter how fun it was for me to solve that question when I was in college physics, I do my students a disservice by assigning it. AP Physics tends to focus on a reasonably deep conceptual understanding of the behavior of circuit components and generally requires only basic calculations in circuit problems.
- So what kinds of homework questions do I assign? To begin with, I make sure students can perform the basic skills -- simplifying three or four resistors into one equivalent resistor, calculating the current and voltage for each.1 But after that, I try to challenge students' conceptual understanding. Most texts have a section of conceptual questions before their numerical ones. Usually a few of these are appropriate.
- When you do assign numerical problems, be sure that you require students to explain their understanding in words. For example, they should check the reasonability of some of their answers. Parallel resistors should have currents that add to the total current through the branch; series resistors should have voltages that add to the total voltage across the circuit segment.
- Reasonability of the answers to the AP-style question: Interestingly, household bulbs and miniature bulbs can carry similar currents. The miniature bulbs are usually rated in the hundreds of milliamps; I found the household bulbs in the AP-style question to carry 320 mA.
Note
1. I assign an "intense review of basic circuits" from Greg Jacobs and Joshua Schulman, 5 Steps to a 5: AP Physics B & C (New York: McGraw-Hill, 2005
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