Today continued a run of some great class time working on electric circuits. Our whole class period (85 minutes) consisted of looking at the following six circuits:
A student blurted out this would be a short circuit, so things would get hot. Everyone immediately agreed (WHY DID YOU BLURT THAT OUT!). Still time to save it; I ask why it is a short circuit?
Answer: Because the path through the wire is shorter than traveling through the resistors.
Groans from students...then a more refined answer about differences of resistance between the two branches of the wires.
Tell me anything you can tell me about this circuit. If you see something to calculate, calculate it. Build the circuit on the PHET circuit constructor and show that your calculations confirm what happens in the simulator.
Insert student-centered-learning opportunities and fantastic conversations between students here. Students seeing a difference between their answers and what the simulation is telling them causes conflict that they help each other to resolve. Some students bring up the term 'parallel', which I've never said in class. Others don't understand what that is, so there is some fighting. One student describes qualitatively what should happen and then shows he is correct in the simulation, no calculations. Furthermore, this student usually is one that gets anxious when there are limited formulas to cling to, which is the norm in my class.
Repeat the same procedure. Calculate what you can calculate. Build the circuit in the simulator and verify. Explain away differences, or see if there is something you are missing.
Continued progress in recognizing this is a combination of series and parallel resistors, but I don't make a big deal out of this. A couple students look up formulas and discover the idea of finding equivalent resistance (which I have never mentioned to them). This helps, but the simulator telling them what the correct answers are is key. They are compelled to get the simulator's answers through calculation - it's almost as if they feel the simulator is cheating by giving them the answers, so they must understand how to get it on their own. Eventually, they are convincing each other why they are right.
Same as before, tell me anything you can tell me about this circuit. If you see something to calculate, calculate it. Build the circuit on the PHET circuit constructor as a last resort and to show that your reasoning has led to a correct analysis of the entire circuit.
This time the students hit a wall. Some continued finding equivalent resistance and the battery current, but weren't sure how to find the current through the 10 ohm and 30 ohm resistors. One reasoned it would split proportionally, and confirmed the answer using the simulator. Another measured the voltage across one of the 10 ohm resistors using the simulated voltmeter, measured the current, and then calculated the voltage difference across it. Repeating for the other resistor, they figured out the voltage difference across the parallel resistors, which then led to a current calculation. Again, I only had to tap students in the right direction - the rest was them helping each other.
Try to analyze this circuit completely using what you have learned today. Once you are convinced you have accounted for all voltage differences and all current, build it in the simulator to confirm your answers. Find a way to calculate the power used by the 20 ohm and the 10 ohm resistors separately - look it up if you want.
They did a fantastic job of figuring this out - some very quickly and quantitatively. One student that oftenstruggles with concepts figured out how the current between the different branches would compare, and reasoned which ones would have the greatest voltage difference across them.
Then I started lecturing about the equivalence of electrical power and mechanical power, and the magic disappeared. They stopped talking and returned to compliance mode. I saw that happening, so I stopped. Anything I could do at this point would only ruin what was quite possibly a perfect learning experience for them.
When I taught AP Physics, we spent a day on series circuits and deriving resistance formulas, a day on parallel circuits and deriving equations for parallel resistors, and then another day on analyzing circuits that have both. Before today, I had never used the term 'parallel' with my students. This time they brought it up. They now have the ability to analyze the same level of circuits as my former AP students, but this group was able to figure much of it out on their own, with no mention of memorization of formulas and no extended periods spent listening to me blabber on about how 'going through the theory helps you understand'.
There is lots I could say about this, but I think the points made are pretty clear. Let's just say that I'm really proud of my students work today.