Just The Facts: circuits

Been busy busy here, preparing for the USIYPT and writing 6000 words worth of 3rd marking period comments.  Colleagues and readers have asked a few times, "what do I need to teach about foo?" where foo is some sort of physics topic in AP, honors, general, or conceptual physics.  I've wanted to be able to QUICKLY point to a text or handout that gives a good, clear answer.

Problem is, textbooks tend to cover way too much -- the whole point of the textbook is to be comprehensive so the professor can choose what portions of each topic to teach.  The College Board's or the Regents Exam's course descriptions either give too little detail by saying merely "teach circuits", or they go into impenetrable edujargon ("The student should be able to compute the equivalent resistance of a set of series resistors, parallel resistors, or combinations thereof including but not limited to up to 5 resistors connected or not connected to a DC power source, unless there are more than two men on base.")

My colleague Curtis has asked me to write some blog entries giving "just the facts" that I feel are appropriate for an honors or AP introductory physics course.  Without knowing it, I had given him a useful blueprint for teaching conservation of momentum in collisions with this post.  I gave more detail than he wanted in this fluids lesson plan I wrote for the College Board, but he still found the article a useful basis for answering the question "what do I need to cover in static fluids?"

So today, I will list briefly Just The Facts that I teach when covering circuits in my honors physics course.  When I cover this or any unit, I usually start by writing key facts and equations on the board, then quizzing the students the next days to make them remember those facts and equations.  Over the course of a week or two, the class develops their ability to reason with the equations and facts, and to solve problems in the topic area.

In circuits, we need to know the following:

Definitions:

* V represents voltage, measured in volts (V).  Voltage is measured across a circuit component using a voltmeter.

* I represents current, measured in amperes (A).  Current flows thru a circuit component, and is measured with an ammeter.

* R represents resistance, measured in ohms (Ω).

* The symbols for batteries, resistors, ammeters, and ohmmeters

Ohm's Law

Ohm's law relates voltage, current, and resistance by V = IR.  Ohm's law may only be used if the current I and the voltage V are experienced by the resistance R.  (That means we can't randomly pick a voltage and a resistance from the problem and divide to get current; we must be sure the voltage we plugged in is actually measured across the resistance we're considering.)

Power

Power is given by IV, subject to the same usage restrictions as ohm's law.

Series Resistors:

* The current through each is the same, and equal to the total current

* The voltage across each is different, and adds to the total voltage

* The equivalent resistance is given by straight addition of individual resistances.

Parallel Resistors:

* The current through each is different, and adds to the total

* The voltage across each is the same, and equal to the total

* The equivalent resistance is given by an inverse formula, 1/R = 1/R + 1/R

Solving DC circuits up to 4 or 5 resistors with a single battery

* Simplification of basic resistance networks

* Calculating current, voltage, resistance, and power

* qualitative questions: "when another resistance is added in series, what happens to the current from the battery?"

Light Bulbs and circuits in a laboratory setting

* A light bulb's brightness is determined by the power it dissipates.

* A bulb has a known resistance which doesn't change no matter what the bulb is hooked to.

* An ammeter is connected in series with a circuit element

* A voltmeter is connected in parallel with a circuit element

{The following are also required on the AP exam}

Kirchoff's rules

* Current entering a junction equals current leaving a junction, a statement of charge conservation

* Voltage changes around a closed loop equal zero, a statement of energy conservation
* Deal with multiple battery circuits, but NOT with three-equation three-variable problems

Resistance of a wire based on the wire's properties

* R = ρL/A

Please communicate with me

Is this sort of post useful?  I mean, this is everything I teach in circuits.  Sure, I haven't discussed the exact methods by which I teach how to solve for current through the 100 ohm resistor, or the lab activities that I do.  I actually discuss many of those things elsewhere on the blog; please search.  And you may agree or disagree with what I consider fundamental for a first-year physics course.  Conceptual physics would probably eliminate the calculational aspects; AP Physics C needs to include RC, RL, and RLC circuits.  My question is, is this list of facts and skills a useful starting point for you to figure out your own list of facts and skills for your students to understand?  Please comment.

GCJ