And a correction: I gave back some graded HW quiz, and on the 2006 question, Part e, I at first wasn't accepting Lenz's Law as a justification. But upon further thought, writing the answer "increases" on Part e and defending it with Faraday's Law could possibly be partially correct, depending on how the response is worded. If you think you might be eligible for this additional one point of credit, you can read my attachment here where I wrote "Correction" and see if your expressed idea matches. (Again, it only explains part of the phenomenon, and I do think my standard answer is more complete and efficient, but I'm happy to have the conversation if you wrote something relevant involving Faraday's Law. If you're in doubt, see the attachment.)

 

*Note: the version of the attachment that I delivered to people during 6th period on 5/10 did not at that time contain the correction.

 

1-10: BACAEDBECE

11-14: CCCA

15-16: DD

17-25: CDEADECDB

 

Topic List from the Whole Year

 

Attachment 1 - see it, quick key to today's simple inductor circuit grade

Attachment 2 - see it, very thorough resolution to circuit review things I brought up, not sure how much of this review a person needs.

 

And I said that the following are quiz topic candidates for Wed. May 2: "Anything from Unit VIII and time constants in circuits." Since I said time constants, that could mean R/L, RC, or oscillations involving L and C.

 

Look for me to post more Mock AP multiple choice exams very soon.

 

Quiz of 4/30 will involve the following applications:

 

Using the loop rule in a circuit scenario that could have inductor, resistor, and/or capacitor.

Using the junction rule in a circuit scenario that could have inductor, resistor, and/or capacitor.

 

This isn't news. And lots of practice in the workbook in Units V and VIII and in the attachments to this posting. These attachments have been here for a couple days, with the exception of the Diagnosis one I posted on Sunday 4/29.

 

The LC Circuit Analysis note set attached to this will be of limited value, because it has no junctions in the circuit presented. But the LR Notes do have a junction and are high-level practice.

 

Sunday posting: The document (with the word Diagnosis in its title) is a careful diagnosis of the quality of awareness a person has of the main idea described below. FINAL UPDATE: The Diagnosis document has two Diagnostic problems in it, as of 5:50 PM. And it's now complete. You now have more than enough material, because the workbook is thorough on this stuff as well. And I've long since posted workbook Unit VIII solutions.

 

Main ideas:

 

(If someone thinks the list below is too abstract or symbolic and can't visualize it, then don't use it. Everything that's important to stress is in both my and McGehee's practice documents. I'm just naming the big priorities below. I've used symbols as they were on the board, but maybe they don't translate well in this clumsy Edlio format. No matter, the practice docs are good.)

 

Main idea of circuit section of the class of 4/26: to recognize what the voltage forms are. These are RI, (1/C)Q, L(dI/dt). And to recognize the charge forms. These are Q, C*Voltage, the integral off Idt. And to recognize the current forms. These are dQ/dt, I, Voltage/R, the integral of (dI/dt)dt, which means the integral of (Voltage/L)dt. But big deal. The question is do you know what to do with these forms in something like expressing the loop rule. Do you know what to do with these forms in expressing the junction rule. That's why there were setup tasks on the board, where, given a circuit, you were supposed to value writing expressions like "Voltage1 = L(dI/dt) + RI"

 

And anyone who thinks that's a memorized thing has no idea what I'm talking about. The lesson strongly stressed the skill of going from a diagram to making a unique expression in the format of the one above in quotes. Such a unique expression is customized to whatever circuit diagram is being examined, so this is a communication skill that is being stressed NOT KNOWLEDGE OF FORMULAS. Anyone who doesn't know precisely what I'm talking about needs to get up to speed by using the practice applications and posted solutions notes.

 

Exercise: Figure out what circuit should be drawn if one claims that the following two loop expressions are true for it.

 

Voltage1 = L(dI3/dt) + R1I1 + Q1/C1

Voltage1 = R1I1 + R2I2 + Q2/C2 + Q1C1

I1 = I2 + I3

 

If a person doesn't decipher these three to draw a circuit that corresponds fundamentally to the three expressions, then that person doesn't understand what math usage in circuitry is for. Writing math will only hurt such a person.

Furthermore, realize that a meaningful solution-writer should have no trouble changing one of the two equations above (you figure out which) into something like:

 

Voltage1 = [Resistor1 Voltage] + R2I2 + Q2/C2 + [First capacitor voltage]

 

Equation-writing flexibility is what I'm talking about. Those who don't have such flexibility turn the simplest 10-second solutions into a half hour of formula-driven complication, time-wasting, and wrongness. If this little message is failing to show you what flexibility is, then don't trust it. Use my good word documents or McGehee's. And diagnose yourself with those tools.

 

People who speak fundamental circuit language never say, "Oh, I can't do capacitors." That's a copout statement from one who hasn't practiced and doesn't know that Kirchhoff's Laws are universal and apply to all circuit elements, so no circuit element is "the difficult one".

 

How come: Because to do well on the graded thing of 4/26, you had to clearly express the B of a standard solenoid. A number of people who couldn't do that 9 days ago when it was due the first time have now made it common knowledge. Knowing the field of a standard solenoid is not the B-all and Nnd-all, but it is important, and it's why I think it's good recovery for those who adjusted from 9 days ago and know about it now. (And more importantly, knowing how it applies to things like today's question.)

 

The answer was 3.1 milliHenries

 

Significance: my standard solenoids have an L on the order of milliHenries. To get time-dependent inductance-related changes with them, we'd have to consider the value of L/R for these inductors in a circuit with resistance R. L/R is the typical time it takes for big changes in signals to happen. If this time is too low, we'll never notice the change. Well, an L of a few milliHenries is very low. So to get a time that's greater than a second, an R lower than 3 milliOhms would have to be used. Is it possible to get such a low R when my standard solenoid is wired to power? (Hint: how many Ohms are in the 540 turns of wire of the solenoid already?)

 

My conclusion: I can't create a great enough time constant to see current changes with the naked eye when using my lab inductors. Any ideas of how to change this? (This isn't a practice question. I myself do not know how.)

 

Inductance and its effects in a simple inductor circuit: The circuit that had a 12-volt power supply powering a 4-ohm resistor in series with one tiny circle of wire had a starting current of zero but the starting SLOPE of current was 1.2 hundred million Amps per second.

 

Moving on from this, you were to have learned that value of dI/dt was proportional to the voltage across the inductor. If the voltage across the inductor went down (to say 60% of what it had been), then the value of dI/dt also goes down to 60% of its prior value. The constant of proportionality that links voltage across the inductor to dI/dt is called INDUCTANCE. You were to have learned that today. For the numbers of the last paragraph, you could easily divide the voltage by the dI/dt. Do so now.

 

From the ratio that you just got, you found out that the inductance of the tiny circle was only 0.0000000987 Henry, or pretty much 10^-7 Henry. This is a very low inductance. A low inductance means a very large dI/dt. It would appear to a common observer that such a low inductance would yield effectively infinite slope of I at the instant the power is turned on. BUT if you remove that little loop of wire and replace it in the circuit with a coil with greater inductance, that would lower the starting slope of I, and it would be evident that the current ramps up less instantaneously at the instant when power is turned on. Thus, inductance (and therefore Faraday's/Lenz's Law) slows down changes in a circuit. This was a major idea taught on Tuesday 4/24.

 

I therefore said repeat the circuit problem above, but have it be one of my solenoids in series with the 4-ohm resistor, still powered by 12 Volts. I said find what the new value of dI/dt is going to be when the circuit contains a much greater inductance than the first example. My solenoid has 540 loops, a cross-sectional diameter of 4 cm, and a height of 15 cm. From this, find dI/dt at the instant when 12 V are across my solenoid. That's what you are to have been working on. If you haven't done so yet, try again before you keep reading, because I'm about to give some of it away...

 

 

You're back here, because you already tried the inductance calculation of my solenoids, and you're here to check your answer. You're now supposed to know that you relate dI/dt to voltage across an inductor through:

 

Voltage = L(dI/dt)

 

When L was 10^-7 Henry (the little loop example), and Voltage was 12 V, dI/dt was 1.2 hundred million Amps per second. Now, for this real solenoid, L will be much much greater, Voltage will still be 12 V, so dI/dt will be much much less. That was the main idea. So how do you get L of my coil from the fact it has 540 wrappings, its 15 cm tall, and has a cross-sectional diameter of 4 cm?? Big question...

 

THAT detail (if you couldn't figure it out for yourself) was handled on the handed-out set of notes I provided. It was two pages. I'm expecting you to work through it if you didn't get the L of a solenoid on your own. When done correctly, you'll find that the L of my solenoids is 3.07 milliHenry. But don't take my word for it. Learn to prove it. (And the notes mention another imaginary solenoid whose number of turns and height and area are different. That one has an L of 3.8 milliHenry.) From the logic of these notes, you can also prove to yourself that the L of the very first example (the little loop one) was 0.0000000987 Henry. All three of these Henry values is nothing but a combination of geometric factors, and that was stressed in class as well. Don't memorize. Learn how to derive such L's. That's what my set of handed-out notes was for. It's also re-attached to this message. "Origin of Inductance" is the file name.

 

From this, you could proportionally conclude that MY solenoid hooked up in the circuit above would yield a starting slope dI/dt of 3,910 A/s. This slope is far less than before, because the inductance is far greater than before. A greater inductance makes the circuit slower to change. But 3,910 A/s is still a relatively steep slope so my inductors are a relatively low number of Henries.

 

Measure how well you picked up these main ideas from the lesson of 4/24/18. Apply them to the other quick example I just attached. I call it Intro Example 2. It's quick and useful.

 

In a slight subject change, I mentioned how problems like Unit VIII, #4, are valuable in so many ways. So I handed out an enhancement/discussion/solution hints page I did for #4. I think it's a great review problem of BOTH E&M and Mechanics. And it's relevant to physical stunts recently done in class. My enhancement ends up concluding that for the dropped object to reach a terminal velocity in our presence, the B field has to be around 0.13 Tesla. Check out how I reached this conclusion. It's in my notes but not McGehee's solution. (However, McGehee's solution to #4, which you now have, is useful too.)

 

Even though I handed out the Problem 4 enhancement notes in class, they are also attached to this posting. It's called the Grand Review Problem.

 

So two of three attachments here were handed out in class. Also, they mention dates of "April 29" and "May 1" on them. Just ignore that. Those dates were relevant to some prior school year.

 

One more idea - put an inductor into a circuit on PhET. Use this to visualize dI/dt. I just did so, and that's how I came up with Intro Example 2.

 

2 of 3 will count. If you want them all to count, I can easily do that. I'll give some indication of topic areas ahead of time. Like now:

 

The one on 4/26 will certainly relate to the algebraic form of using Faraday's Law. (You've already been graded on the directional part.) Really, anything from Unit VIII is fair game, but I'll stay away from circuits that have junctions. You could be asked to calculate an inductance, to know how to relate an inductance to a voltage in a simple (junction-free) circuit. Any application of delta-flux over delta-time equaling voltage. Anything from Unit VIII is fair game, so don't think a list here in this message is going to be full; I'm just throwing out some examples. How about Motional EMF; there's another one. McGehee doesn't use the phrase "Motional EMF", but it's a phrase you should know. He DESCRIBES IT but doesn't name it "Motional EMF" on Pages 4 and 5 of the workbook. You should re-review my document on Motional EMF. It's still posted from last week. There is a reason that voltage equals BHv, but what does that mean, and what is H, and why are there two algebraic ways to understand where "Motional EMF = BvH" comes from? See my document for that. Also, Unit VIII Problem 3 is a nice little Motional EMF problem. It uses a lower-case L instead of H.

 

Unit VIII problems - Great preparation for 4/26, but not the circuits that involve junctions or the circuit problems that use calculus. And once you've tried any problem, and really honestly feel stuck, you can peak at the thorough solutions, which are attached HERE!.

 

BIG SYMBOL CONFUSION WORRY: The workbook's symbol for EMF: I don't like it. It looks too much like E field. EMF is voltage, and E field is not; E field has different units. We need to clarify this. See my very brief attachment to clarify this. It's catastrophic if you get mislead by the workbook's bad EMF symbol so quickly read my attachment.

 

Meanwhile, I'll give hints on the topics of the 4/30 and 5/2 quizzes later. (4/30 will certainly involve circuits with some calculus usage and could involve capacitors, resistors, and inductors.)

 

I've also posted "What You Need to Take Away from the Lesson of Tuesday 4/24." Look for this. It's important for measuring how caught up you are.

 

- To the circuit problem set up as the lesson at 9:40 AM on Friday 4/20/18. It was the introduction to Inductance lesson, and it involved the idea of a very tiny circle encircling magnetic field flux when a circuit's current is first turned on.

 

Definition of being caught up as of 4/22/18: a student doing everything s/he can to be good at Pages 1 through 18 of Unit VIII right now. A person would find that this attachment connects Pages 1-15 to Pages 16-18.