Mitch, phasors can simply be represented as complex numbers, and the Wolfram Language primitives deal just fine with manipulating complex numbers and then extracting the phase/magnitude after doing those manipulations. I asked ChatGPT (4o) your question, and it returned a completely competent answer:

https://chatgpt.com/share/2d90bf49-19af-43f7-8d7c-18c935d35a88 .

In general, ChatGPT is great for generating little code fragments of Wolfram Language code for questions just like this. Just keep in mind that all of the LLMs will create slightly or completely wonky answers from time to time. Trust, but verify.

Hey Ankit,

Did you see my previous post?

Here is the thing. The learning curve for learning how to use System Modeler is steep. It doesn't really follow the paradigm of Wolfram Language. I start to think I am getting the hang of it, but then I get these weird curve balls. My purpose for following this class is not so much to learn circuit design, but it's to learn how to use System Modeler effectively in circuit design. That's not the emphasis for this class as it turns out, but still, a little help might convince me to buy the too or convince me to convince my corner of Boeing to buy the tool.

Wolfram U prefers that students not discuss quiz answers in the DSG for a course. You should e-mail wolfram-u@wolfram.com or you can put info in the feedback form that pops up at the end of each lecture.

FWIW, I'll also be providing them feedback to the quizzes.

I have checked the questions you mention and it seems that the answer key is incorrect, so the options we took as correct are wrong. I will update the quiz to reflect the correct answers.

Leo, I just had my score on Quiz 1 re-checked. I refreshed the course framework (in my Safari browser). The suspect question is still getting flagged as incorrect. As far as I can tell, the quiz answer sheet has never been updated with the correct answer. It's been almost 3 days since the errors on Quiz 1 and Quiz 2 were reported and over 2 days since you said that they would be fixed. Please fix them promptly. There's some in-course joke I should say about hysteresis at this point, but I can't quite figure out what it is. :)

I apologize for sending this message to the public forum, but this is the only means we're given to contact the instruction staff. If this were in an in-person class, I would speak directly with the teacher or the TAs.

Thanks for the posts, Ankit.

I am running through the Wolfram U package for System Modeler (Wolfram System Modeler: An Introduction) and when I got to section 3 (Create Components and Animations) we are asked to work through building a pendulum simulation. As best as I can tell, I've had duplicated all the instructions both on the video and the down loaded notebook, but I get the following error message when I first run the simulation:

"14.0.017201150762775915755.sim Error: No unit information generated/Users/carlj.hahn/Library/Caches/com.wolfram.SystemModeler/WolframSystemModeler-14.0/sme.14.0.017201150762775915755_units.json Build failed at 10:44:39 (took 00:02)."

I have no idea what that means. Do you?

Can you try to switch the Modelica Version to 3.2.3 and simulate again?

Right-click on Modelica library, go to version and switch to 3.2.3, and try to simulate? Let me know if that works else I will troubleshoot further.

In version 14, we made version 4.0.0 as the default. I am currently updating the Wolfram U videos to use this new version.

In today's class, somebody asked:

why are frequencies represented with imaginary numbers?

I highly recommend ChatGPT for this kind of question. That exact question yields a comprhensive answer in the AI. Since ChatGPT 4o is available freely for anyone who requests an account; I highly recommend using that tool. OpenAI even provides an app for MacOS to help keep things uncluttered on your desktop.

In class today, our instructors were discussing the variety of sinusoidal behaviors associated with electronics and signal processing. I believe they were searching for a particular word. There is a pertinent list of such terms available online in the Electromagnetic Terms section of the Wikipedia entry for Oliver Heaviside. The terms are admittance, elastance, conductance, electret, impedance, inductance, permeability, permittance, and permittivity. Two other terms were coined by Heaviside's peers around the same time: susceptance and reactance. These terms were coined from 1885 to 1894. Some are widely used today in physics and engineering; others have withered into obscurity. Some terms deal with real values; others deal with imaginary values. The Wikipedia article contains links defining each of these terms.

Anyone who thoroughly understands these eleven concepts is a signal processing wizard.

The capacitor model in the Electrical and the Spice library looks the same to me. Unfortunately, we do not support it yet. For this course, you can create all the models using the Modelica.Electrical library.

class Modelica.Electrical.Analog.Basic.Capacitor
  Real v(quantity = "ElectricPotential", unit = "V", start = 0.0) "Voltage drop of the two pins (= p.v - n.v)";
  Real p.v(quantity = "ElectricPotential", unit = "V") "Potential at the pin";
  Real p.i(quantity = "ElectricCurrent", unit = "A") "Current flowing into the pin";
  Real n.v(quantity = "ElectricPotential", unit = "V") "Potential at the pin";
  Real n.i(quantity = "ElectricCurrent", unit = "A") "Current flowing into the pin";
  Real i(quantity = "ElectricCurrent", unit = "A") "Current flowing from pin p to pin n";
  parameter Real C(quantity = "Capacitance", unit = "F", min = 0.0, start = 1.0) = 1.0 "Capacitance";
equation
  n.i = 0.0;
  p.i = 0.0;
  v = p.v - n.v;
  0.0 = n.i + p.i;
  i = p.i;
  i = C * der(v);
end Modelica.Electrical.Analog.Basic.Capacitor;

class Spice3.Basic.C_Capacitor
  Real v(quantity = "ElectricPotential", unit = "V") "Voltage drop of the two pins (= p.v - n.v)";
  Real p.v(quantity = "ElectricPotential", unit = "V") "Potential at the pin";
  Real p.i(quantity = "ElectricCurrent", unit = "A") "Current flowing into the pin";
  Real n.v(quantity = "ElectricPotential", unit = "V") "Potential at the pin";
  Real n.i(quantity = "ElectricCurrent", unit = "A") "Current flowing into the pin";
  Real i(quantity = "ElectricCurrent", unit = "A") "Current flowing from pin p to pin n";
  parameter Real C(quantity = "Capacitance", unit = "F", min = -1.7976931348623157e+308, start = 0.0) = 0.0 "Capacitance";
  final constant Real WSMServices.Machine.Real_MAX = 1.7976931348623157e+308 "Maximum finite Real number.";
  parameter Real IC(quantity = "ElectricPotential", unit = "V") = 0.0 "Initial value of voltage";
  final constant Real ModelicaServices.Machine.inf = 1.7976931348623157e+308 "Biggest Real number such that inf and -inf are representable on the machine";
  evaluated parameter Boolean UIC = false "Use initial conditions: true, if initial condition is used";
  protected Real vinternal(quantity = "ElectricPotential", unit = "V") "Capacitor voltage";
  final constant Real Modelica.Constants.inf = 1.7976931348623157e+308 "Biggest Real number such that inf and -inf are representable on the machine";
equation
  n.i = 0.0;
  p.i = 0.0;
  v = p.v - n.v;
  0.0 = n.i + p.i;
  i = p.i;
  vinternal = p.v - n.v;
  i = C * der(vinternal);
end Spice3.Basic.C_Capacitor;

Hi Leonardo,

I can see how it can be a real advantage to take a more simplistic approach. For example, system modeler is probably never going to be as accurate as a dedicated multi-physics FEA but it will get reasonable ballpark answers very quickly for complex multi-physics system-level problems (which is a big advantage). Accurate simulation for electronics can be very complex, System Modeler seems to be taking a more high-level simpler approach which is nice.

Is there any strategy for automatically taking outputs from software like Ansys, Comsol, LTSpice or other simulation programs and integrate the outputs as part of a system-level multi-physics simulation that System Modeler could model?

This would help solve scaling issues with the packages I mentioned above; they are so computationally intensive that doing large systems are not really feasible. It would be interesting to see some System Modeler examples doing this.

Another application where I'd love to see what System Modeler can do is as a tool something like LangChain where LLM outputs can be chained together to action complex tasks.

Apologies, my question maybe a little off-base, just a few general thoughts/questions.

Hello Dr Ruiz,

In yesterday's lecture 11, towards the end, we went from the simple 2 loop 4 node resistor circuit to what System Modeler did with it, which was very complex. You went by that really fast. We should dwell on that. What all can you do with that model? That seemed to put a finger on the strength of System Modeler. In particular the associated thermal modeling. Can you model resistors whose values change with temperature? Can you model thermal runaway? Can you show the effect of putting a fan on the circuit, or a thermal fin, to prevent thermal runaway? A simple circuit like that seems to be a perfect pedagogical tool for looking at complex issues like that. I've seen circuits fail because even though that had low dissipation, there was no way for the heat to get out. A beginner's mistake, but one that is easy to make because thermal analysis is not traditionally included in circuit analysis.

You can also imagine passing the heat from the resistor to a container (with air) encasing the circuit. This will help in understanding the increased pressure inside the container (when the system is thermally isolated).

Model can be found here: https://amoeba.wolfram.com/index.php/s/7cs8fL3LY8SF3D5

Thank you for your very nice explanation, and the interesting analogy between the electric grid and the arterial network. I have long been wondering why the heart is a pulsatile and not a continuous pump. There does not seem to be much information on this topic in the literature. The scarce information I found, focusses on the generation of blood flow and suggests that anatomically a pulsatile pump is simpler than a continuous pump, and also that a pulsatile pump may adapt (increase or decrease flow) more easily depending on the need (activity or rest). You focus on the alternative explanation that the heart may be a pulsatile pump because a pulsatile blood flow may be transmitted more efficiently through the arterial tree. It is very interesting that AC vs. DC electric current may also be discussed from the perspective of energy generation and energy transmission, and that AC current appears to be more advantageous than DC current from both these perspectives.

Just thinking out loud here: From what you quoted, the imbalance appears to have been in the generator frequencies to start with? I imagine they need to stay synchronized in frequency if they are sharing loads. Otherwise you set up a beat frequency at the difference frequency between the two generating systems, and their voltages will move from being in phase to being out of phase, back to being in phase again at the rate of the beat frequency. I don't know how power grids really work, but I imagine this will cause intolerable voltage variations as they sum in phase and out of phase. Did that happen? It's a simple graph to add two sine waves of equal amplitude but with a slight difference in phase to show what happens.

But upon closer inspection of the article you mentioned it looks like the real complaint was simply that having a slightly lower frequency than the assumed 50 Hz, kitchen equipment that assumes 50 Hz and some kind of zero crossing counter as a clock reference will get a long term clock drift.

As an aside, when we talk about load impedances being a function of frequency, unless the load has a very high Q (lossless resonance), they don't change very much in the vicinity of the frequency of the stimulus. Bio-mechanical systems (a cool topic) are inherently lossy and must have low Qs. To a first order it would be surprising to see much sensitivity to the frequency of the stimulus. But I can see additions and cancellations of multiple stimulus playing a role. And our internal body clocks seem to get reset every day according to the motion of the sun.

Hello. I'm registered for the Daily Study Group!

In early 2018, there was an incident in the European electrical power grid. From the Ars Technica reporting on the incident European grid dispute resolved, lost 6 minutes returned to oven clocks:

Last month, the European Network of Transmission System Operators (ENTSO-E) publicly admonished Serbia and Kosovo for not properly balancing their grids according to previous agreements. "This average frequency deviation, that has never happened in any similar way in the CE [Continental Europe] Power system, must cease," the group wrote. "ENTSO-E is urging European and national governments and policymakers to take swift action."

Two days later, on March 8, the Transmission System Operators (TSOs) from Serbia and Kosovo confirmed that they were back to balancing their grids appropriately.

The incident piqued my curiosity: it's a unique example where load influenced the frequency of the AC power grid. Even though the 50Hz grid never dropped below 49.996Hz, this remains (to the best of my knowledge) a unique deviation from that most-important frequency. Technically, what happened? What was the imbalance, and how could it have this significant an impact on the entire European grid? My understanding is that a 1% drop in the line frequency of a grid could have serious impact on some old (stodgy) generators. Is it possible to have a Wolfram Language simulation showing what happened for the class? What was this imbalance, and how much of an imbalance would it take to produce a 1% drop in the frequency? I'd love to hear a brief discussion about this incident during the class, but realize it may be a bit late to change the presentation. Perhaps a homework example?

The dynamics of electricity is a secondary interest to me. Many other systems -- including mechanical systems like our musculoskeletal system -- use stored energy in their oscillating cycles. The same impedance model used in electrical systems can be applied to many mechanical systems. Impedance is inherently dependent on frequency, but most don't understand the frequency-dependent dynamic in biomechanics. That must change.

Since electricity is discussed far more than any other domain studying impedance, I pay attention when Wolfram Research is discussing such things. Thank you for this WSG.