Started a MOOC, is trig and calc really necessary a beginner DC circuits class?

[Ronan]

So I started Georgia Institute of Technology's MOOC on Linear Circuits 1: DC Analysis https://www.coursera.org/learn/linear-circuits-dcanalysis/home/welcome, presumably it's the most beginner level course I could find (before starting the edX MIT 3 course series).

So I'm auditing the course (so you know I'm not fishing for answers) but I'm frustrated at their insistence on having students not only know trig but be able to apply it to a DC electric circuit problem. For example, this problem (see image attachment):

Determine the power delivered to an element at t=4 ms if the current through the element is given by
i=7cos60πt A
and the voltage is related to the current by the relationship v=4iv=4i

Seriously! Isn't there a better way to ask for the same answer other than relying on trig? There are tons of electronics enthusiasts who have gotten by without diving into trig and calc; is the MOOC just making it needlessly difficult? I'm currently reading through four electronics books (simultaneously, since they overlap content) and I started the Radio Shack Lab Kit and as I go through exercises, none of them remotely touch on trig or calc. I'm wondering if these university courses are a waste of time (with their emphasis on making things more difficult than they need to be) and if I should spend my time elsewhere. I noticed a ton of resources in the Primers & Course Material sticky post but would like some feedback on this.

[helius]

A nice picture was posted in another thread a while ago:


I don't know what books you're reading, but I suppose they cover the difference between DC and AC. An alternating current is a sinusoid—a function that uses sine or cosine. If you care about what is actually happening over time, you need to use those functions and their derivatives. The trace on an oscilloscope (the waveform) is made up of millions of sines and cosines added together, and can't be understood at all without them.

Electrical phenomena were dimly understood hundreds of years ago, but it was only by using calculus that they became scientific knowledge, and advanced to the present state where everyone carries billions of transistors in their pockets or on their wrists. You can be sure that Faraday and Ampère were familiar with calculus before they began their electrical studies.

[Ronan]

Yeah...that's why I emphasized DC. It's a DC circuit class, as it says in the title of the course.

Helius, your response sounds like you think it is necessary to know trig and calc for a DC circuit class...so I'm willing to listen to why you think that is.

I'm sorry that I gave you the impression that I wasn't interested in "getting more educated". I am actually more than happy to read and learn and review my old college courses as I go further into the electronics realm. But I have a problem with is being inundated with math that is not necessary for the moment, such as learning DC circuits, resisters, capacitors, 6V & 12V batters, etc. It seems counterproductive to require a background for a course that does not use the background. This will have a tendency to turn people off, especially when there is no lab or hands on experience in the course.

These are the four books I'm reading:

• Electronics: Learning by Discovery https://www.thriftbooks.com/w/make-electronics-learning-through-discovery_charles-platt/304907/#isbn=0596153740&idiq=4660250
• Practical Electronics for Inventors

https://www.thriftbooks.com/w/practical-electronics-for-inventors_paul-scherz/308734/#isbn=0070580782&idiq=6166414

• Practical Electronics for Inventors

https://www.thriftbooks.com/w/practical-electronics-for-inventors_paul-scherz/308734/#isbn=0070580782&idiq=6166414

• Getting Started in Electronics

https://www.thriftbooks.com/w/getting-started-in-electronics_forrest-m-mims-iii/304700/?mkwid=sUdnfedje%7cdc&pcrid=70112903952&pkw=&pmt=&plc=&pgrid=21329355552&ptaid=aud-420593221365%3apla-366098073672&gclid=CjwKCAjwy7vlBRACEiwAZvdx9nn_zeE5k_Ie-alfHp7J2LD9L8ExM9tlqIyzONX2hOqc8aUW2DMgWRoCLQ0QAvD_BwE#isbn=0945053282&idiq=5534219

• Electronics Demystefied

https://www.thriftbooks.com/w/electronics-demystified_stan-gibilisco/524508/#isbn=0071768076&idiq=10216388
[/list]

[helius]

The Forrest Mims book has a good reputation, but I'm not familiar with the others.

It's possible that the authors of the course don't have quite the same concept of "DC Analysis" as you think. The question in the image describes a circuit element with a time-varying (alternating) current. This material clearly does not only deal with constant current systems. The course might be followed by another that deals with more advanced topics like transmission lines, without the separation of "DC" and "AC" that the course title seems to imply. You'll excuse me if I don't have time to research the course material now.

[Yansi]

Everything under a couple GHz is DC. 

[dmills]

And anything involving a capacitor is AC circuit theory by definition (Caps are open circuits at DC), same with inductors which as just short circuits at DC.

I would expect any course dealing with more then resistors to need at least the rudiments of trig and (probably) complex numbers, ODEs and Laplace can come later.

Electronic engineering is all about the maths, any you will find it very hard to go anywhere much without trig, basic calculus (Including ODEs and Lapalace), complex numbers (if not full up vector spaces), and enough linear algebra to solve systems of equations.

Now I will grant that you can cookie cutter and 'datasheet engineer' some quite sophisticated systems without ever understanding the fundamentals, but you will always find that your designs are sub optimal or don't work for reasons you don't understand unless you have the maths to support the underlying theory.

University is (if done right) about the theory, and that means maths.

[soldar]

Determine the power delivered to an element at t=4 ms if the current through the element is given by
i=7cos60πt A
and the voltage is related to the current by the relationship v=4iv=4i

That is not DC. That is AC.

In any case, it depends how far and deep you want to go into electronics. Trig and calculus are not necessary for soldering but if you want to understand or do any analysis or design you will need them.

If you really hate them then my advice would be to look for something else that does not require them.

[rstofer]

Yes, the first problem is definitely AC but it's not all that deep because, the way I read it, they want the instantaneous power at t=4.

The first part is just 'plug and crunch' to find that the argument to cos() is 240*pi which is the same as cos(0) which is 1.  7 times 1 => 7 Amps.  Figuring out power = voltage * current is now pretty easy.

The second part looks like you have to take a derivative but,in reality, you figure out that since the cos(240*pi) is 1, the slope at that point is 0 so di/dt= 0 and 5 * 0 is still 0.  The voltage is 0 so the instantaneous power is 0.

Here's a couple of hints:
www.symbolab.com  == solving just about everything
www.desmos.com     == graphing

I sure hope I got that stuff right...

[Ronan]

Helius, you're correct. The course is followed by Linear Circuits 2: AC Analysis https://www.coursera.org/learn/linear-circuits-ac-analysis

"This course explains how to analyze circuits that have alternating current (AC) voltage or current sources. Circuits with resistors, capacitors, and inductors are covered, both analytically and experimentally. Some practical applications in sensors are demonstrated."

Interesting that they have not covered anything in AC, but are quizzing on it; which confirms my frustration. Thanks for your input.

[Ronan]

Yes, the first problem is definitely AC but it's not all that deep because, the way I read it, they want the instantaneous power at t=4.

The first part is just 'plug and crunch' to find that the argument to cos() is 240*pi which is the same as cos(0) which is 1.  7 times 1 => 7 Amps.  Figuring out power = voltage * current is now pretty easy.

The second part looks like you have to take a derivative but,in reality, you figure out that since the cos(240*pi) is 1, the slope at that point is 0 so di/dt= 0 and 5 * 0 is still 0.  The voltage is 0 so the instantaneous power is 0.

Here's a couple of hints:
www.symbolab.com  == solving just about everything
www.desmos.com     == graphing

I sure hope I got that stuff right...

You have no idea how this helps me! Thanks. It gives me something to review, with the problem so I can understand it. There was zero trig in the course (at this point) and zero explanation of how the problems were solved, so your little input here does wonders. Thanks!!

[rstofer]

You go nowhere in engineering without a TON of math.  The sooner you make friends with it the better.
There are online tutorials that deal with theory and math.  Khan Academy Electrical Engineering and Digilent's "Real Analog" series are pretty good.

Even in DC circuits, and I mean strictly DC, no switches, no capacitors, no inductors, solving resistor mesh problems and calculating internal resistance and maximum power transfer takes a lot of matrix math.  Kirchhoff's Laws were made to sell matrix algebra.

Given the realities of engineering and math, it's best to get comfortable with a solver.  MATLAB (Home Edition) is my favorite (it costs money plus an annual fee) but GNU Octave will do the same things but possibly not with the same syntax and it's free.  Working through some of my grandson's Physics problems, I often pull up MATLAB and enter the known relationships and calculating results as I go along.  I use MATLAB like a calculator with a file system for recall.

You will really need something when you get more than 3 loop or node equations.  Solving 4x4 matrices is not fun and beyond that point they are a real drag.  Yes, I know how Gauss-Jordan elimination works.  I grew up in the era of slide rules.

AC Circuits is all sin() and cos() functions and the trig identities will be necessary.  Oh, and f(t) kinds of things like the capacitor charging equation vo=vs(1-e^(t/RC))

Derivatives and integrals of trig functions will be all over the place.

[jmelson]

So I started Georgia Institute of Technology's MOOC on Linear Circuits 1: DC Analysis https://www.coursera.org/learn/linear-circuits-dcanalysis/home/welcome, presumably it's the most beginner level course I could find (before starting the edX MIT 3 course series).

For strictly DC circuits, no.  But, that will only last for about a week, then you move on to transient circuits, which is the domain your question is in.
Then, trig does come in, and just a small bit of calculus.

Jon

[rstofer]

Yes, the first problem is definitely AC but it's not all that deep because, the way I read it, they want the instantaneous power at t=4.

The first part is just 'plug and crunch' to find that the argument to cos() is 240*pi which is the same as cos(0) which is 1.  7 times 1 => 7 Amps.  Figuring out power = voltage * current is now pretty easy.

The second part looks like you have to take a derivative but,in reality, you figure out that since the cos(240*pi) is 1, the slope at that point is 0 so di/dt= 0 and 5 * 0 is still 0.  The voltage is 0 so the instantaneous power is 0.

Here's a couple of hints:
www.symbolab.com  == solving just about everything
www.desmos.com     == graphing

I sure hope I got that stuff right...

You have no idea how this helps me! Thanks. It gives me something to review, with the problem so I can understand it. There was zero trig in the course (at this point) and zero explanation of how the problems were solved, so your little input here does wonders. Thanks!!

Wait until somebody agrees before you take my word for it.  It was nice that it broke down to cos(0) because that really simplifies things.

[rstofer]

So I started Georgia Institute of Technology's MOOC on Linear Circuits 1: DC Analysis https://www.coursera.org/learn/linear-circuits-dcanalysis/home/welcome, presumably it's the most beginner level course I could find (before starting the edX MIT 3 course series).

For strictly DC circuits, no.  But, that will only last for about a week, then you move on to transient circuits, which is the domain your question is in.
Then, trig does come in, and just a small bit of calculus.

Jon

True, strictly DC means batteries and resistors.  After explaining and demonstrating Kirchhoff's Laws (node and mesh equations), Norton, Thevenin and superposition, what's left to talk about?  Next up is a capacitor and a switch.  Then the arithmetic gets a little more involved with ln(x) and e^x.

[westfw]

Quote

it's the most beginner level course I could find

Look for classes aimed at getting you a ham radio license...
Quote

The first part is just 'plug and crunch'

Yes.Quote

  to find that the argument to cos() is 240*pi which is the same as cos(0) which is 1.

But that requires knowing some trig.Quote

The second part looks like you have to take a derivative but ... since the cos(240*pi) is 1, the slope at that point is 0

And realizing that requires knowing some trig AND some calc.
ie, they're "easy trick questions", but only if  you know the tricks."sin(60*pi*t)" is home AC, more or less, so perhaps the questions are relevant outside of "signal processing."

[dmills]

"sin(60*pi*t)" is home AC, more or less,"

Only if your domestic power is 30Hz!

Regards, Dan.

[rstofer]

And realizing that requires knowing some trig AND some calc.
ie, they're "easy trick questions", but only if  you know the tricks."sin(60*pi*t)" is home AC, more or less, so perhaps the questions are relevant outside of "signal processing."

I actually went to https://www.symbolab.com and stuffed in '7*cos(60 * pi * 4)'.  The '4' because the problem specifies t=4.  It came back 7.  The first part really is 'plug and crunch'.

The second part does take a smattering of calculus.  When you try to take the derivative of 7 * cos(240 * pi) to get di/dt, Symbolab gives 0 because 7 * cos(240 * pi) is a constant (because t was a constant = 4) and the derivative of a constant is 0.  Or you could do it with slope...

Yes, I actually used Symbolab to get the answers.  Yes, it takes a wee bit of trig and calculus.  I'm not sure why the problems show up in a DC Circuit Analysis course but I don't see how you could spend an entire semester with batteries and resistors.

The thing is, I don't need to be some kind of wizard to work these problems.  There are tools in the realm that make it easy.  You do have to a) know about the tools and b) know which question to ask and how.

Note that when plotting this 7*cos(60*pi*x) function with Desmos, the X-axis probably wants to just go from -1 to, say, 3 and then click 'Degrees'.  The 60 * pi is ok but it fills the screen with ink unless the scale is expanded.  Use the wrench in the upper right corner and set the x-axis as described.  https://www.desmos.com/

These are the tools that got my grandson through Calc I and Calc II.  I don't know what he is using for Calc III but they will be using MATLAB for Differential Equations in the Fall.  I would have loved to have had a tool like that when I took the subject.

Khan Academy is a great help with all kinds of math.  They even have a dedicated EE track.  This site is just great!

Now, if you want to learn math and you don't mind spending a bit of money for 'tuition', CalcWorkshop.com is excellent!  You can learn at your own pace, of course, but the curriculum is expansive.  I have had a subscription (for my grandson) for a couple of years and will maintain it as long as necessary.  It's cheap in the bigger scheme of things!

https://calcworkshop.com/courses/

It may, or may not, be necessary to start with Algebra but I guarantee that it is PreCalc that sinks students who attempt Calc I without doing it first.  Here is where you'll learn trig and all the other tools it takes to succeed in Calculus and beyond.

None of us learned this stuff without a lot of sweat and tears.  It takes time, a lot of time!

[Ronan]

Thanks rstofer!

I think people got the wrong impression about me and math. I enjoy math, I made it through calc & trig before; I just don't like taking quizzes that involve it when there was zero mention of it in the course material, exercises and videos. I just like to be prepared when I get in the trenches and the course did not give me a heads up. I just have an issue with the pedagogy of a school that has both gaps in the tutorials and doesn't inform the student of what they need to be prepared for, along with quizzing on elements not covered in class; it feels a bit like a bushwacking.

I'll look over everything you said and see if I can figure out how the trig works with respect to electronics. I understand SOH CAH TOA, but with respect to a triangle. I'd have to review some more in applying it to electronics. It might help me to just go ahead and take a full blown trig class so I can nail the fundamentals and start the MIT online series with a solid understanding; and your links will definitely help out. So thank you.

[westfw]

I don't need to be some kind of wizard to work these problems.

That's a lot easier to say if you've had trig and calculus, and have merely forgotten the details.
If you're still at the "why isn't di/dt just i/t" stage, it all looks like witchcraft.


Heh.  A former coworker of mine is doing ... something, and will make facebook posts like:

Fun fact of the morning: If a is a unit in a commutative ring then a divides everything in the ring.
(Note that R is a ring rather than a rng!)

Yeah.  Right...  Sorry; they didn't do a lot of theoretical math in the EE curriculum.  But I have few doubts that I feel about the same reading that, as our OP does with the unexpected trig and calc in their homework...

[westfw]

figure out how the trig works with respect to electronics.

It has more to do with circles than triangles.   Polar coordinates and such.
 I don't actually recall exactly when that comes up in math classes; I seem to recall that most beginning trig classes mostly do the triangles...

[rstofer]

I'll look over everything you said and see if I can figure out how the trig works with respect to electronics. I understand SOH CAH TOA, but with respect to a triangle. I'd have to review some more in applying it to electronics. It might help me to just go ahead and take a full blown trig class so I can nail the fundamentals and start the MIT online series with a solid understanding; and your links will definitely help out. So thank you.

You may use SOH CAH TOA when evaluating vectors - or not.  But triangles aren't really much of a topic in EE.  Vectors are...

https://www.electronics-tutorials.ws/accircuits/phasors.html

Where trig really comes up is when the functions are related to time as in sin(wt) where w is called omega and omega is 2*pi*f and f is frequency.  In other words, just a sine wave.  Or a cosine...  You wind up needing a lot of trig identities to solve some of the problems.  Here is a summary:

http://www2.clarku.edu/faculty/djoyce/trig/identities.html

These are about beat to death in calculus courses.

Here is a brief video on the composition of a square wave as a sum of sine waves, specifically odd harmonics of diminishing amplitude:

https://www.khanacademy.org/science/electrical-engineering/ee-signals/ee-fourier-series/v/ee-visualize-fourier-series-square-wave

There are some other similar videos in the Khan Academy curriculum.

I link this just to give you a sense of the kinds of things where trig is used in electronics.  It darn sure isn't used on day one!  I think Fourier Analysis is a 3rd year topic but it's been 46 years since I graduated.  My memory fails...

There are many other applications including various modulation schemes.  In fact, there's a bunch of tricky math in the last couple of years.  Laplace Transforms comes up somewhere around the 3rd year and this is a shorthand notation and approach for solving differential equations and control systems problems.  Khan Academy has a lengthy series on this topic as well.  It will come up in the Differential Equations course that many, if not most, DEs can't be solved analytically. At best you can get a slope field and some family of solutions.  At some point you may get interested in how DEs were 'solved' on an analog computer back in the day.  Lacking such a tool might lead you to using the Simulink package of MATLAB where you can drag and drop integrators and gain blocks to build up a simulation of an analog computer solving a DE.  Now we're having fun!

The best way to look at this stuff is to realiize that hundreds of thousands of engineers learned this stuff and that you can do it too.  Don't let it put a damper on your progress.  You just need to keep your head down and plow through it.

[kulky64]

I actually went to https://www.symbolab.com and stuffed in '7*cos(60 * pi * 4)'.  The '4' because the problem specifies t=4.  It came back 7.  The first part really is 'plug and crunch'.

The second part does take a smattering of calculus.  When you try to take the derivative of 7 * cos(240 * pi) to get di/dt, Symbolab gives 0 because 7 * cos(240 * pi) is a constant (because t was a constant = 4) and the derivative of a constant is 0.  Or you could do it with slope...

You got it wrong. They ask what is the instantaneous power at t=4ms, not 4s.
Here is my attempt at solving these problems:
Problem 1:
i(t)=7*cos(60*pi*t) A
v(t)=4*i(t)=4*7*cos(60*pi*t)=28*cos(60*pi*t) V
p(t)=v(t)*i(t)
p(t=4ms)=28*cos(60*pi*0.004)*7*cos(60*pi*0.004)=104.15347 W

Problem 2:
di/dt=d(7*cos(60*pi*t))/dt=-7*60*pi*sin(60*pi*t)=-420*pi*sin(60*pi*t)
v(t)=5*di/dt=5*(-420*pi*sin(60*pi*t))=-2100*pi*sin(60*pi*t) V
i(t)=7*cos(60*pi*t) A
p(t)=v(t)*i(t)
p(t=4ms)=-2100*pi*sin(60*pi*0.004)*7*cos(60*pi*0.004)=-23045.14177 W

[whalphen]

If you are really interested in doing electronics, then you'll need the right tools to understand it and to get beyond the surface.  You can do some electronics without the trig and calc.  And a person interested in woodworking can build a bookshelf using only a hammer and a saw.  But if he wants to build anything more complex or beautiful, he'll need better tools.  Don't look at math as a barrier.  Look at it as a toolset.  And you don't have to pay for the tools -- many of the great masters of electronic discoveries were self taught.  In electronics, calculus is the magic wand that gives you the ability to understand the art and manipulate electrons to do your bidding.  I learned it all in college, used  it in my career, and now, being retired and free to focus on the things I want to do, I spend a lot of time on electronics.  And, even now, I find it useful to continually refresh my math skills.  I appreciate them now more than ever.  I regret not having spent more time learning math over the years.

My advice to you is to keep learning about electronics.  But, also devote a lot of effort to your math skills.  It takes time.  Get some used books on algebra, trigonometry, and calculus.  Slowly work your way through them.  Familiarize yourself with the concepts in each chapter.  Do practice problems.  Think about the concepts when you have spare time, while waiting in traffic, etc. College courses are helpful, but their major benefit is the forced discipline of working through the material.  If you can learn it in a college course, there's no reason why you can't learn it on your own.  The math has not changed in hundreds of years.  The college courses and the readily available text books all cover the same material and deliver the same concepts.  You just need to be sure to cover them in the right sequence.  If you get stuck you can find excellent videos, etc. on the internet.
 
Think of the skills as new tools in your tool chest.  Use them.  Polish and sharpen them up from time to time.  You'll be surprised at their usefulness in electronics -- and in other disciplines.  Once you get into calculus and can apply the concepts of differentials and integrals, even the world starts to look different.  You'll have the tools to really understand how things work -- and to design things that work really well.

Of course you can see the value of saving money, expanding your network of friends, investing, etc.  Don't overlook the value of building out your skill sets.  In electronics, and most technical disciplines, math skills can give a huge return on the investment.

[luxetveritas]

For a quick solve of an equation, and many other things mathematical, I like to use the online Wolfram Alpha Computational Knowledge Engine:

https://www.wolframalpha.com/

But the most important thing to remember, whenever you're facing a complex problem or exam question, is to be sure to parse it into smaller parts that you can handle.  Professors create difficult questions that are made from much easier parts, and good students are the ones who don't panic and calmly parse these.

[rstofer]

You got it wrong. They ask what is the instantaneous power at t=4ms, not 4s.

Oops!  I missed that part...  Your calculation is correct.
Now the second part definitely requires calculus - at least to the point of knowing how to differentiate cos(n*t) as -n*sin(n*t).  That's about 1/2 way through a Calc I class.

At our community college, there is a course in Circuits but it doesn't come up until the 4th semester and that assumes 3 semesters of calculus before getting there.  And the 2 semesters of Pre-Calc don't count toward a major.  That prerequisite can be tested away (if the student had the material in HS) but it's not a good idea.

So, I wonder if the OPs course was intended to be taught before students have taken Calculus.  There may be some prerequisites.

Then too, the exceptional student will have had Calc I in high school.  Maybe even Calc II.

Purely DC circuits can be taught with just a bit of matrix algebra and the matrices are usually sparse so Gauss-Jordan Elimination is pretty easy to learn and apply.  But MATLAB stands for MATrix LABoratory, it tends to make less sign errors than I do.