Electronics > Beginners

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

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rstofer:

--- Quote from: Ronan on April 12, 2019, 02:01:32 am ---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.

--- End quote ---

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:

--- Quote from: rstofer on April 12, 2019, 01:44:36 am ---
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...


--- End quote ---

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:

--- Quote from: kulky64 on April 12, 2019, 01:43:10 pm ---You got it wrong. They ask what is the instantaneous power at t=4ms, not 4s.

--- End quote ---

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.

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