Natural Response of RL/RC Circuits

[sshoptaugh1991]

I am struggling in my engineering course.  It is first level circuit analysis, and we are on the topic of natural response of RL and RC circuits.  I get the basic idea that you cannot feed a DC signal through a capacitor, only an AC passes, and I understand that a DC signal makes the inductor act as a short circuit.  I get it.  And it is probably naive to say, but I think that is all I need to understand about RC and RL circuits, other than time constants and charge and discharge.  But my point is, why do I have to learn all of this theoretical calculus crap?  This circuit analysis course is seriously making me hate my hobby of electronics.  That is just not right.

There is a few homework problems that I cannot figure out.  This one in particular is an RL circuit with a switch.  We have to find the current of the inductor and current through the switch at like t = 0 and t = 0- and t = 0+.

When the switch is open, current flows through the resistors and the inductor acts as a short, so a current of 0.731A flows.  I get that.  So Io = i(0-) = i(0+) = 0.731A.  I get that.

Now when the switch is closed at t = 0, I am lost.  So current through the closed switch is zero, yes?  No resistance and a closed switch is essentially zero volts.  So Io at the switch is zero for t >= 0.  The time constant tau is 0.05H / 16 ohms = 3.125 ms.

So the expression for i(t) through the inductor when the switch is closed is now,

i(t) = Io*e^(-t/tau) for t >= 0.

Do I understand this correctly?  I keep trying the problems and keep getting them all wrong, and it is really frustrating and discouraging.  Why do I have to know all of this theoretical garbage?  I would rather learn about different circuit building blocks, like boost converters and RF filters, etc.  Just to put application to these components, you know?

[BobsURuncle]

Why would there be no current through the closed switch? There is a difference in voltage potential between the + and - terminal of the source and a conductive path in between - including the closed switch - so current will flow. And there is also a voltage potential from the inductor. 

When you close the light switch in your home do the lights go on or off? An ideal closed switch just acts as a continuation of the wire connected to it.  There is no voltage between two sections of a conducting ideal wire but current can obviously flow through  zero ohm wire.   That branch of the circuit basically collapses into a node when the switch is closed.

The important physical principle here is that the magnetic field (energy) stored in the inductor at t=0 is supported by the current through the inductor. When you close the switch the voltage source is shorted through the 20 and 5 ohm resistors and no current from the source flows through the inductor anymore.  So the coil magnetic field will collapse inducing a voltage in the coil that will maintain the current in the coil at t=0+.  That energy will gradually dissipate through the resistors - 10 and 6 ohms. So for t>=0 your formula is correct for the current in the inductor with a time constant of L/R, R=16 ohms.

The current through the switch is the sum of the current from the inductor and the current from the 30V source.

[danadak]

But my point is, why do I have to learn all of this theoretical calculus crap?  This circuit analysis course is seriously making me hate my hobby of electronics.  That is just not right.

Depends on what you want to do with an Engineering career. If its filling out forms while visually inspecting screws for thread consistency
then maybe the Calculus is a waste. But if you want to learn the art of circuit design, both time domain and LaPlace and Calculus are inte-
gral to that goal.

In your example you might need to specify the wattage rating of the resistors, switch ratings, coil inductance, core area, many facets.
This is how you get to these answers. Once you become competent you can skip some of this thru experience. If you are a software
EE then maybe a lot of these would not be useful, but from experience I can tell you going thru these courses helps make you capable
of tackling almost anything. Its not the topic, its the confidence and ability to think thru design issues and get help when you need it
that is the outcome.

And as an aside most circuit design issues these days are solved by relatively simple models and high school algebra.


Regards, Dana.

PS : The school I went to very theoretical, at times I felt like you, especially in field theory. Looking back it was one of the
best experiences I had. I do not know much, but I am not afraid of anything, and still learning in my retirement.

[Tom45]

Why do I have to know all of this theoretical garbage?  I would rather learn about different circuit building blocks, like boost converters and RF filters, etc.  Just to put application to these components, you know?

But where do those building blocks come from? Somebody had to design them. There will be topics that you aren't interested in now that you will be glad you learned about them at some point in your career.

For me it was a junior year course called Fields and Energy Conversions. It covered transformers, motors, generators, etc. We disparagingly called it "Dynamo Science". The lab was a large room with very high ceilings that looked like something out of a set of a Frankenstein movie from the 30's. I just knew I'd never use any  of that. Yet 5 years after graduating I was working with large DC servo motors.

I will say that 50 years later I still haven't made use of anything from Thermodynamics.

As for your specific questions, those are the foundation of things you will need to know in more advanced courses.

[JS]

  The knowledge is needed for to be an EE, no doubts, my argument about this is about two things. One is that I don't see the point of some teachers to make you be used to make certain kind of calcs very fast a lot of times so you get used to them, since is time consuming you forgot all that as soon as you pass the course, so it was a lot of time wasted. The second point is the responsibility of the teacher on transmit interest and knowledge rather than data.

  I'm close to finishing my degree and I have both very good and very crappy teachers in this criteria, still few teacher to know till the end. Once you give a person the right question to ask and the source of the knowledge is pretty easy for it to learn the answer. Once you give a person the mechanical procedure to solve certain kind of problems is quite hard for that person to learn how to solve it, it just will solve it as long as it doesn't gets away from the initial conditions. I've seen a few excellent professionals with loads of knowledge do loads of harm in front of a classroom and I've also seen people with much limited knowledge make an entire classroom understand a topic, when both things get together magic happens as Walter Lewin from MIT, check you tube, it's worthy.

  From my point of view the education is wrong not because is not up to date (while that would help) but because a conceptual mistake, I sincerely don't know how to do better, but I think the day I need to hire a professional, let's say Engineer, I'm probably won't look as much as the degree, let alone the grades. The chief of an engineering department on a big audio company said once he found in his job hiring engineers who wouldn't find themselves the way out of a wet paper bag and much more capable people who learned electronics in the father's TV workshop. I'm not saying there aren't really good professionals, I'm just saying not all people with a degree are good professionals, and there are people which would get the job done but they don't have the degree. I hope the logic is clear and nobody gets offended.

JS

[rstofer]

Engineering is math - simple as that.  If you don't want to learn the math, you won't be able to design circuits at an engineering level.  Sure, you can put parts together and make something work but you won't be able to prove that it always works.  And you certainly won't understand advanced designs created by others.

Our local university requires 152 units to graduate and requires 3 semesters of calculus plus differential equations and one other course that I can't recall (Discrete Mathematics?)  That is in addition to the math required for Field Theory and Laplace/Fourier transforms and analysis.  College algebra, trigonometry and pre-calculus don't count.  There are just assumed as a prerequisite to 1st semester calculus.


I can't think of a single engineering field that isn't heavy in math.  Civil, Structural, Mechanical, Electrical and electronics.

[basinstreetdesign]

But my point is, why do I have to learn all of this theoretical calculus crap?  This circuit analysis course is seriously making me hate my hobby of electronics.  That is just not right.

Depends on what you want to do with an Engineering career. If its filling out forms while visually inspecting screws for thread consistency
then maybe the Calculus is a waste. But if you want to learn the art of circuit design, both time domain and LaPlace and Calculus are inte-
gral to that goal.

In your example you might need to specify the wattage rating of the resistors, switch ratings, coil inductance, core area, many facets.
This is how you get to these answers. Once you become competent you can skip some of this thru experience. If you are a software
EE then maybe a lot of these would not be useful, but from experience I can tell you going thru these courses helps make you capable
of tackling almost anything. Its not the topic, its the confidence and ability to think thru design issues and get help when you need it
that is the outcome.

And as an aside most circuit design issues these days are solved by relatively simple models and high school algebra.


Regards, Dana.

PS : The school I went to very theoretical, at times I felt like you, especially in field theory. Looking back it was one of the
best experiences I had. I do not know much, but I am not afraid of anything, and still learning in my retirement.

+1 absolutely right

[rstofer]

Employers do follow up with your college.  They often get a copy of your transcript.  They may of may not tell you about it.
Decades ago, I worked with a fellow who claimed to have a BS in some subject.  He seemed like a pretty knowledgeable fellow.  One day they fired him because he didn't have a degree and he lied about it on his application.

[Ratch]

I am struggling in my engineering course.  It is first level circuit analysis, and we are on the topic of natural response of RL and RC circuits.  I get the basic idea that you cannot feed a DC signal through a capacitor, only an AC passes,

No current goes through a capacitor unless it is leaky.  The charges accumulate on one plate and deplete on the opposite plate.  This causes current to be present in the branch containing the capacitor until the capacitor is fully energized to the applied voltage.

and I understand that a DC signal makes the inductor act as a short circuit.

Only after the magnetic field is at its maximum does the coil appear as a wire. 

  I get it.  And it is probably naive to say, but I think that is all I need to understand about RC and RL circuits, other than time constants and charge and discharge.  But my point is, why do I have to learn all of this theoretical calculus crap?  This circuit analysis course is seriously making me hate my hobby of electronics.  That is just not right.

You can probably limp along without calculus and differential equations if you only work with DC and steady state sinusoidal AC.  But if you encounter a ramp, sawtooth, square wave, triangular, etc., you are in for a rough ride unless you know some math.

There is a few homework problems that I cannot figure out.  This one in particular is an RL circuit with a switch.  We have to find the current of the inductor and current through the switch at like t = 0 and t = 0- and t = 0+.

That circuit does  not look too imposing.  It has one time constant for coil energizing, and another time constant for de-energizing.  The switch changes the time constant when it is open or closed, and shorts out the voltage to the coil.

When the switch is open, current flows through the resistors and the inductor acts as a short, so a current of 0.731A flows.  I get that.  So Io = i(0-) = i(0+) = 0.731A.  I get that.

OK, good.  But realize that the current takes about 5 or 6 time constants to build up to its max value.

Now when the switch is closed at t = 0, I am lost.

Why so?  All that happened is that the 30 volt source voltage and some resistance was removed from the coil circuit.

So current through the closed switch is zero, yes?

No, immediately after the switch closed, the magnetic field used its stored energy to keep the current at its max value.  The current will decrease at its new time constant rate.

  No resistance and a closed switch is essentially zero volts.  So Io at the switch is zero for t >= 0.

Wrong! For the reason given above.

  The time constant tau is 0.05H / 16 ohms = 3.125 ms.

Yes, that is its new rate of de-energizing.

So the expression for i(t) through the inductor when the switch is closed is now,

i(t) = Io*e^(-t/tau) for t >= 0.

Yes, that is sure different than zero current at t=0.

Do I understand this correctly?  I keep trying the problems and keep getting them all wrong, and it is really frustrating and discouraging.  Why do I have to know all of this theoretical garbage?  I would rather learn about different circuit building blocks, like boost converters and RF filters, etc.  Just to put application to these components, you know?

No, I don't think you understand that the coil will keep its charge carriers flowing for a transient amount of time when the voltage changes.

You cannot go very far in the engineering sciences without math and a lot of it.

Ratch

[Dave]

I'm going to help you out and serve you the answer on a silver plate, because you're clearly just going to forget it the very moment your professor gives you a passing grade.

Current through the coil equals:
$${I_{L,0-} = \frac{V_1}{R_1+R_2+R_3+R_4}=731.7\text{ mA}}$$

The current through the switch before switch-on is clearly 0, since current can't flow through an open circuit.
Now we close the switch.

The current flowing through the switch that is caused by the voltage source is:
$${I_{sw1,0+} = \frac{V_1}{R_1+R_2}=1.20\text{ A}}$$

But this isn't the only current that is now flowing in the circuit, you still have an energized coil in the circuit and it wants to resist the change of current. And it does, so in the very moment of switching, the current through the coil is still going to be exactly what it was before switching, except now it takes a different path, through the switch. The only difference is that we are observing the current flowing through the switch downwards, but the current from the coil is going to flow through it upwards, so we get a negative current.
$${I_{sw2,0+} = -I_{L,0-} = -731.7\text{ mA}}$$

The total current through the switch is simply going to be the sum of both currents. They partially cancel out
$${I_{sw,0+} = I_{sw1,0+}+I_{sw2,0+} = 468.3\text{ mA}}$$
_________________________________________________________________

Why do I have to know all of this theoretical garbage?

Learning and understanding things like calculus (beyond high school jokery), Fourier and Laplace transforms, differential equations and such have probably been the most valuable circuit analysis tools that I ever put in my toolbox. I only really started to appreciate this knowledge after I figured just how easy circuit analysis becomes if you attack the problems with this toolset.

I would rather learn about different circuit building blocks, like boost converters and RF filters, etc.  Just to put application to these components, you know?

With this mindset, you're likely going to end up being one of those "SparkFun engineers", that just throw premade shit together and hopefully something sticks ends up working (poorly), most likely due to sheer coincidence.

[CraigHB]

Engineering is math - simple as that.

I would agree.  Understanding the math is what makes the difference between an engineer and a technician.  You don't typically have to use higher math to design circuits.  Most of the time you use a simulator to solve those problems.  Though there does need to be a mathematical understanding even if you don't actually have to solve complex equations by hand.

I've probably forgotten more math than I learned since I got my EE degree.  I don't use higher math much, but every now and then I may need to review something to understand an application.  People often say, "why should I learn something if I'm never going to need it."  It does seem like a reasonable statement, but you never know what skills or understanding you might need down the road.  Better to know it and not need it than need it and not know it.

[Tom45]

"Sparkfun Engineers"

I like that term.

Without knowing that term, the first time I was exposed to the concept was when I saw reference to a product and went to their web site to learn more about it. All they had was a generic description of what it was. No electrical specs at all. The input characteristics and levels? Nothing. The output source/sink specs? Again nothing. Switching speeds? You guessed it, nothing.

It was a device to buy and play with. Not something to engineer into a product.

[IanB]

Now when the switch is closed at t = 0, I am lost.  So current through the closed switch is zero, yes?  No resistance and a closed switch is essentially zero volts.

No, your intuition is wrong here. The current through the closed switch is not zero. And this is important to the next question.

Do I understand this correctly?  I keep trying the problems and keep getting them all wrong, and it is really frustrating and discouraging.  Why do I have to know all of this theoretical garbage?  I would rather learn about different circuit building blocks, like boost converters and RF filters, etc.  Just to put application to these components, you know?

I think you have the answer to your question. The reason you have to do this theoretical work, painful though you may find it, is to correct your intuition.

If you do problems now and get them wrong, then if you try to design basic circuits now they probably won't work the way you think they should work. You have to work through the fundamental theory and problem solving steps until your mental model of how circuits work is correct, so you can eventually look at a circuit and without doing any calculations estimate how it will behave.

Even though it may seem painful, you should keep at it until you can confidently predict the answer to such problems without having to work them out.

[IanB]

Just a hint about formatting of engineering equations. The units of measure should normally be not be italicized and should be separated from the value by a space:
$${I_{L,0-} = \frac{V_1}{R_1+R_2+R_3+R_4}=731.7\text{ mA}}$$
See the example above for how to do this.

[Dave]

Thanks, Ian. I fixed the post above.

[sshoptaugh1991]

I'm not stupid.  And I am not lazy.  I don't want anyone to get that idea.  It just really makes me angry that I cannot grasp a concept right away when it is introduced.  It seems to have been a trend this entire course so far that I don't start to understand things until a couple of weeks after our tests.  I know I have to understand things I think are a waste at this point in time.  My current state of anger is just driving my rhetoric and I wish I didn't let this stuff get to me so easily, but it does.

Let me try to understand this problem again....

1. The switch has been open for a long time at t < 0, so the current in the circuit is I = 30 V / 41 ohms = 0.731 A.

2. When the switch is closed, t = 0.  But because a current through an inductor cannot change instantaneously, I(0-) = I(0+) = Io.

3. The current through the inductor at t >= 0 is then I(t) = Io * e^(-t / tau).  Tau = L / R,   0.05 H / 16 ohms = 3.125 ms
    So, I(t) = Io * e^(-320*t) for t >=0

4. The current through the closed switch is I = 30 V / 25 ohms = 1.2 A.

At this point I do not know where to go now.  Because the switch is closed, all the source current flows through the path of R1, R2 and the switch, so the inductor is discharging now?

I am just trying to figure out what is supposed to be going on.

[Tom45]

I'm not stupid.  And I am not lazy.  I don't want anyone to get that idea.  It just really makes me angry that I cannot grasp a concept right away when it is introduced.

We all know that feeling of not getting it. It is different subjects for each of us.

1. The switch has been open for a long time at t < 0, so the current in the circuit is I = 30 V / 41 ohms = 0.731 A.

2. When the switch is closed, t = 0.  But because a current through an inductor cannot change instantaneously, I(0-) = I(0+) = Io.

3. The current through the inductor at t >= 0 is then I(t) = Io * e^(-t / tau).  Tau = L / R,   0.05 H / 16 ohms = 3.125 ms
    So, I(t) = Io * e^(-320*t) for t >=0

4. The current through the closed switch is I = 30 V / 25 ohms = 1.2 A.

At this point I do not know where to go now.  Because the switch is closed, all the source current flows through the path of R1, R2 and the switch, so the inductor is discharging now?

I am just trying to figure out what is supposed to be going on.

At the moment after the switch closes, there will be 1.2 A from the voltage source as you say. But there is also a decaying voltage from the field in the inductor going through the two resistors on the right hand side and through the switch. As time increases the current through the switch approaches 1.2 A.

[sshoptaugh1991]

Is that decaying voltage the voltage that is calculated with V = L * di/dt?  So when current no longer flows through the inductor after the switch closes, that voltage in the inductor discharges through R3 and the switch?

[Tom45]

Is that decaying voltage the voltage that is calculated with V = L * di/dt?  So when current no longer flows through the inductor after the switch closes, that voltage in the inductor discharges through R3 and the switch?

The inductor discharges through R3 and R4, but otherwise yes.

So the current through the switch at t > 0 is the sum of the 1.2 A from the 30 volt supply and the decaying current from the collapsing field in the inductor.

PS,
This forum flags inductor as a spelling error. Resistor and capacitor are OK.

[Zero999]

This forum flags inductor as a spelling error. Resistor and capacitor are OK.

It's nothing to do with the forum. It's the dictionary installed on your computer.

Anyway, back to the original topic: yes, it's true many people forget a lot of the maths they learn in college. I recently spent an hour or so remembering how to calculate how long it would take for a capacitor to reach a certain voltage in an RC circuit. I asked someone else at work who had only finished his physics degree two years ago for advice and he couldn't remember either! Fortunately I remembered how to do it and figured it out. I think if I'd never learned it in the first place, I probably would have taken much longer to solve it, if ever.

[Tom45]

Thanks Hero999.

After a bit of research I have enabled a custom dictionary for Chrome and added inductor.


Tom

[IanB]

It just really makes me angry that I cannot grasp a concept right away when it is introduced.  It seems to have been a trend this entire course so far that I don't start to understand things until a couple of weeks after our tests.

I think you have a valid complaint here and it is the mode of teaching that is at fault. I often felt I was the last person to grasp a new concept and sometimes I didn't "get" it until weeks or months later. In truth I don't think the human mind works that way. It isn't possible to instantly learn new things, it takes time for the understanding to really sink in. So testing people on things right after they have been taught is quite unreasonable.

I was fortunate that I went through a system where I was examined on things at the end of each year and not more frequently, and this was beneficial as I had time to learn, absorb and inwardly digest before exam time came around. I feel for people in today's environment where students are tested every few weeks or so.

[rstofer]

My grandson is embarking on his EE education and I have to get up to speed.  I find the Khan Academy videos quite helpful.

https://www.khanacademy.org/

This isn't the only set of videos out there but they are quite good.  Unfortunately, they are presented for math students and don't necessarily focus on EEs.  Nevertheless, they are very helpful.

Maybe not focusing on EEs is a good thing.  Perhaps the presentation is more complete.

[CraigHB]

I often felt I was the last person to grasp a new concept and sometimes I didn't "get" it until weeks or months later.

I had a hard time at first in engineering school.  I actually had to take a couple years off midway to kind of do a reset mentally.  I was determined since electronics was a hobby from an early age and I wanted that degree, but I was not naturally academic.  I did end up doing well, but I sure as hell didn't breeze through it.  Even now I sometimes have to review basic AC concepts.  The stuff gets complicated really fast.  I'd be lost without a circuit simulator.  In any case my feeling is it's more a matter of determination than natural ability.