That's definitely one of the classic ways of doing it. And it involves a very useful trick that is often and easily overlooked -- namely adding a second voltage source in parallel with the first, moving it onto the other side of the circuit, and then realizing that no current will flow in the connecting wire so that it can be severed. Do this breaks up the bridge circuit.

I ran across this tidbit which illustrates the "just use a formula" technique which you so rightfully disparage:

http://www.clever4hire.com/throwawa...eering-notes/Weston2-5.pdf?attredirects=0&d=1

Starting on page 6, under the heading "Wheatstone bridge--List of circuit equations", we find the canned solution.

 

You may be looking for this method:
http://www.hallikainen.com/rw/theory/theory6.html

Hi thanks for this, I found this one a couple of days ago, it is very good in terms of discussing the Wheatstone bridge. But it invokes all kinds of things, like it being balanced ect. My circuit is definitely unbalanced type. But it seems that one needs to invoke some tricks. That is why I used Delta-Y type of thing. BUT once again I am looking to see if this type of circuit can be done with just regular KCL-KVL.

 

I ran across this tidbit which illustrates the "just use a formula" technique which you so rightfully disparage:

http://www.clever4hire.com/throwawa...eering-notes/Weston2-5.pdf?attredirects=0&d=1

Starting on page 6, under the heading "Wheatstone bridge--List of circuit equations", we find the canned solution.

Wow this is amazing stuff!!!
You found a very interesting thing.
There are tonnes of equations!
But the interesting thing is to know how all of these were derived!
You are definitely going in the right direction with this link!

By the way, I don't disparage the use of canned formulas, but as being trained as a scientist first, the Science Mantra is this basically : "You do not understand anything well unless you can derive it and or provide a real PROOF".
After one understands where it comes from, then I don't have a problem with using canned Forumulas.
But the general training in Engineering, is just follow these formulas, and it will work.
BUT the problem with this Engineering mentality is you will have a less developed mind to analyze complicated systems!

 

Hi thanks for this, I found this one a couple of days ago, it is very good in terms of discussing the Wheatstone bridge. But it invokes all kinds of things, like it being balanced ect. My circuit is definitely unbalanced type. But it seems that one needs to invoke some tricks. That is why I used Delta-Y type of thing. BUT once again I am looking to see if this type of circuit can be done with just regular KCL-KVL.

As I've stated several times, yes, it can be done with only KVL/KCL. The first step to doing it properly is to clearly annotate the diagram with the branch currents. Why won't you do that?

It is trivially easy:


Took less than two minutes using Paint.

The directions you assign to the currents are arbitrary -- you could flip a coin. If the value for one of them turns out to be negative, then you know that the current is actually flowing in the other direction. But it's good practice to assign them in the order you are pretty sure the current will actually flow in so that you have a built in alarm when one turns up negative telling you that you need to look at it with an eye to the probability that it is wrong.

Also notice that the polarity of your voltage source was not indicated. As shown, there was no way to determine which node was connected to the positive terminal. Attention to detail is critical in engineering!

You have seven unknowns, so you need to come up with seven independent equations using a combination of KVL and KCL. Doing so is pretty straight-forward, but you do have to make sure that they are independent. This is where the beauty of Mesh and Nodal analysis come into play because they are formalized so that you have three equations (in the case of nodal analysis) or four equations (in the case of mesh analysis) and you know that they are independent. But we can tackle it with just raw KVL and KCL.

The next step is to start coming up with the relationships between these various currents using KVL, KCL, and Ohm's Law.

 

Hi thanks for this, I found this one a couple of days ago, it is very good in terms of discussing the Wheatstone bridge. But it invokes all kinds of things, like it being balanced ect. My circuit is definitely unbalanced type. But it seems that one needs to invoke some tricks. That is why I used Delta-Y type of thing. BUT once again I am looking to see if this type of circuit can be done with just regular KCL-KVL.

The bridge analyzed there is definitely NOT balanced.

 

Sorry WBan, I am running around multi-tasking, I was planning to redo the circuit diagram with the current directions. I was going to do it and put it up tomorrow. I am in the Eastern Timezone, and I have to get going now. BUT, thanks for posting this diagram with the directions. This circuit will be a good exercise in KVL and KCL. So I see that you are basically saying that this reduces to solving a system of algebraic equations. OK, so that is what I wanted to know.

 

As I've stated several times, yes, it can be done with only KVL/KCL. The first step to doing it properly is to clearly annotate the diagram with the branch currents. Why won't you do that?

It is trivially easy:
View attachment 87674

Took less than two minutes using Paint.

The directions you assign to the currents are arbitrary -- you could flip a coin. If the value for one of them turns out to be negative, then you know that the current is actually flowing in the other direction. But it's good practice to assign them in the order you are pretty sure the current will actually flow in so that you have a built in alarm when one turns up negative telling you that you need to look at it with an eye to the probability that it is wrong.

Also notice that the polarity of your voltage source was not indicated. As shown, there was no way to determine which node was connected to the positive terminal. Attention to detail is critical in engineering!

You have seven unknowns, so you need to come up with seven independent equations using a combination of KVL and KCL. Doing so is pretty straight-forward, but you do have to make sure that they are independent. This is where the beauty of Mesh and Nodal analysis come into play because they are formalized so that you have three equations (in the case of nodal analysis) or four equations (in the case of mesh analysis) and you know that they are independent. But we can tackle it with just raw KVL and KCL.

The next step is to start coming up with the relationships between these various currents using KVL, KCL, and Ohm's Law.

Hi there, I just briefly checked the original diagram, and I think that in your diagram you need to reverse the direction of current I3.

 

Wow this is amazing stuff!!!
You found a very interesting thing.
There are tonnes of equations!
But the interesting thing is to know how all of these were derived!
You are definitely going in the right direction with this link!

By the way, I don't disparage the use of canned formulas, but as being trained as a scientist first, the Science Mantra is this basically : "You do not understand anything well unless you can derive it and or provide a real PROOF".
After one understands where it comes from, then I don't have a problem with using canned Forumulas.

Let me get this straight, you are looking to understand where formulas come from but think that a link to 10 MB of canned formulas is going in the right direction. Hmmm....

But the general training in Engineering, is just follow these formulas, and it will work.
BUT the problem with this Engineering mentality is you will have a less developed mind to analyze complicated systems!

No, that is not the general training in Engineering (though I must admit that the overall trend is moving in that direction), that was the training in engineering you received at a really crappy school.

 

Hi there, I just briefly checked the original diagram, and I think that in your diagram you need to reverse the direction of current I3.

Why?

First and foremost, as I said, the directions assigned to the currents are arbitrary. Your modified circuit gives no preference to one over the other since it indicates no polarities for any of the voltages (not even the DC source!). Hence the current polarities can be assigned arbitrarily -- they can literally be chosen by flipping a coin for each one. When (and if) we assign voltages drops across the elements, we need to put their polarities so as to conform with the passive sign convention -- and even this is merely a convention (though an EXTREMELY useful one) and we could flip coins for these two. We will still get the right answer if we pay attention to detail. It might well be useful for you to get a coin and do this and demonstrate that it is true.

I assigned the direction I did because that is the direction that the current will actually flow in this circuit. This can be seen by removing the 8Ω resistor from the circuit and asking which node, C or D, will have the higher voltage. By assigning I3 in that direction I expect to get a positive result for I3 (as well as all of the other currents). If ANY of the currents ends up being negative, then alarm bells go off and I start looking for my error.

 

Wow this is amazing stuff!!!
You found a very interesting thing.
There are tonnes of equations!
But the interesting thing is to know how all of these were derived!

They were derived by the use of KVL, KCL and Ohm's law. There is often a lot of algebra involved in the solution of what would seem to be relatively simple circuits. Modern mathematical software, or a modern calculator, can do the drudgery of massive algebra, but you have to set up your equations correctly, and that requires understanding the circuit behavior.

You are definitely going in the right direction with this link!

I'm not sure what you mean when you say that "You are definitely going in the right direction with this link!". The direction I was intending to go is to show that if we rely on a catalog of formulas for every circuit, we will have a very large collection of formulas. It's better to know how to derive a "formula" (a solution, in other words) for any circuit; to do so requires that you know how electricity behaves. Just applying formulas can easily lead one to apply a wrong formula, because you don't understand the underlying circuit behavior.

By the way, I don't disparage the use of canned formulas, but as being trained as a scientist first, the Science Mantra is this basically : "You do not understand anything well unless you can derive it and or provide a real PROOF".
After one understands where it comes from, then I don't have a problem with using canned Forumulas.
But the general training in Engineering, is just follow these formulas, and it will work.
BUT the problem with this Engineering mentality is you will have a less developed mind to analyze complicated systems!

My comment was directed to WBahn. I didn't know your attitude toward using canned formulas until now.

 

This circuit will be a good exercise in KVL and KCL. So I see that you are basically saying that this reduces to solving a system of algebraic equations. OK, so that is what I wanted to know.

They didn't even teach you that!

 

I ran across this tidbit which illustrates the "just use a formula" technique which you so rightfully disparage:

http://www.clever4hire.com/throwawa...eering-notes/Weston2-5.pdf?attredirects=0&d=1

Starting on page 6, under the heading "Wheatstone bridge--List of circuit equations", we find the canned solution.

One of the big problems with canned formulas and solutions -- and I'm sure you agree with this fully -- is that such formulas are almost always specific to particular problems and circuit topologies. Unless you have EXACTLY the topology the formula is for, throwing values into the canned solution will do nothing except produce a result that is wrong. It's one thing for a technician that lacks even rudimentary algebra skills to rely on books filled with canned formulas -- when you have to refer to a sheet that has V=IR, I=V/R, and R=V/I all on it, your very lack of mathematical literacy forces you into that. But this is unacceptable for a properly educated engineer (and most properly trained technicians, too).

Even with such simple formulas as the voltage divider equation we see time and time again this equation being used in situations in which it simply does not apply. But the person using it is incapable of deriving it and has no idea what constraints are imposed by it - they merely sees it as a formula that you through at any problem in which you need a voltage and you have some other voltage and at least two resistances. Even Ohm's Law is regularly abused because people using it don't have the faintest clue what it means and so if they have a voltage somewhere at the left hand side of the circuit and a current in some branch over on the right hand side, they will throw those at Ohm's Law in order to get the value of the unknown resistance in a branch somewhere in the middle.

 

Just a brief clarification on me saying things about "canned formulas", I also said "going in the right direction".
With the "right direction: I meant to say, that the material you sent was focused on Bridge-based circuits and analyzing bridge type of circuits.
For the "canned formulas", I know that canned formulas are for very specific circuit topologies, but even for those, you should understand how it was derived. My whole point is that one should understand the circuit at hand.
That's all I meant.

WBahn, in term of the circuit directions, recall I told you I saw a star-asterisk type of symbol near each resistor element in the original diagram, and I assumed it indicated direction of flow into the element.
I am just going based on that.

And in terms of me having gone to an Engineering that wasn't that great, you don't need to keep reminding me about that. It was a nightmare to go thru that system that they setup. Especially me knowing that they were not teaching me well, and there was no support system to help. It felt like going thru World War 2, it was very awful psychologically, very damaging. Until you have gone thru the system I have gone thru, you won't understand how bad the psychological torture was.

 

WBahn, in term of the circuit directions, recall I told you I saw a star-asterisk type of symbol near each resistor element in the original diagram, and I assumed it indicated direction of flow into the element.
I am just going based on that.

And that's entirely fine and reasonable. I'm merely going on the problem (the one with just resistors) as you gave it, which included none of those indicators. If you want to encourage the use of specific assignments, then your diagram needs to include details that encourage the use of those specific assignments.

And in terms of me having gone to an Engineering that wasn't that great, you don't need to keep reminding me about that.

I'm not trying to keep reminding you of it, but when you make sweeping generalizations that appear to be rooted in your specific experience (which we all do), I'm going to point it out.

It was a nightmare to go thru that system that they setup. Especially me knowing that they were not teaching me well, and there was no support system to help. It felt like going thru World War 2, it was very awful psychologically, very damaging. Until you have gone thru the system I have gone thru, you won't understand how bad the psychological torture was.

Out of curiosity (and you don't have to answer), why did you stay there? It's one thing for the poor ignorant souls that don't realize the poor quality of the education they are getting, but why someone would stay there, even if someone else is paying for it, knowing that they are getting a largely worthless education baffles me.

 

Hi,
I will answer this.
After completing a Bachelors of Science, I went into Engineering.
I wanted to stay local to the city I lived to not incur additional living expenses.
There were only 2 universities offering Engineering programs in the city at that time.
The other one was top notch and world renowned, but extremely difficult to get into.
I did not think that this other one was bad, because I had a friend that went thru it and said it was not bad.
BUT I had a lot of transfer credits from my sciences, so I did not see much per se, of first year. I knew it was not as good, but I thought due to them trying to weed people out, I thought it would be just in 1st and or 2nd year. By second year it was awful, because they got rid of the most that way, in very unfair ways I might add.
BUT I thought, surely, by THIRD year they will have the the good ones they want, and train us properly going forward.
When I got to the THIRD year, it was the same bad treatment.
They continued to get rid of a certain amount of students in 3rd and 4th year.

SO you see I had HOPE that things would get better, but it never got better.
I was contemplating going to a different university, but by this point, I had been in University for 8 years, I did not want to start over, and also HOW do I know how the other University would be any better!
NO body is willing to tell you the truth of what goes on at different Univeristies, out of pride because they go there or other reasons.

My friend that went to this university, and said it was ok when I first asked him about it.
When I told him that this place is very bad, my friend then basically admitted to me, "Well if you found it bad already having a prior degree, WELL what about ME, what about ME!!!! I went in directly from highschool! And he started to cry and got into the fetal position, in a traumatized state!

SO, you see its about not wanting to waste any more time in University and not spending any more money.
SO unless you are rich, your options in general, based on the time-money constraints, are very limited.
SO getting a bad Engineering degree, is better than no Engineering degree.

This was back in the 90's early 2000 time period.

I can go into many stories of how I got some of the faculty to admit they were not playing
fair, and created this bad learning environment to generate money.
BUT, I digress.
They even told me well since you have figured out our system, why don't you leave then!

AND like I mentioned above, its all about the constraints!
The poor, don't have many options without making their financial situation worse.

P

 

Wow this is amazing stuff!!!
You found a very interesting thing.
There are tonnes of equations!
But the interesting thing is to know how all of these were derived!

They set up a set of circuit equations using KCL, KVL and Ohm's law and solved them for the various currents.

They didn't have the advantage of modern mathematical software, or a modern calculator. Here's how I would find a "formula" for the current in the resistor they labeled "g". I set up loop equations, using the designators for the resistors from the Weston article circuit on page 6 of that document.

I formulated the equations in matrix form, and solved them in a few milliseconds using Mathematica (Wolfram Alpha has the essentially the same functionality, and is available on the web). I also solved them on my HP50 calculator in about 3 seconds. All the "formulas" for the various currents in the circuit are available from this result, not just the "formula" for Ig.

Here's the solution; it's just this easy. There's absolutely no reason to keep tables of formulas around when solving the exact circuit in question is so easy, and you don't have to worry if you're using the right "formula".

To do this properly, one needs to understand what's behind this system of equations. Learning that is well worth the effort. You can teach yourself beyond what you learned in school; just get a circuit analysis text (or two, or three) and work through it.

 

They set up a set of circuit equations using KCL, KVL and Ohm's law and solved them for the various currents.

They didn't have the advantage of modern mathematical software, or a modern calculator. Here's how I would find a "formula" for the current in the resistor they labeled "g". I set up loop equations, using the designators for the resistors from the Weston article circuit on page 6 of that document.

I formulated the equations in matrix form, and solved them in a few milliseconds using Mathematica (Wolfram Alpha has the essentially the same functionality, and is available on the web). I also solved them on my HP50 calculator in about 3 seconds. All the "formulas" for the various currents in the circuit are available from this result, not just the "formula" for Ig.

Here's the solution; it's just this easy. There's absolutely no reason to keep tables of formulas around when solving the exact circuit in question is so easy, and you don't have to worry if you're using the right "formula".

To do this properly, one needs to understand what's behind this system of equations. Learning that is well worth the effort. You can teach yourself beyond what you learned in school; just get a circuit analysis text (or two, or three) and work through it.

Hi "The Electrician",
This is very interesting that you thought of doing this in Mathematica.
I have used Mathematica, along with Matlab and Maple.
SO, I see this would be very intensive on paper with a large algebraic based system of equations.


In terms of books on electric circuits, I have obtained many of them, but they all seem to lack in general, applying principles in more complex topologies.

Thanks again, you have shown a great wealth of resources.
Sincerely,
P

 

First, thanks for sharing.

SO you see I had HOPE that things would get better, but it never got better.

This is a common trap that I suspect every falls into from time to time. We look at things with rose covered glasses and tend to look at the bright side that things are sure to get better. Hell, it's even explicitly mentioned in our own Declaration of Independence: "and accordingly all experience hath shewn, that mankind are more disposed to suffer, while evils are sufferable, than to right themselves by abolishing the forms to which they are accustomed."

Inertia is a powerful force in human affairs; we stay in bad marriages, bad jobs, bas neighborhoods, bad friendships, bad hobbies, bad habits,... and bad schools... long after prudence should have led us to walk away.

I was contemplating going to a different university, but by this point, I had been in University for 8 years, I did not want to start over, and also HOW do I know how the other University would be any better!

While a very valid point -- and bitten once twice shy plays a role -- what you can do (and this may help for some future situation) is take stock of what you have learned makes your situation bad and leverage that to better research the alternatives. No guarantees, but it greatly stacks the deck in favor of you at least making the situation better.

SO getting a bad Engineering degree, is better than no Engineering degree.

This is a very common fallacy of thought. I have seen tons of people that would have been FAR better off not getting an engineering degree at all (and I'm talking about degrees from good schools) because all they ended up with was a piece of paper and a ton of debt but without the skills to back up the degree. Most of them were unemployable in engineering and ended up in jobs that paid little, if any, better than what they could have gotten without a degree at all, particularly when you factor in where they would have been with four or six or eight years of time on the job accruing promotions and raises over that time.

I've seen people that have built up a mountain of debt and then got trapped in the mindset that now they couldn't drop out because the only way they could service the debt was to finish the degree and get a good paying job. So they kept piling up even more debt despite the fact that even they admitted that they lacked the knowledge and skills to ever be a practicing engineer. It's a very sad thing to see and I can only imagine how depressing and even terrifying it must be to be in that situation.

 

In terms of books on electric circuits, I have obtained many of them, but they all seem to lack in general, applying principles in more complex topologies.

That's because the idea is for you to learn the concepts that apply to ALL circuits (within broad constraints, such as being linear, or being in steady state, or whatever) and to show you how to use them with the basic categories of topologies from which (nearly) all more complex topologies are constructed or can be broken down into. There is no way for any text to cover all of the complex topologies that are possible. If you limit the circuit to eight components or so, the number of possibilities becomes daunting.

Consider an example -- you were shown how to find the equivalent resistance of two resistors in series and then shown how to extend this to three resistors. You were not then shown examples that had twelve resistors in series because it was assumed/hoped that you could extend the concept from three resistors to twelve resistors on your own. Now, that's somewhat of a bad example because you were almost certainly shown how to extend the result for two resistors to N resistors, but hopefully the idea is there.

 

View attachment 87674

The next step is to start coming up with the relationships between these various currents using KVL, KCL, and Ohm's Law.

I'm really hoping you will carry through on this because we can use it to develop all of these techniques that you've said you want to learn where they come from.