How to treat internal resistance in calculations ?

[I like Serena]

Well, now there's a contradiction!

In my earlier problem I also had a circuit that had a parallel component!

So how come using the combined voltage with kirchhoff's voltage law in my earlier problem was okay:

But using the combined voltage with kirchhoff's voltage law in this problem is not okay?

Perhaps it would have been better if you hadn't combined the voltage sources.
You'd include the separate voltage sources in the voltage sum.
And in this case you'd see that they do add up! ;)

I've written it on the paper. I got to the point where the "voltage drop" was more than the voltage. It's on my post before this one.

Yeah, the problem is that you're using a calculated I₁ that is based on an 18 V voltage source. With the 18 V the voltage drop does not exceed the voltage source. :)

 

[jhae2.718]

To throw in my $0.02, it's probably better to just use KVL and KCL* to solve the circuits without combining the voltage sources. Of course, you get some nasty systems of equations, but a little matrix algebra makes it easier.


*I actually prefer to use \int\mathbf{E}\cdot d\mathbf{r} = 0, as it makes for an easier transition to taking a time variant magnetic flux into account.

 

[Femme_physics]

Earlier, you were considering the case when the switch was open. Then, the circuit contained a single loop and all the components were in series. Thus, for purposes of determining currents, you could simply combine the voltage supplies into a single "net" supply

When the switch is closed, another loop is created. Now both supplies will have independent influences on what happens in it, and there will be an interaction between the loops that alters the overall currents and voltages. Stand by for simultaneous equations!

A) Love your enthusiasm lol! :DB) Hmm, so I can't take the result of the open switch and apply it to the closed switch (in this case, anyway)?

Perhaps it would have been better if you hadn't combined the voltage sources.
You'd include the separate voltage sources in the voltage sum.
And in this case you'd see that they do add up! ;)

So are you telling me that whenever I have 2 voltage sources and I want to use kirchhoff's law for voltages, I mustn't combine them?

To throw in my $0.02, it's probably better to just use KVL and KCL* to solve the circuits without combining the voltage sources. Of course, you get some nasty systems of equations, but a little matrix algebra makes it easier.

Woah. Hefty.
It's not in our course to solve things that way. I would be losing contact with my classmates if my solution papers would include high-level methods!

Yeah, the problem is that you're using a calculated I1 that is based on an 18 V voltage source. With the 18 V the voltage drop does not exceed the voltage source. :)

Hmm, okay, fine, but when I'm considering the 10V source, does its current split in the crossroad to both right and let, or just right? (and if it's just right, how am I supposed to know? I learned that a current flows from positive to negative. Now the current has 2 options of how to flow, by diverging left or by diverging right. [shown in drawing]

http://img849.imageshack.us/img849/8716/theloop.jpg

 

[gneill]

Unfortunately, until you write and solve the equations you can't be certain of how much current is going to be going where. It is possible that the 10V "source" is actually sinking current (current flowing into the + terminal of the battery, not out) rather than supplying it. In the single loop circuit, what was the direction of the current? Clockwise, right? So the current then was flowing out of the 18V supply and into the 10V supply.

For this "new" problem with two loops, there are several possible approaches depending upon the concepts you've already covered in class. You've mentioned KVL and KCL, the basic "workhorses" of analysis. A pure KVL approach using what are called "loop currents" will produce two equations in two unknowns to solve. A nodal analysis employing KCL and and a bit of KVL will result in 4 equations; one for each circuit branch and one for the top node where they meet (they're not particularly tricky to solve). Either way is fairly straightforward with this circuit.

 

[I like Serena]

B) Hmm, so I can't take the result of the open switch and apply it to the closed switch (in this case, anyway)?

No. :)

So are you telling me that whenever I have 2 voltage sources and I want to use kirchhoff's law for voltages, I mustn't combine them?

It's a matter of choice.
You can combine them, but only if they are in series with no branches in between.
It's a good (double or triple) check not to combine them straight away, but only if the algebra of Kirchhoff's laws shows that you can.

Woah. Hefty.
It's not in our course to solve things that way. I would be losing contact with my classmates if my solution papers would include high-level methods!

Yeah, well, you'll have to figure that one out on your own.

It might also give you the opportunity to pull your class along in new and unprecedented directions! :)
I expect you'd get the support from your teacher if you try. ;)

Hmm, okay, fine, but when I'm considering the 10V source, does its current split in the crossroad to both right and let, or just right? (and if it's just right, how am I supposed to know? I learned that a current flows from positive to negative. Now the current has 2 options of how to flow, by diverging left or by diverging right. [shown in drawing]

You don't know yet how the current will flow until you've solved the equations.
In mechanics, it's exactly the same. You won't know which way the forces will go until you've calculated them. A negative sign means it was actually the other direction.

Think of it this way.
If you look at an electron that can move freely in the wire, it feels the electric field from both batteries. The one battery pushes it in one direction, the other battery pushes it in the other direction. The way it will go depends on which force is strongest.

Actually, there's a concept called "superposition" that treats the circuit as if there's only one battery at a time, and calculate the effective currents.
Then the same with the other battery.
And finally adding everything up (which is why it is called superposition).

It's possible you'll get this method in class.
Either way, the method with Kirchhoff's law is easier, less work, and less prone to errors.

 

[Femme_physics]

You don't know yet how the current will flow until you've solved the equations.

But, I can know for sure it will flow from plus to minus and not the other way around. That's just a core principle of electronics with respect to voltage sources and how they flow. No?

Unfortunately, until you write and solve the equations you can't be certain of how much current is going to be going where. It is possible that the 10V "source" is actually sinking current (current flowing into the + terminal of the battery, not out) rather than supplying it.

I never heard about a sinking current! How is that possible? Again, from my conclusion above, flow must go from + to -. I was never told otherwise!

In the single loop circuit, what was the direction of the current? Clockwise, right? So the current then was flowing out of the 18V supply and into the 10V supply.

Is it necessarily clockwise? What about this case->

http://img15.imageshack.us/img15/2613/thiscase.jpg

Uploaded with ImageShack.us

Looks like it would go counterclockwise to me!

You can combine them, but only if they are in series with no branches in between.

I see, so in the other exercise they were combinable. Here they're not because crossroad B in the middle separates them

http://img69.imageshack.us/img69/9650/samecross.jpg

Uploaded with ImageShack.us

Correct?



(if I missed something, I'll repost later. Too much confusion over the stuff I've written above for now)

 

[I like Serena]

But, I can know for sure it will flow from plus to minus and not the other way around. That's just a core principle of electronics with respect to voltage sources and how they flow. No?

I never heard about a sinking current! How is that possible? Again, from my conclusion above, flow must go from + to -. I was never told otherwise!

No.

It can go the other way. This means the battery is being "charged".
Think of a car, where the battery is charged, when the engine is running, by a dynamo.
The dynamo is a second voltage source in the same circuit which gives off a higher voltage.

Note that in a circuit with only one voltage source, the current will always go from + to -, which I think is what you're referring to.

Is it necessarily clockwise? What about this case->

Looks like it would go counterclockwise to me!

You're quite right.
It is not necessarily clockwise! :)

I see, so in the other exercise they were combinable. Here they're not because crossroad B in the middle separates them

Correct?

Yep!

(if I missed something, I'll repost later. Too much confusion over the stuff I've written above for now)

I see little confusion in your questions.
Seems you already understand perfectly, but are as yet not ready to claim that.

 

[gneill]

For circuits with a single voltage supply the current direction is unambiguous -- current will flow out of the + terminal, wander through the circuit, and return to the - terminal.

When you have multiple sources they can "oppose" each other and force current to enter some sources while it leaves others. Note that when we force current into a battery in this "reverse" direction, the battery is said to be "sinking" the current -- that's how a real life battery gets recharged.

The direction of current flow around a given loop (clockwise or counterclockwise) depends upon the location and polarity of the voltage or current supply in the loop. You can always redraw the loop to change the direction that you perceive -- just flip the drawing over!

In your original drawing of the circuit when the switch was open and you had the single loop with the 18V and 10V batteries (and R1 and R2), it is clear that the 18V battery is going to "overwhelm" the 10V battery and force the current to flow clockwise in the circuit as drawn. Thus the 18V battery will be "sourcing" current, while the 10V battery will be "sinking" (taking in) current.

Don't worry overmuch about this. The math takes care of the details in the current direction. The important thing to remember is that ideal voltage supplies will source or sink ANY amount of current required to maintain their designated potential difference (voltage) across them.

 

[Femme_physics]

[edit] Gneill I didn't see your reply before I posted-- will reply to it later[/edit]

Note that in a circuit with only one voltage source, the current will always go from + to -, which I think is what you're referring to.

It can go the other way. This means the battery is being "charged".

Really? How does it work? One voltage source "charges" the other voltage source and in turn the other voltage source decides to change direction?

I don't see how the effect of another voltage source can change the direction of another voltage source.

I can't relate to your dynamo example, I don't know the first thing about cars!

Yeah, well, you'll have to figure that one out on your own.

It might also give you the opportunity to pull your class along in new and unprecedented directions! :)
I expect you'd get the support from your teacher if you try. ;)

Well, students in my class are struggling enough. There's no need to bombard them with new fancy methods the way I see it! But, an interesting idea, just less practical to start being too innovative while the rest of them still have question marks popping over their heads over Kirchhoff laws.

You don't know yet how the current will flow until you've solved the equations.
In mechanics, it's exactly the same. You won't know which way the forces will go until you've calculated them. A negative sign means it was actually the other direction.

I always like examples from mechanics :)

Actually, there's a concept called "superposition" that treats the circuit as if there's only one battery at a time, and calculate the effective currents.
Then the same with the other battery.
And finally adding everything up (which is why it is called superposition).

It's possible you'll get this method in class.
Either way, the method with Kirchhoff's law is easier, less work, and less prone to errors.

Duly noted. I actually heard the term "superposition" said by our teacher, but he didn't bother to explain that. Teachers can throw a lot of fancy terms and then tell us "oh, nevermind, you don't know that. That would be too hard for you." *chuckles*

But I thought I USE Kirchhoff laws with superposition, no? That way I get more equations I think (like isolating beams on a frame), than if I look at the circuit as a whole without isolating any component.

 

[Femme_physics]

Don't worry overmuch about this. The math takes care of the details in the current direction. The important thing to remember is that ideal voltage supplies will source or sink ANY amount of current required to maintain their designated potential difference (voltage) across them.

Good! Glad that's clear.

When you have multiple sources they can "oppose" each other and force current to enter some sources while it leaves others. Note that when we force current into a battery in this "reverse" direction, the battery is said to be "sinking" the current -- that's how a real life battery gets recharged.

I'll take your word for it and won't worry about it as per your next post...->

Don't worry overmuch about this. The math takes care of the details in the current direction. The important thing to remember is that ideal voltage supplies will source or sink ANY amount of current required to maintain their designated potential difference (voltage) across them.

Very well, then let me worry about the math. These are the equations to get the answer of I₁ when the circuit is closed.

http://img690.imageshack.us/img690/5826/solvingi.jpg [/QUOTE]

We have appeared to have decided, in equation#2, that the current will not flow through R₁. Based on what "math" can I know that? Or is it based on a principle?

 

[I like Serena]

Really? How does it work? One voltage source "charges" the other voltage source and in turn the other voltage source decides to change direction?

I don't see how the effect of another voltage source can change the direction of another voltage source.

I can't relate to your dynamo example, I don't know the first thing about cars!

Well, a voltage source doesn't "decide" to change direction.
It gets fed electrons more forcefully than it can spew them out.

Bad example with the car then.
How about a rechargeable battery? Like the one in a mobile phone?
You plug it in, in a wall socket, and the battery in the phone gets charged by the stronger wall power.
If current would only flow from the battery outward, in the time the mobile phone would be dead and the battery would have to be replaced.

Well, students in my class are struggling enough. There's no need to bombard them with new fancy methods the way I see it! But, an interesting idea, just less practical to start being too innovative while the rest of them still have question marks popping over their heads over Kirchhoff laws.

Wait then till your teacher starts teaching it.
You'll be ahead and people will be eager to learn from you! :)

I always like examples from mechanics :)

:)

Duly noted. I actually heard the term "superposition" said by our teacher, but he didn't bother to explain that. Teachers can throw a lot of fancy terms and then tell us "oh, nevermind, you don't know that. That would be too hard for you." *chuckles*

You'll be turning the tables on them. ;)
Be careful though, their self esteem might not take well to a student knowing better than a teacher. :)

But I thought I USE Kirchhoff laws with superposition, no? That way I get more equations I think (like isolating beams on a frame), than if I look at the circuit as a whole without isolating any component.

Usage of Kirchhoff's laws implies superposition. It's all rolled into 1 equation.

It's different however from looking at a whole system, as in mechanics.
As yet we're talking about isolated circuits that have no interaction with the real world.
It's like a mechanical system without smachims, but just standing loose.

That will come though, but later.
Then you'll be applying for instance an input signal to a circuit, and the circuit might produce another output signal (this is a kind of "filter").

 

[Femme_physics]

[edit] made a post just before yours :) [/edit]

Well, a voltage source doesn't "decide" to change direction.
It gets fed electrons more forcefully than it can spew them out.

Makes sense.

Bad example with the car then.
How about a rechargeable battery? Like the one in a mobile phone?
You plug it in, in a wall socket, and the battery in the phone gets charged by the stronger wall power.
If current would only flow from the battery outward, in the time the mobile phone would be dead and the battery would have to be replaced.

So the current in the wall MUST be stronger than the current in the battery, otherwise it would be the battery "charging" the wall, and that's just stupid!

Usage of Kirchhoff's laws implies superposition. It's all rolled into 1 equation.

So I can't use Kirchhoff's laws WITHOUT superposition?

It's different however from looking at a whole system, as in mechanics.

Hmm. In mechanics when we look at the whole system we look at "external forces."


Re:

Wait then till your teacher starts teaching it.
You'll be ahead and people will be eager to learn from you! :)

Maybe it's not in our material plan? How can I know for sure? Or, if it is, how can I know if it's for this semester? I seem to be struggling with basic concepts. I rather get them straight first!

You'll be turning the tables on them. ;)
Be careful though, their self esteem might not take well to a student knowing better than a teacher. :)

Let alone, a gurrrl student!
Meh, they already know I'm a studies freak, but I doubt I'll know better than my teacher! But, thanks for the super vote of confidence! :)

 

[I like Serena]

[edit] I'll slow down my responses a little to keep everything in sync then!

I think we're "superimposing" a second thread in this thread here! [/edit]

We have appeared to have decided, in equation#2, that the current will not flow through R₁. Based on what "math" can I know that? Or is it based on a principle?

No, current will flow through R₁, also in equation #2.

In equation #2 Kirchhoff's voltage law is applied to the loop in which R₁ is not present. This means the loop is treated as an isolated system with an unknown current leaking out to R₁, but which is not relevant to the equation.

Note that in equation #1 the voltage law is applied to the loop in which R₂ is not present.

 

[Femme_physics]

[edit] I'll slow down my responses a little to keep everything in sync then! [/edit]

As you please :)

No, current will flow through R₁, also in equation #2.

Aha! Then how come we didn't include it? Or, did we make a mistake?

In equation #2 Kirchhoff's voltage law is applied to the loop in which R₁ is not present. This means the loop is treated as an isolated system with an unknown current leaking out to R₁, but which is not relevant to the equation.[

Note that in equation #1 the voltage law is applied to the loop in which R₂ is not present.
/QUOTE]

That's right. So what we did in these equations is superposition with isolation?


Superposition is just using one voltage source. Isolation, well, that's isolating a loop. If I understand correctly.

 

[gneill]

Very well, then let me worry about the math. These are the equations to get the answer of I₁ when the circuit is closed.

http://img690.imageshack.us/img690/5826/solvingi.jpg

We have appeared to have decided, in equation#2, that the current will not flow through R₁. Based on what "math" can I know that? Or is it based on a principle?

Hmm. Perhaps it's me, but I seem to recall that R1 was 50Ω and R2 30Ω. But otherwise, your methodology looks fine.

What you've done is chosen two KVL loops that cover all the components in the circuit. Good. You can choose any set of loops that you like as long as all the components in the circuit are traversed by at least one of them. It's perfectly fine that the first loop does not pass through R2 and V2; the second loop does that.

 

[Femme_physics]

Thanks gneill :)

indeed R1 is 50 ohms and R2 is 30 ohms, but there's also internal resistance of 10 which I added in series (that's why you see 60 and 40 instead of 50 and 30). I thought that makes sense, no?

 

[gneill]

Thanks gneill :)

indeed R1 is 50 ohms and R2 is 30 ohms, but there's also internal resistance of 10 which I added in series (that's why you see 60 and 40 instead of 50 and 30). I thought that makes sense, no?

Ah! Yes, that makes sense.

 

[I like Serena]

I merged your 2 replies here to get back into sync. :)

So the current in the wall MUST be stronger than the current in the battery, otherwise it would be the battery "charging" the wall, and that's just stupid!

Actually, it's not the current, it's the voltage.
And yes, if the voltage of your battery is higher than the voltage of the wall power, you will charge the wall!
(This is actually done in practice as well!)

So I can't use Kirchhoff's laws WITHOUT superposition?

Hmm, that seems to be a little black and white.
Actually you can choose. :)

If you apply Kirchhoff's laws including all voltage sources, you're using the laws INCLUDING superposition.

If you apply Kirchhoff's laws with only 1 voltage source, you're using the laws WITHOUT superposition. That way you can do the superposition afterward.

Hmm. In mechanics when we look at the whole system we look at "external forces."

Yes in electronics we look at "external power supplies" that are not part of the circuit itself.

Maybe it's not in our material plan? How can I know for sure? Or, if it is, how can I know if it's for this semester? I seem to be struggling with basic concepts. I rather get them straight first!

Don't you have books or stuff? You can look it up! Or ask your teacher.

And I think you are doing a fine job grasping the basic concepts (you're just grasping a little more at the same time).
You'll see when you're in class again.

Let alone, a gurrrl student!
Meh, they already know I'm a studies freak, but I doubt I'll know better than my teacher! But, thanks for the super vote of confidence! :)

:)

Aha! Then how come we didn't include it? Or, did we make a mistake?

It's not part of the isolated loop. No mistake.

That's right. So what we did in these equations is superposition with isolation?

Huh? I don't understand.

Superposition is just using one voltage source. Isolation, well, that's isolating a loop. If I understand correctly.

Yes, these are 2 different things.

In the isolated loop everything is still superimposed.

 

[Femme_physics]

Ah! Yes, that makes sense.

:)
Appreciate it.

Huh? I don't understand.

It's not part of the isolated loop. No mistake.

If you apply Kirchhoff's laws including all voltage sources, you're using the laws INCLUDING superposition.

If you apply Kirchhoff's laws with only 1 voltage source, you're using the laws WITHOUT superposition. That way you can do the superposition afterward.

I figured there's a 3rd way to apply Kirchhoff's law. With only 1 voltage source and WITH superposition. Or is that not allowed?

Don't you have books or stuff? You can look it up! Or ask your teacher.

We don't. We only have what we copy from the board. Our material in electronics is very specific to our needs at the moment.

And I think you are doing a fine job grasping the basic concepts (you're just grasping a little more at the same time).
You'll see when you're in class again.

Thanks :)

 

[I like Serena]

I figured there's a 3rd way to apply Kirchhoff's law. With only 1 voltage source and WITH superposition. Or is that not allowed?

Not sure what you mean.
What do you have in mind?

We don't. We only have what we copy from the board. Our material in electronics is very specific to our needs at the moment.

That's an awkward way to learn!
Can't look ahead and forces you to do things exactly in the pace the teacher sets.

 

[Femme_physics]

Not sure what you mean.
What do you have in mind?

My bad. I forgot Kirchhoff law is applied only to a single closed loop. But why did we necessarily choose the right divergence to the 10V source? Would picking the left side divergence of the closed loop using the 10V source legit as well? (the loop marked in red)
http://img6.imageshack.us/img6/7064/isitokay.jpg

That's an awkward way to learn!
Can't look ahead and forces you to do things exactly in the pace the teacher sets.

Same way in materials science. We cope with what we get, and try to solve exercises often a bit our of our league. :-/

 

[I like Serena]

My bad. I forgot Kirchhoff law is applied only to a single closed loop. But why did we necessarily choose the right divergence to the 10V source? Would picking the left side divergence of the closed loop using the 10V source legit as well? (the loop marked in red)

Random choice.
But yes, you can also choose your red loop. :)

Same way in materials science. We cope with what we get, and try to solve exercises often a bit our of our league. :-/

Then it's good that you already know a bit more about electronics!
If you get an exercise now, it won't be out of your league, but it'll be easy peasy! :)

 

[Femme_physics]

Random choice.
But yes, you can also choose your red loop. :)

+29xp points
*LEVEL UP*
Femme_Physics is now a level 2 electrician!
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NOW it's clear :) I feel so empowered to do math and electronics now! You wanted me to find I₂ though? Well, I have 3 equations with 3 unknowns, I just plug the result of I₁ to the equations to get what I need.

#1
-60 x 0.2 -20I_L+18 = 0
I_L = 0.3 [A]


Plugging that to the last equation:
I₁+I₂-I_L=0
0.2+I₂-0.3=0
I₂=0.1 [A]
There!

 

[I like Serena]

+29xp points
*LEVEL UP*
Femme_Physics is now a level 2 electrician!
*Chooses new feat: Voltage power*
*Chooses new attribute: +1 intelligence*

+29xp points
*LEVEL UP*
I like Serena is now a level 2 homework helper!
*Chooses new feat: Kirchhoff's laws*
*Chooses new attribute: +1 wisdom*

NOW it's clear :) I feel so empowered to do math and electronics now! You wanted me to find I₂ though? Well, I have 3 equations with 3 unknowns, I just plug the result of I₁ to the equations to get what I need.

Oh yeah, I'd completely forgotten about that! :)

#1
-60 x 0.2 -20I_L+18 = 0
I_L = 0.3 [A]


Plugging that to the last equation:
I₁+I₂-I_L=0
0.2+I₂-0.3=0
I₂=0.1 [A]
There!

Very good!

However, I'm afraid I miss remembered. I thought I₂ would come out negative, meaning that the 10 V battery would be charging.
Anyway, I think that point is kind of moot now.

 

[Femme_physics]

Anyway, I think that point is kind of moot now.

It'd probably come up in other problems :)

+29xp points
*LEVEL UP*
I like Serena is now a level 2 homework helper!
*Chooses new feat: Kirchhoff's laws*
*Chooses new attribute: +1 wisdom*

:D This is by far the longest homework help thread I ever had! Much obliged, ILS, gneill. You rock^^

Never thought I'd pass the 70 replies!

 

[I like Serena]

This is by far the longest homework help thread I ever had! Much obliged, ILS, gneill. You rock^^

Never thought I'd pass the 70 replies!

Apparently you were given a problem that you wouldn't be able to solve with the knowledge they imparted on you.

And not only did you solve the problem anyway, but you learned an entire new field of science to handle all of these problems!
I'm sorry it took us over 70 posts to teach you this entire field. :P

I suspect you will be the only one in your class that will have solved this problem, unless another student has an unfair advantage.