Voltage Division and Finding a Current

[ScottS]

Ahhhh, that flew over my head lol. Quick side-question-But after finding a Req for the 3 and 6 ohm resistors its best to put the Req inbetween the AI1 and Vout,since were trying to find the Req by Vout. Or it doesn't really matter since either way will have the same result.

But after I find the Req and find that (Vout=2AI1), I then move over to the other side of the circuit and repeat the same process, since it looks like Vs is in parallel with the two 12 ohm resistors, and once I find (Vs=9I1). I then plug it into my Vout equation to find A=40.5?

But a thought occurred to me that since we found the voltage for both pair of resistors in parallel, should I backtrack to apply ohms law to find the current through them?Like divide the 3 ohm and 6 ohm resistor by 2AI1 and then KVL them?

You are WAY overthinking this LOOK at the circuit, trace all current paths. First rule you need to remember: Vs is NEVER in parallel with the circuit it supplies (study up on the terms source and sink for more information on this) A voltage source can ONLY be in parallel with another voltage source. It can be in SERIES with a current source. but it can NOT be in parallel with a circuit as it is PART of the circuit as it is the voltage Source. Next voltage of parallel resistors is equal. ALWAYS. regardless of their values. As they are in PARALLEL the only difference can be current through them, based on their individual values (Ohms Law). The other side of the circuit is irrelevant since it is not a complete circuit, As there is no path for current flow since there is not both V+ and V- the circuit physically does not exist. I wish I would have run across this when you first posted this. This is nothing more than a simple exercise in Ohms Law and circuit simplification. Remember, when a circuit seems od or cumbersome, redraw it in the most simplified terms, even if it takes several steps, just as simplifying any math equation. In this instance redraw the parallel 12 ohm resistors as one 6 ohm resistor. It is always much easier to work these problems on paper, and then use colored pencils to redraw over the original circuit and annotate with that color, allowing multiple paths that can be done over each other. The principle you need to use is called the KISS principle, (Keep It Simple Stupid)don't try to think past the obvious. electricity just doesn't think at all.

 

[The Electrician]

there is no Vout , the circuit is incomplete and there is no voltage in this branch.

For Problem 1 the answer for Vout is 0 (zero) volts. CAREFULLY EXAMINE the circuit. the branch circuit where you are calculating Vout is incomplete. As there is no V+ there is no Vout.... the circuit is incomplete

You should take your own advice and carefully examine the circuit. The dependent source A*I1 is providing the current which generates the voltage at Vout.

 

[MrAl]

In reference to MrAL said "look up current division"...

Current is not divided in resistor circuits. OHMS LAW... you may have branch current but total current is ALWAYS based on the total resistance of the circuit. As the first circuit ONLY has a total of 9 ohms the current is Vo/9 (parallel resistance law of note in this instance is resistors of equal value in parallel are calculated by the value of one resistor divided by the number of parallel resistors hence 12ohms divided by 2 = 6 ohms, plus the single 3 ohm resistor =total value of 9 ohms) and remember the rest of the resistors are just for show since they are not part of the circuit as there is no current path available to them.

Hello ScottS,

Not sure what you mean by "Current is not divided in resistor circuits".

In a two resistor parallel resistor circuit current splits between the two paths created by the two resistors. This is often referred to as "Current Division" mostly because we can use a division equation to get the currents in the two resistors.
It is similar but not exactly the same as Voltage Division in a series circuit.

So in the series circuit we have Voltage Division, and in the parallel circuit we have Current Division. You can always look up Current Division on the web for more information if you like.

 

[ScottS]

You should take your own advice and carefully examine the circuit. The dependent source A*I1 is providing the current which generates the voltage at Vout.

Abusive remarks have been deleted MOD Team...

 

[ScottS]

In reference to MrAL said "look up current division"...



Hello ScottS,

Not sure what you mean by "Current is not divided in resistor circuits".

In a two resistor parallel resistor circuit current splits between the two paths created by the two resistors. This is often referred to as "Current Division" mostly because we can use a division equation to get the currents in the two resistors.
It is similar but not exactly the same as Voltage Division in a series circuit.

So in the series circuit we have Voltage Division, and in the parallel circuit we have Current Division. You can always look up Current Division on the web for more information if you like.

 

[ScottS]

Current never "splits" it branches. you always have to apply Ohms law. ALWAYS. when you have an equal voltage across two parallel resistors you calculate current by VOLTAGE DIVIDED BY RESISTANCE, AND THEN ADD THE CURRENT VALUES TOGETHER (caps to differentiate from the rest of the text only) Current is NEVER divided in a parallel circuit, it is increased based on the reduction of impedance as a result of the act of parallel resistance REDUCING the actual resistance. There is no need for me to "look this up" as I hold a Masters in Electronics Engineering. And have taught this to literally thousands of students, in the lab and proven this time and again. Branch current is NOT current division. it is JUST current in a specific branch of a circuit. What I WOULD suggest is the exercise of thevenizing a complex circuit so that you will see that there really is no such thing as current division, since current is solely dependent on resistance of the load and the supply voltage. Here is a link to help you break down the circuit to its most basic model so that you can understand this more readily.
http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Source/Source2.html

As for your attempt to explain parallel current. it is entirely incorrect. You only can mathematically determine the values of required resistances to get a given total parallel resistance, for example, to increase the power dissipation of a purely resistive impedance. However this does NOT give you your parallel current. after the circuit is designed you can THEN calculate it, but that is akin to having the horse PUSH the cart as your design parameters already tell you what your power dissipation must be. Instead you simply apply Ohms Law. Derive the voltage on the parallel network, then calculate the current through each resistor via Ohms law, and sum the currents for your total current. This is NOT current division. It is a very basic LAW of physics that determines that current can not be divided. it is this law that when explained mathematically is known as Ohms law.http://www.ohmslawcalculator.com/ohms_law_wheel.php

 

[JimB]

ScottS said:

When you turn to insult Make sure you KNOW what you are talking about lest you expose yourself, as you just have, as an abject fool, "know it all know nothing AT ALL". You may want to do yourself a favor and take an electronics course, particularly one on reading Schematic diagrams your "Dependent Source" is a reference not an actual SUPPLY , this is High School level diagram reading. and you just failed the course

Oh dear!
You are rather opening yourself to ridicule.
The circuit under discussion is not a practical circuit, it does not need a supply. (It could represent the equivalent circuit of a transistor).
The item marked as A*I1 is a current source.

If it is of any consolation to you I agree that Vout is zero, but not for the reasons which you offer.
In the circuit as drawn, and as it displays on my computer, there is a short circuit across Vout, and the voltage across any short circuit is zero.
However, I think that the short circuit representation is more due to the OPs lack of knowledge and experience than a requirement of the question.

For someone who claims to hold a "Masters in Electronics Engineering" you present several points of electrical engineering which to this
Ordinary Degreed "generalist" seem to be a bit off the mark.

As someone who has just arrived in the forum, please be a little more courteous and get to know the strengths and weaknesses of the various members before you wade in with all guns blazing, (Taliban Hunting mode?).

JimB

 

[The Electrician]

The poster does seem a little bold.

An examination of all the posts that went before will show the reader that the apparent short at Vout should really be interpreted to be a voltmeter. That's what earlier responders assumed.

 

[JimB]

The poster does seem a little bold.

A very diplomatic way of describing the situation.

An examination of all the posts that went before will show the reader that the apparent short at Vout should really be interpreted to be a voltmeter. That's what earlier responders assumed.

Without trawling through four pages, that is what I assumed was really intended.

JimB

 

[MrAl]

Current never "splits" it branches. you always have to apply Ohms law. ALWAYS. when you have an equal voltage across two parallel resistors you calculate current by VOLTAGE DIVIDED BY RESISTANCE, AND THEN ADD THE CURRENT VALUES TOGETHER (caps to differentiate from the rest of the text only) Current is NEVER divided in a parallel circuit, it is increased based on the reduction of impedance as a result of the act of parallel resistance REDUCING the actual resistance. There is no need for me to "look this up" as I hold a Masters in Electronics Engineering. And have taught this to literally thousands of students, in the lab and proven this time and again. Branch current is NOT current division. it is JUST current in a specific branch of a circuit. What I WOULD suggest is the exercise of thevenizing a complex circuit so that you will see that there really is no such thing as current division, since current is solely dependent on resistance of the load and the supply voltage. Here is a link to help you break down the circuit to its most basic model so that you can understand this more readily.
http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Source/Source2.html

As for your attempt to explain parallel current. it is entirely incorrect. You only can mathematically determine the values of required resistances to get a given total parallel resistance, for example, to increase the power dissipation of a purely resistive impedance. However this does NOT give you your parallel current. after the circuit is designed you can THEN calculate it, but that is akin to having the horse PUSH the cart as your design parameters already tell you what your power dissipation must be. Instead you simply apply Ohms Law. Derive the voltage on the parallel network, then calculate the current through each resistor via Ohms law, and sum the currents for your total current. This is NOT current division. It is a very basic LAW of physics that determines that current can not be divided. it is this law that when explained mathematically is known as Ohms law.http://www.ohmslawcalculator.com/ohms_law_wheel.php

Hello again ScottS,

You are basically telling me that when current flows through a single wire connected to two resistors in parallel that i can not say that the current "splits" between the two resistors. You are telling me that i must say that the current "branches".

You are also telling me that for that same circuit i can not call it "current division".

Yet when i look up the word "split" and the word "branch" in the dictionary i find that when used as verbs their definitions are very similar. I find that there is no problem with saying, "The current splits into two different paths".

Also, when i look in circuit analysis books i see "Current Division" for two resistors in parallel clearly defined as:
i1=Is*G1/(G1+G2)

where
i1 is the current through R1,
Is is the source current (the total current),
G1 is the conductance of one resistor,
G2 is the conductance of the other resistor.

Note the similarity to the voltage division formula:
v1=Vs*R1/(R1+R2)

and note that v1 is on the left and R1 is on the right in the NUMERATOR and the sum of the two is in the denominator.
This is the same as the current division formula above except we are using the conductances instead of the resistances, as we see i1 on the left and G1 on the right in the NUMERATOR, and current instead of voltage.

Converting the current division formula above into all resistances, we get:
i1=Is*R2/(R1+R2)

and note that although we have i1 on the left again we now have R2 in the NUMERATOR on the right instead of R1 or G1. This is also known as current division, but here the opposite resistance is in the numerator now (opposite to what current we are trying to solve for).

What you have described is a technique for solving for the current through the two parallel resistances knowing the VOLTAGE across the two resistors. What current division is for is when we want to solve for the current through either resistor knowing the total CURRENT through both resistors.

So if we know the voltage across the two resistors or we can solve for the voltage across the two resistors then we can use your idea, but if we know the current through the two resistors then we can solve for the current in either resistor more directly without having to first solve for the voltage.
If we investigate this further we find that doing it either way gives us the same result.

Im sure there are plenty of references on the web to "Current Division". If you've never heard of this before then let me be the first person to inform you of such a thing

BTW what school did you go to?

 

[Ratchit]

Current never "splits" it branches. you always have to apply Ohms law. ALWAYS. when you have an equal voltage across two parallel resistors you calculate current by VOLTAGE DIVIDED BY RESISTANCE, AND THEN ADD THE CURRENT VALUES TOGETHER (caps to differentiate from the rest of the text only) Current is NEVER divided in a parallel circuit, it is increased based on the reduction of impedance as a result of the act of parallel resistance REDUCING the actual resistance. There is no need for me to "look this up" as I hold a Masters in Electronics Engineering. And have taught this to literally thousands of students, in the lab and proven this time and again. Branch current is NOT current division. it is JUST current in a specific branch of a circuit. What I WOULD suggest is the exercise of thevenizing a complex circuit so that you will see that there really is no such thing as current division, since current is solely dependent on resistance of the load and the supply voltage. Here is a link to help you break down the circuit to its most basic model so that you can understand this more readily.
http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Source/Source2.html

As for your attempt to explain parallel current. it is entirely incorrect. You only can mathematically determine the values of required resistances to get a given total parallel resistance, for example, to increase the power dissipation of a purely resistive impedance. However this does NOT give you your parallel current. after the circuit is designed you can THEN calculate it, but that is akin to having the horse PUSH the cart as your design parameters already tell you what your power dissipation must be. Instead you simply apply Ohms Law. Derive the voltage on the parallel network, then calculate the current through each resistor via Ohms law, and sum the currents for your total current. This is NOT current division. It is a very basic LAW of physics that determines that current can not be divided. it is this law that when explained mathematically is known as Ohms law.http://www.ohmslawcalculator.com/ohms_law_wheel.php

Whenever a conduction path from one branch divides into two or more conduction branches, Kirchoff's current law (KCL) is followed. That law states that the total current entering a branch point must be the same as the current leaving the same point. If the current in each sub-branch were the same as the main branch, that would be a neat way of multiplying current. But it doesn't happen that way. The total current in the sub-branches will equal the current in the main branch. It has to do so because the law of mass conservation must be followed.

Ratch

 

[ScottS]

ScottS said:


Oh dear!
You are rather opening yourself to ridicule.
The circuit under discussion is not a practical circuit, it does not need a supply. (It could represent the equivalent circuit of a transistor).
The item marked as A*I1 is a current source.

If it is of any consolation to you I agree that Vout is zero, but not for the reasons which you offer.
In the circuit as drawn, and as it displays on my computer, there is a short circuit across Vout, and the voltage across any short circuit is zero.
However, I think that the short circuit representation is more due to the OPs lack of knowledge and experience than a requirement of the question.

For someone who claims to hold a "Masters in Electronics Engineering" you present several points of electrical engineering which to this
Ordinary Degreed "generalist" seem to be a bit off the mark.

As someone who has just arrived in the forum, please be a little more courteous and get to know the strengths and weaknesses of the various members before you wade in with all guns blazing, (Taliban Hunting mode?).

JimB

JimB I suggest you educate yourself and rather quickly. I don't know what program you are using but it isn't using the circuit supplied because the circuit is incomplete, so it is you that is open to ridicule Next you can not have a current source without a voltage source. this is a simple fact based on the law of physics.. I question the source of your "degree" if you can not see this simple fact... As for the "strengths and weaknesses" it is YOU that needs to consider them. It is YOU who has joined one other insulting and vile individual. The fact that you NEED a program to interpret a circuit you should be able to simply look at and understand removes any validity of your claims of knowledge. Particularly since the simulation is ONLY as valid as the accuracy of your entry of the circuit. As for my "arrival" This is not my "arrival" here, it is a return after a long sabbatical after dealing with other sophomoric fools such as yourself that nearly shut the forum down in the past. it is time for you to remove your foot from your mouth and sit back and LEARN instead of fudging your way through with simulations.

 

[ScottS]

Whenever a conduction path from one branch divides into two or more conduction branches, Kirchoff's current law (KCL) is followed. That law states that the total current entering a branch point must be the same as the current leaving the same point. If the current in each sub-branch were the same as the main branch, that would be a neat way of multiplying current. But it doesn't happen that way. The total current in the sub-branches will equal the current in the main branch. It has to do so because the law of mass conservation must be followed.

Ratch

While you properly quote Kirchoffs law you are misusing the terms around it . a circuit does not divide it branches, hence the term NETWORK. the sum of all current equals the total current, this is correct, HOWEVER, this does not mean current is being divided, When something is divided it is reduced. when you add branched circuits you are adding parallel current paths, which INCREASES current paths and in turn current flow. And next, the law of mass conservation is NOT valid in electronics. for all intents and purposes electrons have no volume and no mass. hence your ideology in this is flawed. the nearest plausible theory that does come close is branch flow in fluid dynamics.
The point you NEED to understand is this. WHEN a circuit is branched, resistance is effectively reduced as seen at Vs due to parallel resistance allowing greater current flow. and YES this DOES increase total current flow. for example: 2 1K resistors in parallel represent 2 branch circuits of 1K impedance each. they supply a total load of 500 ohms to the Vs, assuming Vs ia 10 volts, we have total current of 20mA... to keep it simple lets add 2 more branch circuits of 1K each, this results in a total parallel resistance of 250 ohms as seen by Vs , giving a total of 40mA The SUM of the current in all branches equal the total current. THIS is Kirchoff's current law

https://www.facstaff.bucknell.edu/mastascu/elessonshtml/Basic/Basic5Kv.html
The following may explain it a bit easier for you
https://physics.bu.edu/~duffy/py106/Kirchoff.html

 

[ScottS]

Hello again ScottS,

You are basically telling me that when current flows through a single wire connected to two resistors in parallel that i can not say that the current "splits" between the two resistors. You are telling me that i must say that the current "branches".

You are also telling me that for that same circuit i can not call it "current division".

Yet when i look up the word "split" and the word "branch" in the dictionary i find that when used as verbs their definitions are very similar. I find that there is no problem with saying, "The current splits into two different paths".

Also, when i look in circuit analysis books i see "Current Division" for two resistors in parallel clearly defined as:
i1=Is*G1/(G1+G2)

where
i1 is the current through R1,
Is is the source current (the total current),
G1 is the conductance of one resistor,
G2 is the conductance of the other resistor.

Note the similarity to the voltage division formula:
v1=Vs*R1/(R1+R2)

and note that v1 is on the left and R1 is on the right in the NUMERATOR and the sum of the two is in the denominator.
This is the same as the current division formula above except we are using the conductances instead of the resistances, as we see i1 on the left and G1 on the right in the NUMERATOR, and current instead of voltage.

Converting the current division formula above into all resistances, we get:
i1=Is*R2/(R1+R2)

and note that although we have i1 on the left again we now have R2 in the NUMERATOR on the right instead of R1 or G1. This is also known as current division, but here the opposite resistance is in the numerator now (opposite to what current we are trying to solve for).

What you have described is a technique for solving for the current through the two parallel resistances knowing the VOLTAGE across the two resistors. What current division is for is when we want to solve for the current through either resistor knowing the total CURRENT through both resistors.

So if we know the voltage across the two resistors or we can solve for the voltage across the two resistors then we can use your idea, but if we know the current through the two resistors then we can solve for the current in either resistor more directly without having to first solve for the voltage.
If we investigate this further we find that doing it either way gives us the same result.

Im sure there are plenty of references on the web to "Current Division". If you've never heard of this before then let me be the first person to inform you of such a thing

BTW what school did you go to?

No current does NOT SPLIT . Current JUST flows. The terms you use are VITAL to what you are actually saying when you are talking about electronics. SPLIT implies reduction of the source, this simply does not happen, when you branch off you are adding another current path, thus creating the ability to INCREASE current flow. You do not say voltage flow, or current force, these are completely opposite of what they actually do. As such you do not say current "SPLITS" it doesnt it branches, just lie a tree branch it grows... gets greater... the terms used are very critical because of what they mean. And the more branches in a circuit the more paths for current flow. (The sum of all currents equal the total current "Kirchoff's Law".) For all intent and purpose a conductor (wire) has a conductance, resistors DO NOT they have impedance. You are entirely skewed in your thought process. you MUST have two figures to derive the third. and there is NO such thing as current division. This Idea has been proven flawed and out dated. Robert Paynter a once accredited electronic text book author, was quite literally was run off and discredited for pushing the theory of current division back in the 1990s. Division reduces, YET when you add branch paths you are adding additional sources for current flow and can keep going up to the point where the sum of the parallel resistance equals much less than one ohm which can become catastrophic to the conductors and or, voltage source, such as shorting out an automotive battery. You can keep arguing the inverse of resistance (conductance) but then you must allow for resistance of the conductors for accurate calculations which is why it simply is not used. It is akin to going 180 around the globe to reach a destination 3 miles in the opposite direction. there is no valid reason for it, and it creates substantial accuracy issues that compound themselves as the circuit grows beyond a handful of components due to tolerance issues. In short it fails due the induced error of working with the inverse characteristics of impedance. Before you continue pushing this issue, you really need to learn to thevenize some complex resistive networks. It will remove this "current division" ideology and replace it with the proper branch current flow knowledge.
As for the University I attended not that it mattered, I am an MIT grad.

 

[The Electrician]

What a unique posting style!

 

[MrAl]

Hi Scott,


At first is sounded to me like you were just arguing semantics, but now you seem to be introducing some new theory that we are no longer allowed to use lumped circuit elements, but must consider everything that can occur in nature.

But for such a simple problem we dont make it more complicated by introducing everything and anything unless it is something that really has relevance. For this problem, introducing the resistance of the wiring for example is not necessary.

Also, representing resistances as conductances is not a problem, at least not the way you are making it sound. Even if we consider the wire resistance we can still represent a resistance as a conductance.

You also state some sort of inaccuracy in using conductance instead of resistance, but the formulas always come out the same. And if we use voltage to calculate the current vs "Current Division" we get the same answer so there's no difference.

Current Division is called that because we can call "current" as single object even though it is not really a single object. This is very common. Just as a tree branch can split into two smaller branches, we can say that current 'splits' into two paths, or we can say that it 'divides' into two paths because current flows through elements.
We usually dont say that the voltage splits though, because voltage appears across elements not through them.

"SPLIT implies reduction of the source, this simply does not happen, when you branch off you are adding another current path, thus creating the ability to INCREASE current flow"
We are not adding ANOTHER current path when we use the current division formula. All the current paths are already there and existed BEFORE we started the analysis. This means we cant increase any current. It's whatever it was before we started.


If i had to guess i'd say you are really a law student practicing your argumentative techniques by starting unusual arguments that are sure to go on for a long time and thus give you plenty of practice. I wont press this though as you are free to say what you want within the limits of the forum rules whether this is true or not.

In spite of all this i will still yield the floor so if you've got something to teach us all here then by all means present your theories and i am sure that i'll be all ears

@Electrician:
I had to chuckle at your reply...very unique theory or whatever it is too

 

[Ratchit]

While you properly quote Kirchoffs law you are misusing the terms around it . a circuit does not divide it branches, hence the term NETWORK. the sum of all current equals the total current, this is correct, HOWEVER, this does not mean current is being divided, When something is divided it is reduced. when you add branched circuits you are adding parallel current paths, which INCREASES current paths and in turn current flow. And next, the law of mass conservation is NOT valid in electronics. for all intents and purposes electrons have no volume and no mass. hence your ideology in this is flawed. the nearest plausible theory that does come close is branch flow in fluid dynamics.
The point you NEED to understand is this. WHEN a circuit is branched, resistance is effectively reduced as seen at Vs due to parallel resistance allowing greater current flow. and YES this DOES increase total current flow. for example: 2 1K resistors in parallel represent 2 branch circuits of 1K impedance each. they supply a total load of 500 ohms to the Vs, assuming Vs ia 10 volts, we have total current of 20mA... to keep it simple lets add 2 more branch circuits of 1K each, this results in a total parallel resistance of 250 ohms as seen by Vs , giving a total of 40mA The SUM of the current in all branches equal the total current. THIS is Kirchoff's current law

https://www.facstaff.bucknell.edu/mastascu/elessonshtml/Basic/Basic5Kv.html
The following may explain it a bit easier for you
https://physics.bu.edu/~duffy/py106/Kirchoff.html

The charge carriers in a wire are electrons. They do have a mass, which has been measured to a high degree of precision. See **broken link removed**. If they have mass, then they are subject to the law of mass conservation. You are wrong is averring that they do not have mass. All of us are talking about a circuit where one branch divides into two or more sub-branches. You are talking about adding parallel resistance to an circuit that already exists. All of us know that adding parallel resistance reduces the total resistance and increases the current. So, confine your discussion to the case where no additional resistance in inserted into the circuit. Your statement pertaining to the sum of the currents equalling the total current means the same as what I said about KCL.

Ratch

 

[Ian Rogers]

MrAl The Electrician ScottS

This is going nowhere..... Current split, current divide, current branch... It all means the same thing, we all have learnt Kirchhoff's law, we all know Ohms law... This debarkle is not helping the OP one tiny bit... Please let it be explained to the OP without all this!!!

This could be a good thread for youngsters to learn... Do not overcomplicate it!

 

[MrAl]

Hi again,

Ian:
I was hoping he really did have something to teach us here, but it looks like just semantics plus the inability to separate theory from practice. I hope he can clear this up.

Ratch:
Thanks for posting that link, it looks interesting.

 

[Ian Rogers]

As for the University I attended not that it mattered, I am an MIT grad.

I'm pretty sure they don't teach you to belittle everyone at MIT....
You have been removed from this thread....