# Analyzing Power from Current Source

#### DGElder

Joined Apr 3, 2016
351
It doesn't matter, except that the purpose of this thread was to educate the OP in an electrical engineering convention, not to confuse him with volumes of sophistry. I just hope he left a dozen posts ago.

#### WBahn

Joined Mar 31, 2012
25,548
Ah, so you want him to just memorize a dogmatic approach by rote, not understand the underlying concepts, and be hopelessly confused every time he runs into the many situations in which circuits will be analyze on the basis of the power form sources equaling the power to loads. Got it.

#### DGElder

Joined Apr 3, 2016
351
He said it makes sense to him. He is not confused.

#### WBahn

Joined Mar 31, 2012
25,548
And hopefully he will be able to work it out when he comes across a circuit analysis that doesn't blindly obey your dogmatic interpretation. Neither he nor we have any way of knowing that at this point. So how about we both give it a rest?

#### MrAl

Joined Jun 17, 2014
7,468
Hello again
And hopefully he will be able to work it out when he comes across a circuit analysis that doesn't blindly obey your dogmatic interpretation. Neither he nor we have any way of knowing that at this point. So how about we both give it a rest?
Well maybe i dont understand you correctly. How do *you* define the passive sign convention?
Sometimes they abbreviate it as simply PSC.
Note we may have to do some drawings to make this all clear.

Here's a reference i found:
--------------------------------------------------------------------------------
Passive Sign Convention:
Current arrow pointed towards the terminal where
the voltage is marked positive.
Power Absorbed:
Product of the voltage and current if passive sign convention has
been observed. A negative value means positive power is being
supplied.
--------------------------------------------------------------------------------

Here's an excerpt from an engineering circuit analysis book written by one professor from Perdue and one from California:

#### stoltz1986

Joined Sep 21, 2015
7
This is a reference page I made from assorted pictures and definitions from my textbook. I am going to follow this for a while until I get a solid grasp of this convention then I'll look at other conventions and variations after that.

MrAl, to answer a question from one of your earlier posts about why I had assigned polarity to the current source the way I did, I did some digging and for some reason I thought that all sources had to have positive current exiting the positive terminal. I have since done some rereading and a bunch of practice problems to get my glitch straightened out.

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#### WBahn

Joined Mar 31, 2012
25,548
Well maybe i dont understand you correctly. How do *you* define the passive sign convention?
I'm not dogmatic about it and can work with either common interpretation. But when left up to me I prefer the interpretation that positive power is positive in a load that is absorbing power and positive in a source that is supplying power. This is for two reasons -- first, I prefer to (when practical) work with reference assignments such that if any quantity end up being negative that it can serve as a flag letting me know that I need to look at things more closely because either I didn't properly estimate the circuit behavior or I made a mistake somewhere in the analysis. Second, consider the following circuit:

In order to adhere to the passive sign convention as interpreted by you and DGElder, you have to provide TWO currents for this circuit.

If you want to use a single current, then you have no choice but to assign one of the voltages such that it will turn out to be negative.

or

Do you want to work with any of these assignments? Wouldn't you agree that any of them increases the likelihood of making a mistake and also the potential for not catching it.

Doesn't the following seem much more reasonable:

Isn't this how you would set things up? But does this conform to your interpretation of the passive sign convention?

Note that it DOES conform to my preferred interpretation.

And it is NOT just MY interpretation. As an example:

From "Principles and Applications of Electrical Engineering" by Giorgio Rizzoni:

To avoid confusion with regard to the sign of power, the electrical engineering community uniformly adopts the passing sign convention, which simple states that the power dissipated by a load is a positive quantity (or, conversely, that the power generated by a source is a positive quantity). Another way of phrasing the same concept is that if current flows from a higher to a lower voltage (+ to -), the power dissipated will be a positive quantity.
Now, I disagree with his claim that the electrical engineering uniformly adopts this interpretation of the passive sign convention -- though it isn't surprising that adherents to this interpretation can be as strident in claiming that it is the only interpretation, just like DGElder is in his claim -- but just as the case of the example above, consider how YOU generally assign reference polarities when you analyze circuits. I'd wager that you more commonly work in a manner consistent with this interpretation than with the one in which power delivered by sources is negative.

#### MrAl

Joined Jun 17, 2014
7,468
I'm not dogmatic about it and can work with either common interpretation. But when left up to me I prefer the interpretation that positive power is positive in a load that is absorbing power and positive in a source that is supplying power. This is for two reasons -- first, I prefer to (when practical) work with reference assignments such that if any quantity end up being negative that it can serve as a flag letting me know that I need to look at things more closely because either I didn't properly estimate the circuit behavior or I made a mistake somewhere in the analysis. Second, consider the following circuit:

View attachment 106192
In order to adhere to the passive sign convention as interpreted by you and DGElder, you have to provide TWO currents for this circuit.

View attachment 106193
If you want to use a single current, then you have no choice but to assign one of the voltages such that it will turn out to be negative.

View attachment 106194
or
View attachment 106195

Do you want to work with any of these assignments? Wouldn't you agree that any of them increases the likelihood of making a mistake and also the potential for not catching it.

Doesn't the following seem much more reasonable:
View attachment 106196
Isn't this how you would set things up? But does this conform to your interpretation of the passive sign convention?

Note that it DOES conform to my preferred interpretation.

And it is NOT just MY interpretation. As an example:

From "Principles and Applications of Electrical Engineering" by Giorgio Rizzoni:

Now, I disagree with his claim that the electrical engineering uniformly adopts this interpretation of the passive sign convention -- though it isn't surprising that adherents to this interpretation can be as strident in claiming that it is the only interpretation, just like DGElder is in his claim -- but just as the case of the example above, consider how YOU generally assign reference polarities when you analyze circuits. I'd wager that you more commonly work in a manner consistent with this interpretation than with the one in which power delivered by sources is negative.
Hello again,

I still dont understand one thing you are referencing: the assignments of voltage polarities in the diagrams. I am not sure why you would want to assign anything other than the last one, where both the source has upper positive lower negative, and the load has upper positive and lower negative. That arrangement satisfies the passive sign convention just perfectly, doesnt it? In the load, the current ENTERS the positive terminal of the load so the load absorbs power and is deemed positive power. In the source, the current LEAVES the most positive terminal so it is supplying power and is deemed negative in the strictest sense of the convention, so i dont see why you would want to reverse any voltage polarity.
[MUCH LATER: I see now you were just trying to explain another way to do it if we did not use the signed current method.]

In that last diagram, the source is supplying power to the circuit, and in the strictest sense the power is deemed to be negative, but i also use the more relaxed convention of calling the power delivered positive too in more casual conversation but only if it is clear that everyone already knows or should know that the source is actually delivering power.

Note that we dont really need two currents. If we say that a current flowing from left to right is positive then if we reverse the current arrow we say it is negative. We dont actually create a new current in doing this we just flip the sign, and then the positive source times the negative current equals a negative quantity.

In a simple circuit where there is only one source there is little to confuse anyone about if it is supplying power or not, especially in a passive circuit. When things become more complicated though as with multiple sources, it's good to have a signed power so that sources that are absorbing power can be quickly distinguished from sources that are supplying power. That's why i was looking at the questions about the three source circuit i mentioned. If you care to draw up a circuit like that where maybe one source is dissipating power and two are supplying power, then we might see how handy this idea becomes. We dont have to write "supplying power" and "dissipating power" for example, we just write the sign of each power.

It's always up to the individual of course how they want to do it. The most common method is to use the passive sign convention i guess and that's mostly what i see in literature. If they dont use signed power then they always mention it if something unusual comes up like a source absorbing energy (like a battery charger) unless it doesnt seem necessary to spell it out.

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#### WBahn

Joined Mar 31, 2012
25,548
Hello again,

I still dont understand one thing you are referencing: the assignments of voltage polarities in the diagrams. I am not sure why you would want to assign anything other than the last one, where both the source has upper positive lower negative, and the load has upper positive and lower negative.
I wouldn't want to use any of the others -- and apparently neither would you. That's my point.

That arrangement satisfies the passive sign convention just perfectly, doesnt it?
Not as you and others are insisting it be used. You maintain that PSC has the reference direction for current for any element, source or load, be INTO the positive terminal (per the reference voltage for that item). That way you multiply the current by the voltage and if it comes out positive you are absorbing power and if it comes out negative you are supplying power. Well, in that last circuit both the current and the voltage will be positive. The only way to then end up with a negative power for the source is to apply a magical mystery minus sign!

In the load, the current ENTERS the positive terminal of the load so the load absorbs power and is deemed positive power. In the source, the current LEAVES the most positive terminal so it is supplying power and is deemed negative in the strictest sense of the convention, so i dont see why you would want to reverse any voltage polarity.
The whole point of things such as the passive sign convention and others is specifically so you don't have to do a bunch of "deeming" things to be this or that and apply magical mystery minus signs to things as a consequence of the "deeming" process. The purpose is to define reference directions for the symbolic quantities such that, no matter how complicated the circuit gets, the math takes care of itself.

You see the same thing happen when people use "capacitive" and "inductive" reactance in which both are positive quantities and then they subtract the latter from the former. This only works well if things are reduced to numerical quantities as each step because as soon as you combine two reactances symbolically you don't know whether the end result is going to be capacitive or inductive and all of your later work is dependent on which it turns out to be. If you instead define reactance to simply be the imaginary part of the impedance, then it becomes a signed quantity and the "type" of reactance takes care of itself no matter how complicated the analysis becomes.

Note that we dont really need two currents. If we say that a current flowing from left to right is positive then if we reverse the current arrow we say it is negative. We dont actually create a new current in doing this we just flip the sign, and then the positive source times the negative current equals a negative quantity.
But note that all you have done is used the two currents as in the first diagram, you just have not written them down. This is fine, except now as you describe things to people you will likely find yourself either talking about currents that are not defined (such as saying that the source has a current of -10 A when the only current defined on the diagram has a value of +10 A) are applying magical mystery minus signs in order to take a voltage of +20 V and a current of +10 A and get a power of -200 W.

In a simple circuit where there is only one source there is little to confuse anyone about if it is supplying power or not, especially in a passive circuit. When things become more complicated though as with multiple sources, it's good to have a signed power so that sources that are absorbing power can be quickly distinguished from sources that are supplying power. That's why i was looking at the questions about the three source circuit i mentioned. If you care to draw up a circuit like that where maybe one source is dissipating power and two are supplying power, then we might see how handy this idea becomes. We dont have to write "supplying power" and "dissipating power" for example, we just write the sign of each power.
I'll throw something together, probably later this week. I'm up against the clock right now on getting some stuff finalized and submitted.

#### MrAl

Joined Jun 17, 2014
7,468
Hello again,

Well there must be a reason this idea was adopted so widely. There must be a need to keep things as orderly as possible.

Accounting is the same way, we can either make debits negative and credits positive, or say that debits are positive too (no such thing as negative money). Either way it works, but if we keep the negative it travels with the number and then whenever we see it again we know right away it's a debit. I do my checking account program that way too because that way the debits dont need to carry an extra property that says they are debits...they already have the negative amount.

If you dont like doing that either that's up to you, but it may be hard to change the way so many others are doing it this late in the game

Note this is partly semantics, but the literature i always see tells me most authors want to do it one set way. It's always up to you how you want to do it though.

A good example i think would be the three source circuit, with maybe two resistors connecting them. The question would be to list the power in each element, resistors and sources. That would mean five different powers to list. So we would have V1, V2, V3, R1 and R2, and we'd have to list the power in each element.
If we say that V1 and V3 are higher than V2 then V2 is absorbing energy, so we could either list as:
V1: 5 watts delivering
V2: 10 watts absorbing
V3: 10 watts delivering
R1: 2.5 watts absorbing
R2: 2.5 watts absorbing

or list as:
V1: -5 watts
V2: 10 watts
V3: -10 watts
R1: 2.5 watts
R2: 2.5 watts

so here we make use of the minus sign, which takes care of the accounting of each one's power level without the need for extra notes.

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#### WBahn

Joined Mar 31, 2012
25,548
You don't need extra notes in either case. The alternative (and widely used) interpretation is that the power absorbed by a nominal load is positive and the power delivered by a nominal source is positive.

#### MrAl

Joined Jun 17, 2014
7,468
Hi again,

Ok then here is the list without any signs and any extra notes:

V1: 5 watts
V2: 10 watts
V3: 10 watts
R1: 2.5 watts
R2: 2.5 watts

#### WBahn

Joined Mar 31, 2012
25,548
Hi again,

Ok then here is the list without any signs and any extra notes:

V1: 5 watts
V2: 10 watts
V3: 10 watts
R1: 2.5 watts
R2: 2.5 watts
Who said that you throw away all directional information? Here you are claiming that all three sources are either delivering power or that they are all absorbing power (depending on which interpretation you are using).

If you use the PSC you are pushing as being the ONLY interpretation, you would have:

V1: -5 W
V2: 10 W
V3: -10 W
R1: 2.5 W
R2: 2.5 W

If you use the alternative interpretation, you would have

V1: 5 W
V2: -10 W
V3: 10 W
R1: 2.5 W
R2: 2.5 W

Notice that, even without any other indications, which interpretation is in use is easy to figure out (unless the person is using some ad hoc reference direction assignment, in which case they HAVE to provide that information).

But at the end of the day, the passive sign convention is largely only used rigorously when learning the basics. As such, the student uses whichever interpretation their text and/or instructor uses. Once they gain a sufficient grounding in the fundamentals, they generally abandon strict adherence to either interpretation and assign symbolic voltages and currents in whatever manner makes the most sense for what they are doing at the time. If they need to interpret power quantities, then they are usually in a position to understand intuitively that current flowing from a positive voltage to a negative voltage represents power absorbed/dissipated and can translate any of the other possibilities in their head.

#### MrAl

Joined Jun 17, 2014
7,468
Hello again,

It appears that we are just not understanding each other because there are too many discrepancies cropping up that would not be there if we actually did understand each other. For example, i never said that the three sources were either ALL delivering or ALL absorbing, i said that either of them could be either delivering or absorbing, but they dont have to all do the same thing, and you said you dont like to use negatives yet you used a negative in your last example. All this leads me to believe we wont be able to progress in this discussion without 10 more replies back and forth
Perhaps in a PM would be more appropriate, if you're still interested that is

#### WBahn

Joined Mar 31, 2012
25,548
Hello again,

It appears that we are just not understanding each other because there are too many discrepancies cropping up that would not be there if we actually did understand each other. For example, i never said that the three sources were either ALL delivering or ALL absorbing, i said that either of them could be either delivering or absorbing, but they dont have to all do the same thing, and you said you dont like to use negatives yet you used a negative in your last example. All this leads me to believe we wont be able to progress in this discussion without 10 more replies back and forth
Perhaps in a PM would be more appropriate, if you're still interested that is
I don't like having conversations by PM unless it is something that is confidential. Other people can read and learn (or ignore) as suits them.

I was referring to your post:

Hi again,

Ok then here is the list without any signs and any extra notes:

V1: 5 watts
V2: 10 watts
V3: 10 watts
R1: 2.5 watts
R2: 2.5 watts
Where you just simply got rid of all the signs and all the notes. That means that you are saying that V1, V2, and V3, all have powers that are positive. If you are using any kind of consistent sign convention, then positive power on a source either means that it is delivering power or that it is absorbing power. But regardless of which you choose, the three sources above all have the same sign and so they are either all delivering power or all or all absorbing power. You have to do something to distinguish the two possibilities and that is either use a sign or use a notation.

Aside: Note that you should NOT use both because if you say:

Vs = -50 W delivering

Then this could (and often would) be reasonably interpreted as delivering -50 W which is the same as absorbing +50 W. If you want to use both the sign and an informative label, then they should be disassociated somehow, usually with parenthesis and even better with an "i.e." or something similar.

Vs = -50 W (i.e. delivering)

Moving on, when I said that I prefer not to use negative signs I tried to make it clear that I prefer to set things up so that having something turn out to be negative is unusual. Not that I'm not perfectly willing to work with negative signs if that's how things turn out, but I prefer that when a source is acting like a source, that the voltage, current, and power associated with it are all positive quantities. The same for a load when the load is acting like a load. If a source is acting like a load, then I want the voltage and current to have opposite signs and the power to be negative. The same for a load that is acting like a source.