OPEN FORUM
A Simple Rule for Determining Direction of Power in an Electrical Circuit
I am presenting here a simple rule for determining the direction of power in a circuit.
Once seen, it seems so obvious that you might be tempted to say, "Well, everybody knows that!" But, strange, although the concept is simple, I have never seen it expressed as a general and concise "rule" requiring only minimal mental manipulation.
This concept of a rule occurred to me during the 1990's while I was studying the transfer of energy between segments of a two-conductor transmission line exhibiting standing waves. I knew the instantaneous directions of current in each segment and the instantaneous voltage polarities of the segments, but, since I considered determining the direction of energy flow to be a problem in electromagnetism, I started out by using these parameters of the current and voltage to obtain the directions of the magnetic and electric fields between the conductors. I then applied Poynting's theorem of electromagnetism to the fields to find the Poynting vector, which specifies which way power in each segment is traveling at that instant.
Since doing this was tedious, I decided to ascertain power direction directly from the voltage and current, skipping the intermediate fields determinations.
As author John D. Kraus [1] implies, a duality can be considered to exist such that power transfer in a transmission line can be seen either as an electromagnetic phenomenon taking place in the space between and around the conductors or, alternatively, a phenomenon of charge movement within the conductors.
This concept led me to formulate a rule, using the circuit parameters of voltage and current, which would produce immediately the direction of energy flow in the circuit in agreement with the result that the electromagnetic Poynting theorem provides.
The very general circuit rule I came up with turned out to be simple:
-
"In any electrical circuit, energy is flowing in the same direction as the current carriers are moving in the conductor with the same polarity as the current carriers."
The phrase "current carriers" is used because, depending on your profession (physicist, engineer, or military electrical technician) you may have been taught to consider current to be carried by either nameless positive charges or by negative charges called electrons, and therefore you should look at the direction of your chosen current or charge carrier in the conductor of the same sign.
This rule can be proven by "exhaustion", that is, by considering all eight possibilities that can be found by multiplying the four possible ways of assembling a simple circuit (power source on right or left, positive terminal on top or bottom) by the two types of current carriers, (positive charges or negative charges.)
Alternatively, if you are "into" electromagnetism, you can verify that this rule is in agreement with the determination of power direction using Poynting's vector by considering the directions of the electric and magnetic fields that the voltage and current produce between and around the conductors.
This rule is applicable to alternating current by considering the instantaneous values of voltage and current. As I said earlier, I have found instantaneous application of the rule to be useful in analyzing sections of a transmission line upon which standing waves are present to see how energy is traveling and being reflected on given sections of the line at that particular instant.
Also, note that the conductors need not be solid at all - an example would be energy transfer in the cathode ray tube of an oscilloscope - the (negative) path of the electron flow through the vacuum from the cathode to the phosphor screen being one "conductor", and the return (positive) path through the chassis being the other. Application of the rule in this case will tell you that energy is flowing from the cathode to the phosphor, which is certainly true.
As I mentioned at the beginning of this discussion, that since it might be assumed that anyone can determine the direction of power on a case by case basis by looking at the current and voltage parameters of the conductors and then imagining what the configuration of power source and sink must be to produce them, it might be asked why bother stating this as a rule. The answer is that using this rule makes the job faster and less prone to error.
But despite this usefulness, as far as I have been able to ascertain, nobody has ever stated this determination of direction of power in a circuit as such a concise, succinct rule.
Yes, you will find discussions in elementary electrical engineering texts about such things as setting up "reference directions" for use in calculations and also something called the "passive sign convention" whereby power caused by positive current entering the positive terminal of a device should be called "positive power" and the device should be considered to be a "load." Conversely, if the positive current enters the negative terminal, the power is "negative power" and the device is a "source."
Therefore people might point to these textbook discussions and ask whether the rule I have given is not just another way of stating what these textbooks have been saying for years. My answer is that although the above-mentioned textbook concepts and the rule are in agreement, the rule is actually more basic in that it doesn't require a load or a source and their terminals to be shown and considered in circuit diagrams, only the conductors themselves.
So, for example, the rule could be applied to a power company's overhead or underground conductors to determine in which direction lay the utility's generators and in which direction lay their customers.
Moreover, the rule is more general in that it allows for its use with charges of either positive or negative polarity.
In fact, it might be argued that the "reference direction" and "passive sign convention" are themselves derivable from this rule, implying that the rule is more basic than either of these conventions.
Reference
[1] Kraus, John D., Electromagnetics, New York, NY: McGraw-Hill, 1984, p. 184
Robert J. Smith (Email: rjsmith2@earthlink.net )