voltage (1) (electromotive force) (general) (along a specified path in an electric field). The dot product line integral of the electric field strength along this path.
Notes: 1.
Voltage is a scalar and therefore has no spatial direction. 2. As here defined, voltage is synonymous with potential difference only in an electrostatic field. 3. In cases in which the choice of the specified path may make a significant difference, the path is taken in an equiphase surface unless otherwise noted. 4. It is often convenient to use an adjective with voltage, for example, phase voltage, electrode voltage, line voltage, etc. The basic definition of voltage applies and the meaning of adjectives should be understood or defined in each particular case.
[rbalex note: unfortunately ?instantaneous? is not one of the other adjectives defined and I ?coined? it in one of my posts above relative to the voltage gradient defined below.(The ?E? with an arrow above it) While I believe I have used it properly and consistently, it is not a regularly defined term, and is legitimately challengeable ]
potential gradient (1) A vector of which the direction is normal to the equipotential surface, in the direction of decreasing potential, and of which the magnitude gives the rate of variation of the potential.
(2) See also: voltage gradient.
voltage gradient ? is equal to and is in the direction of the maximum space rate of change of the voltage at the specified point. The voltage gradient is obtained as a vector field by applying the operator
In fairness to you,
IEEE Std 100 doesn?t directly define ?complex power?
complex power See: power, phasor; phasor power
phasor power (rotating machinery) The phasor representing the complex power. See also: asynchronous machine.
(Honest these are the entries)
However,
power, phasor has a very lengthy entry ? over a full page, in fact. I apologize that I can?t post it here. The bulk of it is the mathematical models used to describe and manipulate it. And it took me almost the entire morning just retrieving the graphics under ?voltage gradient.? It is initially defined as you described it:
S = P + jQ , but I can honestly say ?vector? was not mentioned except for this brief statement:
The phasor power is expressed in Voltamperes when the voltage is in volts and the current in amperes. Note: This term was once defined as ?vector power.? With the introduction of the term ?phasor quantity,? the name of this term has been altered to agree with the change in the sign of reactive power.
However two commonly referenced terms in the entry may be valuable:
phasor quantity (A) A complex equivalent of a simple sine-wave quantity such that the modulus of the former is the amplitude
A of the latter, and the phase angle (in polar form) of the former is the phase angle of the latter. (B) Any quantity (such as impedance) that is expressed in complex form. Note: In definition ?A,? sinusoidal variation with t enters; in definition ?B,? no time variation (in constant-parameter circuits) enters. The term ?phasor quantity? covers both cases.
phasor ? [Rbalex note: definition (1) has to do with metering systems].
(2) A complex number expressing the magnitude and phase of a time-varying quantity. Unless otherwise specified, it is used only within the context of steady-state alternating linear systems. In polar coordinates, it can be written as Ae^j? , where A is the amplitude or magnitude (usually rms, but sometimes indicated as peak value) and ? is the phase angle. The phase angle ? should not be confused with the space angle of a vector. See also: electric field strength.
(3) A complex equivalent of a simple sine wave quantity such that the complex modulus is the sine wave amplitude and the complex angle (in polar form) is the sine wave phase angle. See also: vector.
Steve,
But for the fact that you already know the difference, most people would say mass and weight are the same. They sure look a lot a like and many times they may be used fairly interchangeably it takes a while to communicate the difference. Geese share a lot of the same properties with ducks ? but you are correct, they don?t quite quack the same.
To address the issue ??treating power as a vector giving "close" answers.? I don?t believe I?ve quite said that. I?ve said something to the effect that VAs may be added arithmetically to give close enough answers. We do it routinely. But we always do it assuming the power factors are also close enough.
To both of you
While complex numbers may indeed be used to model vectors they aren't vectors themselves.
I?ve said several times that there are two forms of vector products. Take the dot (scalar) product of instantaneous voltage and current with a specific angle between them at a specific point in a circuit - the resultant is still readily recognizable as power, but it is a scalar by definition. But take the cross (vector) product of the same two vectors - what has been computed?
I have to dig very deep in my own memory but one of the reasons we use the ?VA? and ?VAR? dimensions rather than ?apparent watts? (AW maybe?) or ?watts reactive? (RW?) is to maintain the distinctions that they are constructs to make the math work rather than ?natural? qualities.
