Given that electricity is generated in an alternator's magnetic field under the poles; then how can we demonstrate that the formula
Energy= volts x amps x Cos "thi" can be interpreted as an "in phase" dimensionless quantity of power?

CliveS

1. The quantity we obtain when we multiply voltage by current is "Power" not "Energy".

2. Power is not "dimensionless". All you have done, is to obtain either the "rms power" by multiplying the "rms voltage" by "rms current" and a factor to address the vector difference in the phasor domain between the voltage and current (the "power factor").

So, strictly, your power is in "W rms".

In "dimension terms", we can write:

"W rms" = "V rms" x "I rms" x "cos(phi)"

-------------------------
Eur Ing Graham Kenyon CEng MIET

Thanks Graham

Yes; you are correct Energy is Power times time
Energy=VxIxCos"thi"xTime.
The problem is that a Sin wave is considered by us engineers as a 2 dimensional wave rather than 3. However, I think you will agree that current is measured in amps/ square metre whereas voltage is measured in volts/metre.
This means to me that current is complex in itself and should be the resultant of the excitation current Ix amps in the x direction and its interaction with the conductors charge current Iy amps in the y direction.
So electrical power could be considered as an area of current loop ( using Maxwells model) moving forward in space [ or inside a conductor] in the 90 degree z direction.
Thus imagine that the current loop can only move if a voltage is applied to it at rightangles to the loop in the Vz direction.
So we have 3D electromagnetic power = Vz*[root Ix*Iy]*Cos"thi" which if it continues over a period of time is energy.
CliveS

No, I definitely disagree.

Current is measured in Amperes -or "Coulombs per second".

"Current Density" is measured in "Amperes per sq m".

Voltage is measured in "Joules per Coulomb", i.e. it represents the energy that a Coulomb or charged particles possesses.

"Electric field strength" is is measured in "Volts per metre".

I think what you are describing here, is how electric fields interact with charge-carrying particles (and/or the charge itself, depending on your point of view: I suppose there's an element of uncertainty in our understanding of electricity at this level) to produce the effect we see? And yes, we do exploit the fact that charged particles can be moved in three dimensions all the time.

But certainly, because the definitions you used initially are "invalid assumptions", the conclusion does not follow.


In fact, when we look at a.c. power in a wire, we have the picture of the "coulombs" passing back and forth past an infinitely thin "slice" of the wire. We don't have to consider whether the charge is vibrating radially through the slice in our "model" for a.c. current flow.

Personally, I can't decide whether "electrons" actually move in all cases of so-called "current flow": do adjacent atoms/molecules simply pass energy, to the next one? I'm not sure that we can actually tell in all cases, or whether it really matters?

-------------------------
Eur Ing Graham Kenyon CEng MIET

Thanks Graham
The problem with the model using a charge passing back and forth past an infinitely thin "slice" of wire is three fold
1. The infinitely thin slice has area x,y which current also has; but no 3D volume x,y,z.
2. Having charge implies that there is a particle involved which cannot be true as particles can never reach the speed of light which of course electricity can.
3 It appears that the magnetic frequency per second is irrelevant which in the case of electromagnetic radiation is untrue.
Trying to unravel a correct model for electricity is a major problem for engineers and physicists alike.
Happy Easter
CliveS

So I can't observe how many race cars pass a point on the F1 circuit in a given time? I clearly can, and this is what current flow is all about. A better comparison may be water flow: Litres per second passing a point in a pipe (current), and pressure (voltage)?

Search "Wave-Particle Duality" (if memory serves) and I think this will give an answer to this point.

Could you explain a little more what you mean here - I may be able to help.

I'm not sure we can do that 100%. But for Engineers, it may well not matter because so long as we know the bounds within which our observations operate in the prescribed manner, we can make things work, fix things, and predict outcomes within those bounds. The Art of Engineering.

-------------------------
Eur Ing Graham Kenyon CEng MIET

Anyone else like to join in?

-------------------------
Eur Ing Graham Kenyon CEng MIET

No - your doing a fine job flying solo Graham

OMS

-------------------------
Failure is always an option

. . . and when I've given myself enough rope

-------------------------
Eur Ing Graham Kenyon CEng MIET

Just to clarify:

We define

Energy = Power x time

It takes 1 joule of work to move 1 coulomb of charge between two positions M and N in an electric field, then between M and N there is a potential difference of 1 volt. (note that it makes no difference what path the coulomb of charge takes to move from M to N, the end result is still you will only get 1 joule of work done. 3D electricity is not applicable in here.)

1 J = 1 W x 1 s = 1 coulomb x 1 V
1 A = 1 coulomb / 1 s
Hence 1 W = 1 A x 1V

The definitions:
Active Power = Volt x Current x cos (phi), and
Reactive Power = Volt x Current x sin(phi)
distinguish active power performs real work such as heat or motive energy and reactive power feeds the magnetic field in an inductor or the electric field in a capacitor. If you correct the (phi) = 0 degree, the capacitor will supply enough electric energy to feed the inductor's magnetic field and vice versa. No reactive power from the source of energy is needed to feed the capacitor or inductor.

-------------------------
Tony Sung

Yes, Tony
That is what we have been taught; but it is incorrect to envisage electricity as 2 dimensional only.
Graham has said electricity is like water flowing thro' a pipe with pressure difference being likened to potential difference or voltage. I think this is a better 3D model but can be improved by considering electrical energy as a volume of gas in a vacuum tube. But we do know that not only voltage and current and external magnetic Cos or Sin "thi" fields will affect the energy in the tube but also the frequency is most important and must be in the formula E=VxIxCos"thi"xT What if we substitute V for flux turns per second. That could result in a 3D equation that includes all the necessary parts
E=[Fluxturns x frequency]z x root( Ix x Iy) x Cos"thi"
CliveS

I think the equation of power derived from volts and amperes is from a macroscopic view taken up by engineers in everyday's applications. The generation of electricity was first discovered through static electricity which does not involve magnetic flux at all . At that time, only d.c. electricity was known and there was no equation to include the (phi) in the joule energy equation. One good example of static electricity is the Van de Graaff generator.

Many physicists devote a lot of their efforts to understand and explain the flow of electricity in vacuum and the microscopic voids of metals when the electron was discovered by JJ Thompson. They came up with the theory that, under the influence of an electric field (volts), the electron will move from a high potential to a lower potential. As the movement of the electron may not be in a straight line, with the classical definition of work done is the product of force times distance, the energy incurred by one electron will be different to another - which makes it difficult to calculate for billions of them to move in an electric circuit. So they use the 'mean free path', 'drift velocity' and 'Fermi energy' theory to explain how the electrons move in the lattice maze of metals - this they developed the microscopic view of Ohms law (Link). It was also observed that the path of a travelling electron can be influenced when a magnetic or gravitational field is (or both) present, the CRT is a good example.

Michael Faraday and James Clark Maxwell developed the law of electromagnetic induction and duality theory of electricity and magnetism helped electrical engineering science become one of the most important and respected professional disciplines in our society.

It has been observed that an electron (a) has a finite mass that is why they can be influenced by the gravitational field (b) the presence of a magnetic field changes its conduction path. I have not read any microscopic explanation of these pheonomena yet. Your hypothesis is interesting, it is worth exploring further to validate it or vice versa.

-------------------------
Tony Sung

Thanks Tony
The electron as dealt with by Fermi and others is of course the electron particle which works extremely well for DC and electrochemical examples. The problem is that electricity can and does move at around the speed of light and therefore cant be particle based.
In my view electrostatic energy is equivalent to potential energy [ a rock on top of a hill has no energy in my opinion until it demostrates that energy by falling which then gives it kinetic energy; which is real energy]. Voltage ; or potential difference is in the same category it has no energy until an area of current starts to move; then we get electromagnetic energy which is the movement of a volume of magnetic flux which is real energy. This volume of magnetic flux [magnoflux] can move in a vacuum at around the speed of light.
Einstein did not find that photo electricity is electrostatic but electromagnetic only. Therefore the formula for electromagnetic energy requires somehow to acknowledge that flux is the basis of electrical energy hence my suggestion that V=NdO/dt be reinstated into the formula. [ Note that N is the product of both turns of amp area and frequency]
CliveS

The Poynting vector P (or in Wiki, S) represents the particular case of an energy flux vector for electromagnetic energy. It is rather mathematical in its very nature.

This Link explains how ac transmission power (real power) relates to Poynting vector P = E x H.

Hope the link can help explain how electromagnetic waves relate to power.

-------------------------
Tony Sung

Thanks for the link Tony
The Poyning vector P is based on Volts per metre in say the z direction and then H ampturn at presumably right angles.
To finalise the equation into a 3D x,y,z format we require the amps to be a complex area of current in the x and y direction. This is not necessarily clear from the Poynings vector [which is 2D only].
Wikipedia definitions also mentions that we could as well have taken flux per metre and amps per square metre as alternative axis which of course I agree. In the end we need an area of current the square root of Ix*Iy moving forward in the direction of the voltage to make the model 3D electricity.
BTW it turns out that real power is only obtained from the square root of the minimum Ix or Iy squared the excess just creates a power factor shift.
CliveS

Not sure about you are saying the 2D Poynting vector? Mathematically, the cross-product of two vector fields E and B yields a third vector field S perpendicular to the two fields. Any vector can be resolved into x, y and z components.

The electric current I is in fact a scalar quantity that it has no x, y or z components. E.g., under dc conditions, it has no vectorial property. Only under 'sinusoidal' ac conditions, like a simple harmonic oscillation, it can be mathematically described using a phasor to simplify electrical calculations. Same as the 'impedance' Z which can be represented by a phasor but it can only be resolved into real and imaginary parts. Hence, the V, I and Z phasors do not have any x, y or z components inside a conductive medium. Also, the equation Active Power P=V x I x cos(phi) is giving us the average real power [based on instantaneous power =instantaneous vp x sin(omega x time) and ip x sin(omega x time + phi)]. V and I are root-mean-square values of the v(omega x time) and i(omega x time + phi) functions respectively. The RMS V and I are ac effective values that will give the same heating effect as in dc circuits. They do not have any physical x, y or z components.

By Faraday's Law, Maxwell's theory and Poynting vector, the flow of electricity (electrons) in a conductor was caused/will result in E and B fields around it. This physics journal paper gives a qualitative explanation of how the power developed by a resistor relates to the E and B fields around it. It does not use that many mathematical formulae but explained the relationship very well.

-------------------------
Tony Sung

Yes; Tony
I have read this clever piece of maths before, but unfortunately it does not help in my attempt to find a unified equation which can be used to conceive electro-magnetic energy.
We need an equation that will not only explain electricity in a wire but microwaves, MRI scanners and even light as well. To envisage this we need to embrace the magnoflux concept and try and find a general equation that suits all frequencies of electromagnetic energy.
This improvement can only be made if flux [¬] is prominently brought into the equation. To realise this objective voltage has to be expanded to flux [¬] x frequency[f] x turns [N]. I know that this seems complicated because we can read voltage on a meter but we need to acknowledge that it is the result of flux movement not just a numerical value.
Electricity = ¬ * f * N *root (Ix *Iy)*Cos"thi" *t
Where
Ix is the excitation current of a generator or a micro-wave oven or MRI scanner which is at right angles to Iy which is charge current particular to the medium through which the volume of flux is moving in the z direction.
I trust this new 3D concept will help in unifying all forms of massless electromagnetic energy instead of having different subjects for, electromagnetics, light and radio everything will be covered by one the one formula.
CliveS

Clive,
From the equation you gave, it appears that you have an inductor coil such that Electricity = real power and 'thi' should be a function of frequency f. The outcome of the expression could well be zero.

What you are proposing is certainly something different from what the conventional theory is currently used universally. One small hurdle you will need to overcome is the definition of 'current'. It needs to be either refined or abolished to support your hypothesis.

At this moment in time, there is no three dimensional current Ix, Iy or Iz in existence. Or let's put it this way, it is not possible to split an electron into three parts qx, qy and qz - that is if you accept current is defined as number of charges moved per unit time. However, having said that - to consider it with an open mind - nothing is impossible if you use wave theory to help you prove it.

-------------------------
Tony Sung

Tony
You are correct in assuming that I do not agree that current can be defined as charges moved in unit time. The problem is that charge has e/m implications which means that charge [i*t] can never move at the speed of light which electric current and magnetic flux certainly can. So the physics definition is flawed as it considers a DC electrons Iy only and therefore lacks Ix to turn it into the 2 dimensional area of loop current which is required to make my hypothetical unified electric model complete .
CliveS

I thought charges are equivalent to electrons which are energy carrying particles. I have a few question here:
a. What am I measuring when I put a clampmeter around a single 1.5mm2 conductor which has a volt-drop of 4.15V (the clampmeter says 13A and the length of the conductor is 22m long) ?
b. Why am I getting almost zero current reading when I put a clampmeter on a single phase circuit conductors (phase and neutral)?
c. How do I explain to my apprentice electricians what is 'current'?

Thanks

Marty