## Resistance, Reactance, Permeability and Permittivity

Discussion of electricity, electronics, electrical components and theories of circuit operation.
bperet
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### Resistance, Reactance, Permeability and Permittivity

Since my reply to Horace triggered a new understanding of these concepts, I thought I would start a separate topic on it in the EE forum. (Click on the ↑ after "Horace wrote" to read the original topic.)
Horace wrote:
Tue Jun 26, 2018 5:31 pm
I think the full EE scalar formula is |Z| = SQRT( (XC+XL)2 + R2 )

Thus for XL=20Ω and XC=-20Ω and R=0Ω the scalar magnitude of impedance |Z|=0Ω.
...and for XL=20Ω and XC=-20Ω and R=20Ω the scalar magnitude of impedance |Z|=20Ω.
I am no longer using the linear, "graph paper" approach to impedance, but have taken it into another dimension (literally), based on a quaternion rather than complex quantity (see: Extraordinary Electric Current), in which I treat resistance as "real" (linear) and reactance as "imaginary" (angular)--but as a quaternion, not a complex quantity. I treat quaternions differently, because I do not transform the angular velocity into a 2D, linear one, so I only need a 3-axis representation (not 4, as you'll find with regular math). As described elsewhere, linear motion is a translation along an axis, whereas angular motion is a twist of an axis.

The real axis represents the linear motion of electric current and resistance/conductance, which is analogous to the "progression of the natural reference system" as it always moves at the speed of light, as electric current does. Resistance does not change this speed... the current still flows at c, like the progression does.

The other two axes are used as poles for the angular motion of reactance, the blue is for the typical "j" axis of alternating current, and the red from Steinmetz's work on impulse and oscillating currents. So to get a typical impedance, you have a resistance (radial length) and reactance (angle)--the complex number. The three planes of rotation then form Larson's concept of "speed ranges," of which we stick with the low-speed (1-x) range of DC and AC.

Odd thing about these speed ranges is that low speed and ultra-high speed (3-x) are based in clock time--they have a displacement along the real, DC axis, but intermediate speed (2-x) does not. Intermediate speeds are always at zero on the DC axis, meaning the effect would appear instantaneous, as it occurs without a change in time.

And I just realized something... the red and blue axes must also have a resistance component (translational at the speed of light), due to the symmetry constraints of the RS. And that would infer that capacitance and inductance are the same thing, but from two, reciprocal perspectives... that means the "squished flat" graph-paper form of complex numbers may be incorrectly representing the reactance relationships--being a projection, rather than a 3D structure.

My thought here is that capacitance, having negative reactance, is not in the 1-x range (as complex quantities put it), but in the 3-x range, with only inductance in the 1-x range. Both are time-dependent angular velocities, but would be orthogonal and out of phase by 90°, which may explain the leading-lagging current of impedance.

That would infer that the "resistance" on the blue and red axes would be an indirectly observable quantity--something similar to resistance but nonlocal. If inductive is 1-x, that would make the blue axis permeability and the red axis (3-x), permittivity. A common resistance acts like a membrane, limiting flow through it. Both permeability and permittivity do the same. I will explore this further.
Every dogma has its day...

SoverT
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### Re: Resistance, Reactance, Permeability and Permittivity

bperet wrote:
Thu Jun 28, 2018 10:45 am
Odd thing about these speed ranges is that low speed and ultra-high speed (3-x) are based in clock time--they have a displacement along the real, DC axis
Off topic, but what does axis have to do with clock time (or clock space)? The clock is merely a synonym for the universe taking a step, whether it's a unit step of 1/1, or an accelerated step of 47/23. The progression progresses regardless of observers looking at some arbitrary projection into a preferred reference frame

bperet
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### Re: Resistance, Reactance, Permeability and Permittivity

SoverT wrote:
Thu Jun 28, 2018 11:23 am
Off topic, but what does axis have to do with clock time (or clock space)? The clock is merely a synonym for the universe taking a step, whether it's a unit step of 1/1, or an accelerated step of 47/23. The progression progresses regardless of observers looking at some arbitrary projection into a preferred reference frame
DC current is a speed, s/t, that has a magnitude of 1/1. The DC axis projection of intermediate speed is 1/0, or infinite speed.

Let me clarify... the "clock" is not a "step," but the unit speed datum of measurement. The clock IS the progression. It can be treated as a "step" because the progression progresses in unit increments.
Every dogma has its day...

Horace
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### Re: Resistance, Reactance, Permeability and Permittivity

Take a look at this video and notice how the projection of a sphere onto a plane looks like the Smith Chart of impedance:

...and after differentiation - like the Biradial Matrix.

bperet
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### Re: Resistance, Reactance, Permeability and Permittivity

Horace wrote:
Fri Sep 07, 2018 6:47 am
Take a look at this video and notice how the projection of a sphere onto a plane looks like the Smith Chart of impedance:

...and after differentiation - like the Biradial Matrix.
When you start projecting angular relations (imaginary numbers) as lines, it is common to get these types of diagrams (called "pencils" in projective geometry).

In RS2, I treat the quaternion as a scaled, 3D system--not 4D--since you cannot mix apples (real) with oranges (imaginary), which conventional math does. It is a different way to think, but when you can get to that point, it really clarifies a lot of things.
Every dogma has its day...

Horace
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### Re: Resistance, Reactance, Permeability and Permittivity

I know, they are different but the projection of the angular yin on our 3d linear (yang) perception is at the center of RS.
Your idea to use colors to depict this is good. I think it can be extended by mapping colors to the density of the dots projected onto the vertical line, as shown at the time index 7m 45s of that video.

bperet
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### Conversion of Natural units to Ohms

My theoretical work uses the natural units of the Reciprocal System, just space and time. In order to do anything practical, I need to map the RS natural units to conventional units. In the case of resistance and reactance, that is Ohms. The conventional relation is V/I=R, so if a conversion can be found from natural units to volts and amperes, that would give resistance.

Reactance appears to be the analog of inertia for the "mass" of inductance and capacitance, so a conversion of natural units to Farads (capacitance) and Henries (inductance) is also needed.

Larson made an attempt in Basic Properties of Matter, using now obsolete units of ESU and gram-equivalent. Since his time, those units have been dropped from regular use and the definition of an Ampere has also changed. Secondly, the conversion Larson came up with does not seem intuitively correct... ONE natural unit of resistance being 8.8 gigaohms? That is far outside of conventional use.
BPOM, page 108 wrote:This clarification of the dimensional relations is accompanied by a determination of the natural unit magnitudes of the various physical quantities. The system of units commonly utilized in dealing with electric currents was developed independently of the mechanical units on an arbitrary basis. In order to ascertain the relation between this arbitrary system and the natural system of units it is necessary to measure some one physical quantity whose magnitude can be identified in the natural system, as was done in the previous determination of the relations between the natural and conventional units of space, time, and mass. For this purpose we will use the Faraday constant, the observed relation between the quantity of electricity and the mass involved in electrolytic action. Multiplying this constant, 2.89366×1014 esu/g-equiv., by the natural unit of atomic weight, 1.65979×10-24 g, we arrive at 4.80287×10-10 esu as the natural unit of electrical quantity.

The magnitude of the electric current is the number of electrons per unit of time; that is, units of space per unit of time, or speed. Thus the natural unit of current could be expressed as the natural unit of speed, 2.99793×1010 cm/sec. In electrical terms it is the natural unit of quantity divided by the natural unit of time, and amounts to 3.15842×106 esu/sec, or 1.05353×10-3 amperes. The conventional unit of electrical energy, the watt-hour, is equal to 3.6×1010 ergs. The natural unit of energy, 1.49275×10-3 ergs, is therefore equivalent to 4.14375×10-14 watt-hours. Dividing this unit by the natural unit of time, we obtain the natural unit of power
9.8099×1012 ergs/sec = 9.8099×105 watts. A division by the natural unit of current then gives us the natural unit of electromotive force, or voltage, 9.31146×108 volts. Another division by current brings us to the natural unit of resistance, 8.83834×1011 ohms.
One of the things that came out of the RS2 dimensional analysis (as described in this thread with yin dimensions), is that the Farad and Henry should be reciprocals... they should not be running from 0..∞, but 1/n and n/1 -- Farads and Henries should be reciprocals, since capacitors and inductors behave in a reciprocal manner.

What also needs to be considered is the fact that current (Amperes) is based on the flow of uncharged electrons, whereas electrostatics are based on charge. Larson's values appear to be electrostatic units, not units of electric current--which are the ones that I need to "do something practical" with this research.

I've been working on this for a while, but cannot seem to get any results that make sense. Hoping that someone with better math skills than I could take a stab at doing this. Thanks.
Every dogma has its day...

Horace
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### Re: Conversion of Natural units to Ohms

bperet wrote:
Sun Sep 09, 2018 10:44 am
I've been working on this for a while, but cannot seem to get any results that make sense. Hoping that someone with better math skills than I could take a stab at doing this. Thanks.
I believe that the attached paper will put you on track to cracking this ( especially the Annex )
Attachments Analysing Transformers in the Magnetic Domain.pdf

bperet
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### Natural units for Resistance, Reactance, Voltage, Current

Here is my first attempt at it, which matches Larson's values (off slightly because I used newer values for the constants). Couple interesting things showed up... the Coulomb is the MKS unit of electric charge and two values match 1 amu (atomic mass unit)... energy in Joules and voltage in Volts. That means one "natural unit" of voltage is the same as 1 amu. (Never did understand why they use voltage, a force, to express a mass.)

Code: Select all

``````Constants used:

Rinf     Rydberg Constant  1.097373156865e+7
c       Speed of light  2.997924580000e+8

Calculated Values:

us           Unit space  4.556335252708e-8
ut            Unit time 1.519829845989e-16

E               Joules 1.492418061895e-10 (electric energy = 1 amu)
q             Coulombs 1.602176620826e-19 (electric quantity = electric charge)
I              Amperes  1.054181575032e-3 (current)