## Electrical Impedance--Resistance is Futile

Discussion of electricity, electronics, electrical components and theories of circuit operation.
bperet
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### Electrical Impedance--Resistance is Futile

Gopi wrote:
1 + i/2 - 1/6 - i/24 + 1/120.... = 1 + i/2 + i2/6 + i3/24 + i4/120 ... = ei

This is a MAGNETIC rotation, hence a polar-2D rotation. Also, from the diagram, we can see that it is just the Turn, so we have the relation:

Turn = eix

Shift = eix1 - eix2
It just hit me that if you add a magnitude, Z, and a phase angle θ to the natural exponent form of the Turn, and use 'j' instead of 'i' for the imaginary operator, you get:

Ž = Ze

Which just happens to be the complex form for electrical impedance (the A/C version of resistance).

What I believe this is showing is the magnetic rotations in time (turns) as resistance/reactance to the flow of space (the electron). The momentum of the 2D rotation is t2/s2. The electron, being a unit of SPACE, appears as a "distance" to momentum, and the momentum of an object is altered by distance. The momentum per unit distance = t2/s2 / s = t2/s3 = Resistance (basically a 2D version of Force, t/s2).

When this resistance runs for a period of clock time, t, we get Rt = t2/s3 x t = t3/s3 = MASS.

I think this is a fairly significant conceptual breakthrough. I know that I was stuck in the thinking that resistance was as Larson described, mass per unit time. But considering that "mass" is made up of 2D rotations, NOT 3D, the momentum per unit distance makes a lot more sense.

The energy of the system is either:

E = m c2 (mass)

or

E = Rt I2 (resistance)

Kudos to Dave for his RStheory post on pressure, which got me thinking in terms of momentum!
Every dogma has its day...

davelook
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### Re: Electrical Impedance--Resistance is Futile

davelook wrote:

bperet wrote:

It just hit me that if you add a magnitude, Z, and a phase angle θ to the natural exponent form of the Turn, and use 'j' instead of 'i' for the imaginary operator, you get:
Ž = Ze

Reading about impedance has convinced that Larson is wrong about the dimensions of capacitor charge (Q=t/s) and capacitance (C=s).

First up is the common formula f=1/(2pi*sqrt(L*C)). This only works if Capacitance=s3/t

Also, capacitance depends not only on Area over distance, (s2/s=s), but also on the permittivity (s2/t) of the dielectric - again, the Farad is really s3/t.

The energy of a charged cap is given by 1/2CV2; s3/t * t2/s4=t/s.

So Q really is s(not s/t) because Q=CV; s=s3/t * t/s2. (Ok, so this one is circular reasoning)

So there aren't really 2 forms of coulomb, as laid out in BPoM. I think Larson confused the charge (what is stored) with the energy (how it's stored).

bperet
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### Capacitors

davelook wrote:
Reading about impedance has convinced that Larson is wrong about the dimensions of capacitor charge (Q=t/s) and capacitance (C=s).

First up is the common formula f=1/(2pi*sqrt(L*C)). This only works if Capacitance=s3/t
I just spent a couple hours digging through the equations, and I believe you are right. When capacitance and inductance are viewed separately, Larson's values work. But, when you start connecting them together, as in resonant circuits, Larson's units DON'T work--but yours do (at least with Larson's definitions of magnetism, which may or may not be correct at this point).

I did notice there seems to be a mixup between Q (t/s), q (s) and C (s) and C (s3/t), since they are numerically interchangeable in most cases, having a value of 1 natural unit.

davelook wrote:
Also, capacitance depends not only on Area over distance, (s2/s=s), but also on the permittivity (s2/t) of the dielectric - again, the Farad is really s3/t.
Rainer was telling me of an experiment an instructor did in school, where they had a large capacitor that could be disassembled. They charged up the capacitor, removed the dielectric, and passed the plates around the room to the students. There was no apparent "charge" on the plates. The plates were returned and the dielectric placed back between them, and the wires shorted--ZAP--huge discharge. This demonstrated that the so-called "charge" is actually contained in the dielectric, not the plates, which means the energy would be proportional to volume as you indicated, not just the distance.

Rainer and I were discussing the capacitive situation just moments ago, trying to figure out what is being "stored", given your modification. The dimensions of s3/t can also be interpreted as I x s2, current times area (current--uncharged electrons--are proportional to the cross-section of the wire). Rainer's argument was that there is no current flow in the capacitor, but if consider the situation, "I" is just s/t... electron (s/1) EXISTING in time region (1/t) as "motion" (s/t)--not necessarily "something moving", so you can think of the current as an "electron distance", since electrons ARE units of space (distance), along with the area, comprising a volume. The temporal component is then a property of the time region, 1/t, giving s3/t.

It also supplies some insight into the nature of capacitance, itself. Unlike what conventional electronics says, what is being stored are uncharged electrons ("holes" or positive charges) in the time of the dielectric. Remembering the reciprocal relationship between space and time, a decrease in space is tantamount to an increase in time, so the closer the plates are together in space, the further they are in time. But you need something to "pivot" on for that. The spatial displacement of the dielectric is basically increasing the "space" between the plates, and since that "space" is coupled with a time region, that compression results in more time in less space--the pivot point. Also, the space prevents the flow of electrons across the plates, since the relation of space (electron) to space (dielectric) does not constitute motion.

By using Dave's value in the regular equations concerning capacitance and energy, some flipping between Q (t/s) and q (s) is necessary, but they still work.

Fascinating discovery, Dave!!
Every dogma has its day...

davelook
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### Electrical Impedance--Resistance is Futile

I'll say more about your post, I just wanted to get this out there during my lunch break...

One thing I found interesting was the similarity between a tank circuit and a pendulum...

Potential energy = mgh (mech.), or 1/2CV2 (elec.)

Kinetic energy = 1/2mv2 (mech.) or 1/2LI2 (elec.)

It would be great if we could positively identify every single component that goes into the final product.

For instance, we can easily identify 3 space units from C, (Plate Area=s2, dist. between plates=1/s1), and "h" in mgh is s/1, etc.

Let's try to nail down the rest!

bperet
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davelook wrote:
I'll say more about your post, I just wanted to get this out there during my lunch break...
Here's what I did over lunch...

Your value for the Farad should have been obvious... I spent one afternoon last year complaining to Phil that there were 4 different versions for dielectric units, and none made sense! So I went back to my notes and applied the Dave Farad units... Take a look:

This is one of the "defining" equations in electro-magnetic relationships:

1 = c2 ε0 μ0

Unity = speed of light squared x vacuum permittivity x magnetic constant. Makes conceptual sense; planar speed is balanced by rotational momentum of polar space, yielding unity.

The magnetic constant is fairly well defined in terms of space-time units, having a value of t3/s4... (more on that later).

1 = s2/t2 x s2/t x t3/s4

Making the permittivity units: s2/t

Now look at the definition of capacitance: C = ε A/d

Where A is the plate area (s2) and d is distance (s). If you use Larson's units of C=space, permittivity becomes a unitless constant, which we know from the above equation, it is not.

Plug in the correct permittivity value...

C = s2/t x s2 / s = s3/t

Lo and behold, Dave's Farad appears! So... when can I expect the re-write of those chapters in BPoM???
Every dogma has its day...

Gopi
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### Electrical Impedance--Resistance is Futile

bperet wrote:
When this resistance runs for a period of clock time, t, we get Rt = t2/s3 x t = t3/s3 = MASS.
I think the origin of the term in resistance is due to the two part being included in voltage of a current carrying conductor:

Voltage (force) = m * dv/dt + v*dm/dt

t/s2 = t3/s3 * s/t2 + s/t * t2/s3

The first is the effect of the wire, the second is the effect of the current (s/t) present in it. In other words, mass thru space and space thru mass. The resistance is related to mass just as acceleration is related to velocity.

Thinking back, the capacitor seems to have the same relationship with volume as resistance does with mass:

Mass: t3/s3

Resistance: t2/s3

Volume: s3

Capacitance: s3/t

Hmmm... writing the force terms:

Voltage (force) = Q/C [s/(s3/t)]

Voltage (force) = I*R [s/t * t2/s3]

New capacitance makes sense, seeing that Q/C would be dimensionless otherwise. As to the second equation, still pondering its connection with first...

Gopi
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### Electrical Impedance--Resistance is Futile

davelook wrote:
One thing I found interesting was the similarity between a tank circuit and a pendulum...
Traditionally, the circuit is always compared to a mass on a spring. That way you get the 1/2's in place!

bperet
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### Electrical Impedance--Resistance is Futile

Gopi wrote:
Thinking back, the capacitor seems to have the same relationship with volume as resistance does with mass:

Mass: t3/s3

Resistance: t2/s3

Volume: s3

Capacitance: s3/t
Try this:

1 = c2 ε0 μ0 = s2/t2 x s2/t x t3/s4

μ0 = t3/s4 -- magnetic permeability

c2ε0 = s4/t3 -- electric permittivity

Can you say "reciprocal relation"?

Couple years back when researching magnetism, I came to the conclusion that magnetism was just "cosmic electricity", because of the 1/t2 relation of speed, and the way the equations were inverted. Perhaps this is the case?

The c2 component may indicate a 2D angular velocity, as I suggested earlier. That means we are dealing with polar space, a cosmic effect where space is rotational and time is rectilinear. After all, in RS2, the electron IS cosmic.
Every dogma has its day...

bperet
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### Electrical Impedance--Resistance is Futile

If you look up Farad in Wikipedia, you get 6 definitions (I replaced "C" in the Wiki article with the correct 'q', the electric quantity of the RS):

$\begin{matrix}Farad = & \frac{A s}{V} & \frac{q}{V} & \frac{q^2}{J} & \frac{q^2}{N m} & \frac{s^2 q^2}{m^2 kg} & \frac{s^4 A^2}{m^2 kg} \\= & \frac{(s/t) (t/1)}{t/s^2} & \frac{s}{t/s^2} & \frac{s^2}{t/s} & \frac{s^2}{(t/s^2)(s/1)} & \frac{(t^2)(s^2)}{(s^2)(t^3/s^3)} & \frac{(t^4)(s^2/t^2)}{(s^2)(t^3/s^3)}\\= & \frac{s^3}{t} & \frac{s^3}{t} & \frac{s^3}{t} & \frac{s^3}{t} & \frac{s^3}{t} & \frac{s^3}{t} \end{matrix}$

It seems pretty obvious that the unit of capacitance, the Farad, is s3/t. Conventional electric theory has confused these three values, which seem to appear ad hoc in the equations:

Electric capacity, the Farad (C) = s3/t

Electric quantity (q) = s

Electric charge (Q) = t/s
Every dogma has its day...

bperet
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### Electrical Impedance--Resistance is Futile

From Wikipedia Coulomb:

Wikipedia wrote:
1 coulomb is the amount of electric charge transported by a current of 1 ampere in 1 second.

1 C = 1 A x 1 s

It can also be expressed in terms of capacitance and voltage, where one coulomb is equal to one farad of capacitance times one volt of electric potential difference:

1 C = 1 F x 1 V
If Larson is correct and the farad is "s", then the Coulomb is both s and t/s...

C = s/t x t = s

C = s x t/s2 = t/s

If Dave is correct and the farad is s3/t, then the Coulomb is always s...

C = s/t x t = s

C = s3/t x t/s2 = s

Which means that the Coulomb ISN'T an "electric charge", but a quantity of uncharged electrons, which are not recognized by conventional theory. (Technically, they are, but as "holes", not electrons).
Every dogma has its day...