Amperes squared is energy

If the energy stored in an inductor, 1/2*L*I^2, is joules, then I^2 by itself can't also be joules unless inductance is dimensionless.

Resistance doesn't have dimensions of 1/second as your equations on line

8 and 9 imply.

Where did you come up with this?

R = (kg/Coulomb^2) * meter^2 / second

--

  Rick C. 

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=================

** Physical quantities have "dimensions" - so suspect that is what it hints at. But I believe R is a dimensionless quantity.

That may be the slight of hand you are meant to see.

.... Phil

The volt is a joule/coulomb and an amp is a coloumb per second (post

2019 SI redefinition.)

So you can "define" an ohm that way by taking the quotient of the two by Ohm's law but it's essentially a circular argument, because simplistic form of Ohm's law is empirical, it doesn't directly derive from Maxwell's equations in the way say Kirchoff's voltage and current laws do.

Writing:

IIR = (Coul^2 / sec^2) * (kg / Coul^2) * (meter^2 / second), that way

is the same as writing: V*I.

Which is surely kg * (meter^2 / second^3), power, but when written V*I there's no justification at all to just drop any of those dimensions.

That is to say starting with the assumption I^2*R is power and then defining resistance as V/I, is circular

Inductance is dimensionless when studied in detail. Inductance is about the number of loops. A number has no dimensions. One Henry is a Weber per ampere. A weber has the same units as an ampere. A weber is a flux due to current, an ampere is a current. It is just the direction of flux is perpendicular to the current. They are one phenomenon: flux is beside a current, amperes are in line with current.

Henry units = 1

weber/amp = 1 unit

Hello RickC,

Ohm = Volt / Ampere

Volt = Joules per Coulomb

Joules energy equals force times distance

force is mass times meter per second^2

Joule = kg meter^2 / second^2

Volt = (kg/Coulomb) * meter^2 / second^2

Ampere = Coulomb per second

divide volt by amp...

Ohm = (kg/Coulomb^2) * meter^2 / second

Aren't you the time-cube guy or somethin'

I don't know about time-cubes, but he was the guy who had come up with a nuclear model based on crystal structures which would "explain" magnetism.

--

  Rick C. 

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  + Tesla referral code - https://ts.la/richard11209

What dimensions resistance has depends on how you pick your fundamental units. in CGS everything is unambiguously derived from the centimeter, gram, and second and volts/amp oddly ends up having dimensions of centimeters/second.

In SI volts/amp has dimensions of (kg/Coulomb^2) * meter^2 / second.

The "sleight of hand" such as it is is that Power = V*I = I^2*R = V^2/R are all equivalent ways of saying the same thing, if you start with the physics fact that V*I has units of power, and the (assumption, empirically-invented idea that sometimes holds) relation that V = IR.

Substituting the different ways of expressing the power relation into each other, or any way of expressing V = IR for anything there, results in no novel information, even if you use the dimensions rather than the symbols.

So it's 9 lines of saying the same thing in different ways and then he ends up with an equation for power same as he started with. And then on the last line drops the R and a factor of 1/second and ends up with dimensions of energy, but with no justification at all to do that.

OP may have looked quickly at this definition on Wikipedia:

and seen that V/A = 1/S and mistaken the large S for seconds rather than Siemens.

The power of vooDoo. who do? you do!

=====================

** More conjuring tricks going on here that at a magician's convention.

** Only in an ideal resistor.

** Only in a resistive circuit.

** Mechanical, kinetic & potential energy are equivalent to electrical Joules when converted to heat. ** F=mA is a low of motion.

** Kinetic energy, a moving object's heat equivalent.

E =0.5mV^2

** When ?

** That at least is unambiguous.

** Context shifting is a fool's game.

.... Phil

Hello bitrex,

Error notice:

I made a mistake in the post where I assumed resistance is per second. I was wrong to skip many steps in the algebra. I am sorry.

This apology does not change the title assertion :

E = ampere squared

To get the abstract units of measure, where only meters and seconds are used, the following ideas were used:

Mass equals area: derivation essay

Old science claimed that some units of measure cannot be factored, such as kilogram, Coulomb, and Farad. The new science, which I have introduced, factors all units of measure into meters and seconds.

Outline of the logic and mathematics ____________________________________

1 Understand that electron mobility mu has effectively the same units of measure as conductance g (g = 1/R).

2 Use Ohm?s Law and MOSFET current equation to find that charge is an Area of something. Q = meter^2

3 Understand that the kilogram cannot be isolated on one side of a formula to be equal to any simple term on the other side, using standard science.

4 Use energy equation (E = force * distance) and capacitance definition to bring mass and capacitance into one formula.

5 Bring Farads and kilograms on one side of a formula. The other side only has meters and seconds.

6 Logic indicates that mass = meter^2 and Farad = second^2

Detailed derivation of the Mass=Area fact _________________________________________

Step 1 I = g * V Ohm?s Law

I = mu * (C/meter^2) * (Vgs-Vt)^2 MOSFET current

I = mu * (C/meter^2) * V^2 simplified MOSFET

C is in Farads, V is in Volts

Set units of g equal to units of mu. That is justified by observing their definitions.

g = Q * mu * n * A / L

A is area. L is length, n is electrons per cubic meter, Q is electron charge, g is conductance, mu is mobility. Notice that time does not affect Q, n, A, or L. Time is involved in only g and mu.

Step 2 g = mu

I/V = I * meter^2 / (C * V^2)

g = (Coulomb/second) / Volts = Coulomb / Volt * second

mu = velocity/Electric field = (meter/second)/(Volts per meter)

mobility = meter^2 / (Volt * second)

conductance = Coulomb / (Volt * second)

Charge is area, since the properties of g and mu are the same for making current. They both use time and voltage. When the other factors are examined, they do not involve time. (meter, Coulomb do not depend on time). Q = meter^2 charge equals area, to be used later.

Step 3 In olde science, the kilogram cannot be set equal to anything other than a kilogram. mass = mass kilogram = kilogram There is no way, if mass is alone on the left, to make any other equation after cancelling like factors.

Step 4 Q = C * V = Area Energy = E = force times distance = kg meter^2 / (second^2) V = E/Q so V = kg / second^2 ?after cancelling area over charge

Step 5 V = kg/sec^2 = Q/C = meter^2 / C

kg/sec^2 = meter^2/C therefore

mass * capacitance = meter^2 * second^2 ?The Composite Formula? ??

Step 6 Use logic to evaluate ?The Composite Formula? to propose wa ys that mass can be defined with it.

Choice 1: mass = meter^2 capacitance = second^2

Choice 2 mass = meter * second cap = meter * second

Choice 3 mass = meter^2 * second cap = second

I have selected choice #1 because choice #2 destroys any reasonableness of formulas such as f=ma. Choice #3 is not good because then capacitance equals conductance and mass equals the D diffusion coefficient. Therefore

Mass=Area

so charge=area, from force formula of Mr. Coulomb

so R = 1/second

so

E = ampere squared

I might add more details. Alan Folmsbee

Using empirically-derived mathematical models based on simplifying assumptions of the underlying physics, to define fundamental units to be used to express quantities of the underlying physics itself, is circular

Ok, so what shape is yellow?

A slightly bent curved fruit with a black stem, highly valued by simian animals and homind species.

My Units applicati You have: ohms You want: Definition: ohm = V/A = 1 kg m^2 / A^2 s^3

ne

Hi bitrex,

The advance is made using The Composite Formula:

mass * capacitance = meter^2 * second^2

That advance is the result of realizing that electron mobility is the same unit of measure as conductance with only a magnitude being different. Like tons and ounces both measuring the same thing. The name "electron mobility" only implies that an electron is involved, but conductance explicitly includes q, the electron charge in its formula. So mu = g for units, because the magnitude does not change the units.

E = ampere squared

has been explained, but it is not accepted by you fine EE folks.

ref.