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One way Wikipedia defines Ohm is (this is also teached in school): $$1\Omega =1{\dfrac {{\mbox{V}}}{{\mbox{A}}}}$$ They describe this definition in words, too:

The ohm is defined as a resistance between two points of a conductor when a constant potential difference of 1.0 volt, applied to these points, produces in the conductor a current of 1.0 ampere, the conductor not being the seat of any electromotive force.

The definition of Ohm in SI basic units is: $$1\Omega = 1{\dfrac {{\mbox{kg}}\cdot {\mbox{m}}^{2}}{{\mbox{s}}^{3}\cdot {\mbox{A}}^{2}}}$$ It's really hard for me to get that this definition is correct. It's clear that mathematical calculations confirm this definition. But how do you describe the definition of the SI in words like that paragraph on wikipedia?

Edit: How would you describe it? Although it is not common to do it that way, I think describing it that way, could be very interesting.

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4 Answers 4

up vote 5 down vote accepted

I think the short answer is, you don't. The reason we call the unit of force a Newton and not a kg m/s$^2$ is because it is convenient and it expresses the relation you want to convey when used elsewhere (e.g., $F=-kx$ for a spring).

Similarly, it is convenient to "hide" the MKS base units into a single term, the potential $V$ in this case, so that the formula is easier to remember and that the relation is conveyed, in this case the relation between potential difference, current, and resistance.

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You are totally right. This is the common way to refer to other formulars by using their symbol. But assuming you want to descibe it anyway. So I correct my question to: How would you describe it? I think describe it that way, could be very interesting. –  andrew Feb 15 '14 at 19:00
@andrew: How would I describe an ohm? It's the unit that describes how much the flow of charge is hindered by the material. –  Kyle Kanos Feb 15 '14 at 19:08
Yeah. This is an good answere. But what do you mean with "flow of charge"? Do you mean the Amperage $I$ ? –  andrew Feb 15 '14 at 19:19
@andrew: If you feel more comfortable with it, you could replace "flow of charge" with "bulk motion of electrons," as it is the electrons that are moving in an electric circuit. –  Kyle Kanos Feb 15 '14 at 19:23
So physically the motion of electrons you mean is $I=\frac{Q}{t}$, isn't it? –  andrew Feb 15 '14 at 19:26

I'm not sure there's much of a point to what you're asking. The intuitive way to understand an Ohm is to use $\Omega = V/A$. If you want to use SI units, you can, and the math indeed tells you that your other definition is correct, but you're not gonna get much out of it. Indeed, the most you could do is to separate it like this:

$$\begin{align}\Omega &= \frac{\text{kg} \cdot \text{m}^2 }{ \text{s}^3 \cdot \text{A}^2 }\\ &= \frac{ \text{kg}\cdot\text{m}^2}{\text{s}^2}\cdot \frac1{\text{A}\cdot\text{s}}\cdot \frac1{\text{A}} \\ &= \frac{\text{J}/\text{C}}{\text{A}}\\ &= \frac{\text{V}}{\text{A}} \end{align} $$

This is just a proof of the equivalence between the two definitions, but don't expect to get any nice word description of the SI definition.

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Not sure whether this is correct, but if you have to do it, I think you can say that it is:

the work done by the conductor per unit charge per unit current through the conductor, or in terms of SI units, $\mathrm{\frac JC\cdot \frac1A}$

which is the same as:

the work done by the conductor per unit current per unit time per unit current, $\mathrm{\frac J{A\cdot s\cdot A}}$

We know that the work done is equal to the dot product of the force and the displacement, so it is:

the electric force multiplied by the displacement of the charge carrier per unit time per unit charge squared, $\mathrm{\frac{N\cdot m}{s\cdot A^2}}$

and we know force has SI units $\mathrm{kg\;m\;s^{-2}}$

So I guess you can say that the ohm is the resistance when one newton of electric force causes a charge carrier to displace one meter in one second with a current of one ampere.

I would go on and say that it is the resistance when a charge carrier of one kilogram accelerates at one meter per second squared, and this acceleration causes the charge carrier to displace one meter in one second, producing a current of one ampere. But I'm not very certain about the "charge carrier of one kilogram" part.

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+1 These are also very interesting definitons. –  andrew Feb 16 '14 at 10:44
@andrew actually this is just an attempt to expand the definitions until they fit the SI base units. Be aware that these definitions are all equivalent. –  ace Feb 16 '14 at 12:41
Yeah. But they are kind of different because their context is different.. Anyway, I am with you. –  andrew Feb 16 '14 at 13:53

I would describe it as (example) 120 joules per coulomb (120 volts) divided by 60 coulombs per second (60 amps) equals 2 (ohms) of resistance "which means you have 1/2 or 2 times less the amperes then voltage". so maybe an ohm can be n of VpA (# of volts[SI] per amp[SI] or in this case, # of N Kg per charge for every charge per second). But that's still essentially giving the formulae.

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