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According to wikipedia the only SI fundamental unit for Matters Electrickal is the ampere. Don't you at least need the ohm to derive anything? How would you make volts from only amps?

Perhaps I misunderstand the meaning of "fundamental unit".

Joe Stavitsky
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    I can't speak to why other units aren't there, but Amps are defined as "The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per metre of length" of which you only have to know about "newton" and "metre". So no need to have knowledge of Ohms or Voltage for the sake of the definition. – Kellenjb Dec 09 '11 at 16:07
  • right, but then how do we get Volts and Ohms from there? I guess volts are expressed in terms of resistance and resistance is expressed in terms of lost current? – Joe Stavitsky Dec 09 '11 at 16:18
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    I'm no expert here, but for a pretty good discussion of the fundamental units and how other units are derived from them you might want to take a look at [Frink](http://futureboy.us/frinkdocs/) and it's [units file](http://futureboy.us/frinkdata/units.txt). A great tool to have on your PC anyway. For example, volts is defined as \$m^2·kg·s^{-3}·A ^{-1}\$, which is W/A (\$W = m^2·kg·s^{-3}\$), and Ohms as \$m^2·kg·s^{-3}·A^{-2}\$ which is just the last equation divided by Amperes (e.g W/A = V) – Oli Glaser Dec 09 '11 at 16:25
  • Excellent app, but... Watts are... wait for it... not fundamental units! – Joe Stavitsky Dec 09 '11 at 16:27
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    No, but Watts are derived from mass length and time (\$m^2·kg·s^{-3}\$), which are fundamental units. – Oli Glaser Dec 09 '11 at 16:30
  • Ok, now I feel better. – Joe Stavitsky Dec 09 '11 at 16:31
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    @Oli, I think your comment is the answer -- the other units are not fundamental units because they can be expressed in terms of the fundamental units of meters, kilograms, seconds, and amps. – The Photon Dec 09 '11 at 16:55
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    @Oli - I agree with The Photon that your comments are the answer. I noticed you were having trouble with the TeX; the syntax is `x^{-3}` to get negative exponents. The `{}` causes its contents to be treated as one element, like parentheses. I've fixed them, but I can't make them into an answer from you. – Kevin Vermeer Dec 09 '11 at 17:02
  • This place likes TeX? (goes to learn tex) – Joe Stavitsky Dec 09 '11 at 17:51
  • @KevinVermeer - Ahh that's how it's done, thanks for fixing it. I did try the brackets at one point but I think I must have done x{^-3} or something in my hurry to fix it before the edit time ran out :-) Must try and learn Tex properly at some point... – Oli Glaser Dec 09 '11 at 18:04
  • @Joe - Yes, we do! We have MathJax rendering for complicated expressions. Check out our [sandbox](http://meta.electronics.stackexchange.com/questions/434/test-the-new-latex-markdown-in-this-sandbox-question) if you want to try it out. There are links there to get more help in the restricted subset that we use - TeX is huge; there's a whole Stack Exchange site dedicated to it: [tex.se] – Kevin Vermeer Dec 09 '11 at 19:16

4 Answers4

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Volt is defined as Work done for unit charge. Charge can be derived from product of current and time. So volt can be expressed in terms of mass, distance, time and current.

Now for ohms, it can be defined as the ratio of voltage and current. So it can also be expressed in terms of mass, distance, time and current.

So with just a unit for current combined with other fundamental quantities, we can define all the other electrical quantities.

0xakhil
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The correct term is 'base', not 'fundamental', unit. In SI, there are seven base units, including the ampere. The coulomb is a 'derived' unit, defined in terms of the ampere and the second.

The ampere was chosen as a base unit, because it is easily measured, whereas the coulomb is not.

Interestingly, there is a move afoot to redefine the ampere (which will remain a base unit) in terms of the fundamental charge on an electron (not in terms of coulombs). However, the number of decimal places has yet to be set.

A Waygood
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The Ampere is actually not a fundamental unit. It is Coulombs/second, with Coulombs and seconds being the fundamental units. Other common electrical units can be derived from the non-electrical fundamental units and the Coulomb. For example, a Volt is a Joule/Coulomb, or expressed in fundamental units is a Netwon-meter/Coulomb. A Ohm is a Newton-meter-second / Coulomb^2. You can continue on and derive Farads, Henries, etc, similarly.

Added:

I noticed that I used Netwons above, which is also not a fundamental unit. A Newton is a Kg-m/s^2. A Volt expressed in terms of fundamental units (Kilogram, meter, second, and Coulomb) is therefore Kg-meter^2/second^2-Coulomb.

Olin Lathrop
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  • But wikipedia says it is (according to SI anyway). Not saying wiki is always right, just curious. – Joe Stavitsky Dec 09 '11 at 18:29
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    Why did u say ampere is not a fundamental unit? :/ – 0xakhil Dec 09 '11 at 18:54
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    As strange as it seems it is Ampere that is basic unit. The Coulomb is defined as Ampere times second. See:http://physics.nist.gov/cuu/Units/units.html – mazurnification Dec 09 '11 at 19:10
  • @0xakhil looks like a matter of preference/conventions - see the wikipedia article on fundamental units http://en.wikipedia.org/wiki/Fundamental_unit – Chris Stratton Dec 09 '11 at 19:15
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    I guess it's who you ask. After all there is nothing in the physics that makes one quantity more fundamental than others. This is purely how we perceive them. Back when I was taught about this, we considered the Coulomb the fundamental unit. After all, it's just a pile of electrons. To me at least this seems more "fundamental" than how many electrons are passing by in a second. – Olin Lathrop Dec 09 '11 at 19:26
  • Silly rabbit logic is for logicians =P – Joe Stavitsky Dec 09 '11 at 19:47
  • If the Coulomb is defined in terms of amperes and seconds, does that mean that the ratio between the smallest measurable charge (one electron) and a Coulomb of electrons isn't a defined constant, but is subject to change with future measurements? – supercat Dec 09 '11 at 19:48
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    @supercat - I think so, yes. According to the motes at the bottom of the Wiki page, there is talk of redefining Ampere (amongst other things) to reference the fundamental constant of electron charge, which would probably sort things out (well at least for a few years till they get bored and decide to change things around again...) Also see section 7.1 in the [Wiki reference](http://www.bipm.org/utils/en/pdf/CIPM2005-EN.pdf). – Oli Glaser Dec 09 '11 at 20:19
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    OP asked about the "SI fundamental units". If you learned in school that cuolombs are fundamental and amperes are a derived unit, you learned about something other than the SI system, so this answer isn't relevant to the question. – The Photon Jul 11 '13 at 16:24
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Ultimately, all SI units must be traceable to Mass, Length and Time. The current definition of the Ampere is:

The constant current which will produce an attractive force of 2 × 10–7 newtons per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum.

As the Newton is a measure of force, and therefore given by Mass * Acceleration (second order speed, distance / time), the definition ultimately reduces to a form that is derived from only Mass, Length and Time.

All other electrical units may be derived from this, as noted in other answers.

Peter Smith
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  • "Ultimately, all SI units must be traceable to M, L and T." No. This principle is true for the cgs systems (emu, esu, etc.), but not the SI. The fact that the principle seems to hold for this (now old) definition of the ampere is a historical accident: the SI electrical units were made equal to the "practical electrical units", which were defined as certain power-of-ten multiples and submultiples of the emu cgs units, to make sizes more convenient. But even in 2015, the definition of the kelvin was "1/273.16 of the thermodynamic temperature of the triple point of water"—no link to L, M, T. – linguisticturn Jun 20 '23 at 20:28