# Why is the Ampere the only SI fundamental unit for electricity?

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".

• 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 9 '11 at 16:07
• 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 and it's units file. 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 9 '11 at 16:25
• No, but Watts are derived from mass length and time ($m^2·kg·s^{-3}$), which are fundamental units. – Oli Glaser Dec 9 '11 at 16:30
• @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 9 '11 at 16:55
• @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 9 '11 at 17:02

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.

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.

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.

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.

• But wikipedia says it is (according to SI anyway). Not saying wiki is always right, just curious. – Joe Stavitsky Dec 9 '11 at 18:29
• Why did u say ampere is not a fundamental unit? :/ – 0xakhil Dec 9 '11 at 18:54
• As strange as it seems it is Ampere that is basic unit. The Coulomb is defined as Ampere times second. See:physics.nist.gov/cuu/Units/units.html – mazurnification Dec 9 '11 at 19:10
• 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 9 '11 at 19:26
• @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. – Oli Glaser Dec 9 '11 at 20:19

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.

## protected by Dave Tweed♦Jul 17 '15 at 10:59

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