## Which is more ‘fundamental’, the ampere or the coulomb?

©2019 L A Waygood

An American electrical engineer, William J Beaty, who runs the excellent website (challenging the way in which electrical science is taught), entitled ‘K-6 Misconceptions, which I highly recommend, poses the interesting question: ‘Which is the more fundamental: the ampere or the coulomb?’

In his article he argues that, because charge is more fundamental than current, therefore, by extension, the coulomb must be more ‘fundamental’ than the ampere.

As much as admire and agree with most of Mr Beaty’s articles, I feel that in this particular case, he is wrong. I believe that he has made the fundamental mistake of confusing quantities (i.e. ‘current’ and ‘charge’) with their corresponding units of measurement (i.e. ‘ampere’ and ‘coulomb’).

His argument is, essentially, that because electric current is defined in terms of the quantity of charge transferred per unit time, then it follows that the coulomb must, therefore, be more ‘fundamental’ than the ampere.

But SI doesn’t use the term, ‘fundamental’; rather, it uses the term ‘base’. And it considers the ampere to be a ‘base unit‘ while the coulomb is considered to be a ‘derived unit‘. By definition, all ‘derived units’ are defined in terms of ‘base units’.

Where Mr Beaty’s argument falls flat is that he bases most his argument on his belief that the ‘definition’ of the ampere is a ‘coulomb per second’. If this were true, then it would be difficult to disagree with his argument.

But, in fact, the ampere is NOT defined in terms of the coulomb and the second… and it never has been! So, the ampere is not reliant on, and thus ‘less fundamental’ than, the coulomb.

So, if the ampere isn’t defined as a ‘coulomb per second’ (and a lot of North American textbooksm, in particular, mistakenly claim this!), then how is it defined? Well, there are three ‘effects’ of an electric current: the heating effect, the chemical effect, and the magnetic effect. Theoretically, any one of these effects could be used to define its unit of measurement: the ampere. For example, prior to 1948, the ampere was defined in terms of the  chemical effect of an electric current:

The ‘international ampere‘, as it was then called, was an early attempt at defining the ampere, as ‘that current that would deposit 0.001 118 g of silver per second from a silver nitrate solution’

Later, more-accurate measurements revealed that this current was actually 0.999 85 A, and not 1 A as thought! So, in 1948, it was decided to redefine the ampere in terms of the magnetic effect of an electric current! So, since 1948, the ampere has been defined as follows:

The ampere is ‘that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in a vacuum, would produce between these conductors a force equal to 2×10−7 newtons per metre of length’.

So, you see, the ampere is not, and never has been, defined as a ‘coulomb per second’! For most of its life, it’s been defined in terms of the force between parallel, current-carrying, conductors.

But, after 70+ years, this definition has now changed! Because, from mid-2019, the ampere is now defined in terms of the rate of flow of elementary charges —i.e. the carried by individual electrons, and NOT by a ‘coulomb’s-worth of electrons’.

This new definition of the ampere us now ‘the current in the direction of flow of a particular number (see elsewhere in this blog for the actual number) of elementary charges per second’.

And, as a ‘derived unit’, SI will continue to define the coulomb in terms of the ampere and the second:

The coulomb is defined as ‘the quantity of charge transferred, in one second, by a steady current of one ampere’.

So, while it is perfectly true that electric charge is ‘more fundamental’ than electric current, the same cannot be said about their corresponding units!

So, to summarise. Mr Beaty is quite correct in arguing that charge is more fundamental than current because current is defined in terms of the quantity of charge transported per unit time.

However, the same argument cannot be extended to the SI unit of current, the ampere, because (contrary to Mr Beaty’s belief) it is an SI base unit, and has never, ever, been defined in terms of the coulomb (a derived unit) but, from 1947, in terms of the force between energised conductors and, since 2019, now in terms of the flow of individual elementary particles. ## Current ‘flows’

We often say that ‘an electric current flows through a conductor’. Although widely-used, strictly speaking, this is actually incorrect. If we think in terms an analogy of the ‘current’ in a stream or river, what it describes is a flow of water. It’s actually the water that’s flowing, not the current.

In exactly the same way, an electric ‘current’ describes a flow of charge carriers. It’s the charge carriers that are flowing, not the electric current.

Although describing an electric current as ‘flowing’ is, strictly, a misconception, it is rather pedantic (‘nit-picking’) to insist on not describing current as ‘flowing’ around a circuit —particularly when it’s necessary to describe the direction of charge flow around a circuit. Providing we are aware of the distinction between ‘current’ and ‘charge flow’, it is perfectly acceptable to say that ‘current “flows” clockwise (or counter-clockwise) around…’ a particular circuit.

## Current is a flow of ‘free electrons’

In metal conductors, current is, indeed, a flow of free electrons. But to think that a current is always a flow of free electrons is a misconception.

This is because an electric current can also occur in non-metallic conductors, such as within electrolytes (conducting liquids) and gasses. In electrolytes, for example, the charge carriers are not electrons, but ions. Ions are simply charged atoms, i.e. atoms which either have more electrons than protons (‘negative ions’), or those which have less electrons than protons (‘positive’ ions).

It is, therefore, much more accurate to describe an electric current as being a flow of electric charge carriers, than of free electrons. This definition covers current in both metal as well as other conductors.

But even this definition needs further clarity. This is because ‘flow’ suggests   a significant movement of individual charge carriers in a particular direction. But, as we shall learn, later, for direct current (d.c.) this ‘flow’ is very slow (far less than metres per hour, in some cases!). For alternating current (a.c.), the charge carriers simply vibrate in opposite directions, and don’t ‘flow’ at all!

## Current is  the ‘rate of flow’ of  charge carriers

Not really.

We sometimes hear an electric current being defined as being ‘the rate of flow of electric charges’.

The term, ‘rate of flow’, suggests that we are describing the velocity at which charge carriers are moving through a material. This is a misconception, because what we should be describing is the quantity of charge carriers, not their velocity.

So, if we want to further refine our definition of an electric current, we can say that it is ‘the quantity of charge carriers, moving past a given point in a material, per unit time’.

An electric current is ‘the quantity of charge carriers, moving past a given point in a material, per unit time’.

## The ampere is defined as a ‘coulomb per second’

No it’s not. It never has been!

We have already defined electric current as ‘the quantity of charge carriers, moving past a given point in a material, per unit time’.

Since charge is measured in coulombs (symbol: C) and time is measured in seconds (symbol: s), many students believe that an ampere is defined as a ‘coulomb per second’; indeed, many textbooks (particularly US textbooks) reinforce this misconception! However, the ampere has never been defined in this way!

The ampere is one of seven SI Base Units, from which all other SI units are derived. The coulomb is one of those Derived Units. As SI Base Units cannot be defined in terms of Defined Units, we cannot define an ampere in terms of a coulomb.

Since 1948, the ampere has been defined in terms of its magnetic effect, specifically the resulting force between two, parallel, current-carrying conductors, due to the attraction or repulsion of their magnetic fields, as follows:

The ampere (symbol: A) is defined as ‘the constant current that, if maintained in two straight parallel conductors of infinite length and negligible cross-sectional area and placed one metre apart in a vacuum, would produce between them a force equal to 2 × 10-7 newtons per unit length’.

[Although the newton is derived unit, it is simply the name we give to a ‘kilogram metre per second squared’ —all Base Units.]

Prior to the 1948 definition, the ampere was defined in terms of the mass of silver deposited on an electrode over a specified period of time by electrolysis. So current has NEVER been defined as ‘a coulomb per second’!

However, with effect from 20 May 2019, the definition of the ampere will change to:

The ampere, symbol A,  is defined by taking the fixed numerical value of the elementary charge, e,  to be 1.602176634×10−19 when expressed in the unit coulomb (C), which is equal to the ampere second (A⋅s), where the second is defined in terms of ΔνCs.

Please refer to the ‘News about the ampere‘ page of this blog for an explanation of this new definition.

## Current ‘flows’ close to the speed of light

This is a widely-held misconception!

We have already learnt that it’s not the current that’s flowing, but electric charges. And, most students are surprised to learn, that the velocity of these charges is very, v-e-r-y, low —often as low as millimetres per hour!

It’s been said that an individual electron is unlikely to complete its journey through the filament of a torch (flashlight) within the lifetime of the torch battery!

We call the velocity of electric charges, their ‘drift velocity(v) which, for any conductor, is expressed by the following equation:

$v = \frac{I}{n A e}$

where  v = drift velocity, I = current, n = number of electrons per cubic metre, A = cross-sectional area, and e = charge on one charge carrier.

The number (n) of electrons per cubic metre of conductor depends, of course, on the type of material and its purity. For copper, for example, this figure is generally taken as 85×1027 and, for aluminium, 76.2×1027. And the amount of charge on a single electron (e) is generally taken as 16×10-18 C (coulombs).

So, the drift velocity for a 2.5-mm2 conductor (used for ring-mains in British residences), carrying a direct current of, say, 10 A, would work out to be an incredibly-low 2.9 micrometres per second! Which means that it will take 344 828 seconds, or nearly 96 hours, to travel a distance of just one metre!

While the drift velocity is v-e-r-y slow, the effect of the current is immediate because, of course. all the electrons throughout the conductor start to move at the same time.

Students often ask, ‘If free elections move so slowly, why is there not a delay between operating a light switch, and the lamp coming on?’ Well, of course, the conductor connecting the switch and  lamp is full of free electrons and, when the switch is closed, they ALL start to move at the same time.

## Current direction

The great American physicist and statesman, Benjamin Franklin (1706–1790), believed that an electric current was some sort of mysterious ‘fluid’ which flowed from a higher (positive) pressure to a lower (negative) pressure. From this, it was generally assumed that an electric current flowed (through an external circuit) from positive to negative. After the much-later discovery of sub-atomic particles led to the ‘electron theory‘ of electricity, it was realised that (in metal conductors) electrons actually moved through an external circuit from negative to positive.

When we talk about ‘current direction‘, we are always describing its direction through the external circuit, and never within the source of potential difference (battery, generator, etc.)

To distinguish between the original theory regarding current direction, and the modern theory, we use the terms ‘conventional flow‘ (positive to negative) and ‘electron flow‘ (negative to positive).

Unfortunately, as many of the laws relating to magnetism depend upon a knowledge of current direction, and were based on ‘conventional flow’, this is still widely-used today and is the case with most modern textbooks.

Students have the misconception that ‘conventional flow’ describes a flow of ‘positive charges’ moving from positive to negative. However, this is not really the case. Conventional flow is simply an assumed direction of current and makes no assumptions whatsoever about what constitutes that current. ‘Electron flow’, on the other hand, not only describes direction but also the nature of what constitutes that current. 