## ©2019 L A Waygood

## 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 Δ*ν*_{Cs}.

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:

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 **85×10 ^{27}** and, for aluminium,

**76.2×10**. And the amount of charge on a single electron

^{27}*(e)*is generally taken as

**16×10**(coulombs).

^{-18}CSo, the drift velocity for a 2.5-mm^{2} 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.

You make clearer points than the usual…

Can I ask you to clear up some misconceptions? Maybe give any further example? many thanks 🙂

Hi, Thanks for your comment. Please visit the site regularly, as I will be regularly updating the site with more ‘misconceptions’. I will shortly be publishing a post on misconceptions students have about how energy is delivered.

Much respect for covering this subject. Do you intend to write more?

Hi there would you mind sharing which blog platform you’re using?

I’m planning to start my own blog soon but I’m having

a tough time making a decision between BlogEngine/Wordpress/B2evolution and Drupal.

The reason I ask is because your design seems different then most blogs and I’m looking for something completely unique.

P.S My apologies for being off-topic but I had to ask!

Hi, Catherine:

Thank you for your comment. The platform I am using is WordPress. I haven’t tried any of the other platforms, so I cannot really compare WordPress with any other. All I can say is that I have never created a website before this one, and I was new to WordPress when I began using it, and I have found it very user-friendly. It also has many ‘plug-ins’ which extend its features and which have proved to be useful to me. These include ‘symbols’ (e.g. Greek alphabet and maths symbols) and ‘equation editors’. These particular plugins are essential to any ‘technical’ blog, but there are hundreds more which might be more relevant to your’s. I found Dr Andy Williams’s Amazon-published book on using WordPress to have been extremely helpful (it would have been much harder to set up WordPress without the help of that particular book) and I would highly-recommend it to anyone who wants to set up a website or a blog in WordPress. Dr Williams also has a video course on using WordPress which I found useful. I hope my comments may be of some help with your decision regarding which platform to use, and good luck with your blog. Sincerely, Adrian Waygood

Apologies for spelling ‘Katherine’ as ‘Catherine’!! AW