Why Is Conductivity Important?

Anyone who spends much time around a swimming pool quickly discovers that people are generally very concerned about having electrical devices near the water – all the more so if they happen to be plugged in.

This is true, in fact, of most situations where a sufficient reservoir of water exists anywhere near known flows of electrical current. Thanks to the conductivity of water, the diabolical "toaster in the bathtub" crime is something of a beloved cliche in old-school, murder-mystery stories.

The point here isn't that you can hurt yourself with electricity, though that's always vital to keep in mind; it's that most alert adults, and for that matter middle-school kids, know to steer clear of mixing water with current in any form whether they know physics or not. (In fact, some overly cautious ideas persist, such as the notion you're likely to get a shock if you so much as touch a plastic light switch when your fingers are wet.)

More important for the time being is the question of how electricity "flows" in at least ​some​ liquids when at least ​some​ solids can contain it. Is it just water that interacts with electricity in this way? What about spilled milk or juice? And more generally, what properties of matter contribute to the value of its ​conductivity​?

The phenomenon known as electricity is really no more than the movement of ​electrons​ through some kind of physical medium, or material.

You may not think of air as a material, but in fact, air rich in various molecules you can't see, a lot of which can and do participate in electrical flow. You plainly can't see electrons, so if you believe in electricity, you should believe that astonishingly tiny things play a huge role in the behavior of everyday materials!

Different materials allow for this passage of electrons – and with them, their electrical charges – to different degrees depending on their individual molecular and atomic structures. The fewer the collisions with other tiny objects experienced by zipping electrons, the more easily they're transmitted through the matter in question.

The general equation for current flow is

\(I=\frac{V}{R}\)

where ​I​ is current flow in amperes, ​V​ is electrical potential difference in volts ("voltage") and ​R​ is the resistance in ohms. Resistance is related to conductivity, as you'll soon learn.

Conductivity, or more formally ​electrical conductance​, is a mathematical measure of a material's ability to conduct electricity. It is represented by the Greek letter sigma ​(σ)​ and its SI (metric system) unit is the ​siemens per meter (S/m)​.

•The siemens is also called a ​mho​, which is "ohm" spelled backward. This term had fallen out of common use by the end of the 20th century, however.

Conductivity is just the mathematical reciprocal of ​resistivity.​ Resistivity is represented by the small Greek letter rho (ρ) and is measured in ohm-meters (Ωm), which means that the S/m can also be described as a reciprocal ohm-meter (1/Ωm or Ωm^-1). By extension, you can see that a siemen is the reciprocal of an ohm. Since ​conducting​ something along in the real world is the opposite of ​resisting​ its passage, this makes physical sense.

The conductivity of a material is an intrinsic property of that material and unrelated to how a circuit or other system is assembled, which is accounted for by the "per meter" in the siemens unit. It is related to the resistance of a material, often a wire in physics problems involving these situations, by the expression

\(R=\frac{\rho L}{A}\)

where ​L​ is the length if the wire in m and ​A​ its cross-sectional area in m².

As noted, conductivity doesn't depend on experimental set-up and is just a reflection of how a given material (solid, liquid or gaseous) "is." Some materials naturally make strong conductors (and thus poor resistors) while others can conduct electricity weakly or not at all and make good resistors (or electrical insulators).

With an electrical circuit, you can manipulate the set-up so that you can get whatever level of current you like given whatever combination of resistance elements you include. This is why resistance is designated ​R​ and has no length in its units; it's a measure of a system's properties, not that of a material. Accordingly, ​conductance​ (symbolized by the letter ​G​ and measured in siemens) works the same way. But it's normally more convenient to use ​R​ or ​ρ​ than it is to go with ​G​ or ​σ​.

As an analogy, consider that the coach of a football team can change the strength and speed of its individual players, but in the end, every football team in existence has the same essential constraints: 11 human players to a side, varying in their physical capabilities but having the same basic properties.

The most shocking thing you'll learn in this article (and that's not just a pun, honest!) is that water, strictly speaking, is a terrible conductor of electricity. That is to say, pure H₂O (hydrogen and oxygen in a 2:1 ratio) doesn't conduct electricity.

As you have no doubt already concluded, this means that the encountering truly pure water is something that essentially never happens. Even in a lab setting, it's easy for ions (charged particles) to "sneak" into water that's been condensed from pure steam, i.e., distilled.

Water from pipes and directly from natural sources is invariably rich in impurities such as minerals, chemicals and assorted dissolved substances. This isn't necessarily a bad thing, of course; all of that salt in ocean water, for example, makes it slightly easier to float in the sea if that's your game.

As it happens, table salt (sodium chloride, or NaCl) is one of the better-known substances that can rob water of its insulating properties when dissolved in H₂O.

The conductivity of water in U.S. rivers ranges widely, from about 50 to 1,500 µS/cm. Inland freshwater streams that allow fish to thrive tend to have between 150 and 500 µS/cm. Higher or lower conductivity may indicate that the water is not suitable for certain species of fish or macroinvertebrates. Industrial waters can range as high as 10,000 µS/cm.

Conductivity is an indirect measure of, for example, stream water quality. Each waterway boasts a relatively constant range that can be used as a baseline conductivity of drinking water standard. Regular conductivity assessments done using a ​water conductivity meter​. Major changes in conductivity could signal the need for a clean-up effort.

This article is clearly about electrical conductivity. In physics, though, you're likely to hear about the conduction of heat, which is a little different because heat is measured in energy whereas electricity, which can provide energy, is not.

Changes in a material's thermal conductivity do tend to parallel changes to its electrical conductivity, though not usually on the same scale. One interesting property of materials is that while most of them become poorer conductors as they are heated (as particles whizz around faster and faster as temperature climbs, they are more likely to "interfere" with electrons), this is not true of a class of materials called semiconductors.