# (E1)  The Electric Fluid

Without electricity, our houses would be dark at night, most of our transportation at standstill and our computers non-existent. Yet--what is electricity?

Not an easy question, and no simple answer. The best way to start is to go back two centuries--before radio, before the link between electricity and magnetism was appreciated. People of those days believed electricity was a fluid, flowing through metal wires the way water flows through pipes.

It is an incomplete analogy. It misses not only the many applications of magnetism due to electric currents, but also radio waves, chemical processes and electronics. Still it's a useful way of visualizing the simplest everyday uses of electricity, and it will be followed below as far as possible. Even if you are completely unfamiliar with electricity, it will give you at least a working understanding. All you need is a reading ability and a modest amount of patience.

### Water through Pipes

A most familiar fluid is water. Water is carried into our homes by pipes, and its flow can be controlled by opening and closing faucets. When a faucet (or "tap") is opened, the rate F at which water flows from it--the number of liters per second, or gallons per second--depends on the pressure P which drives the flow.

Usually the water comes from a reservoir in some higher place--a lake behind a dam in the high country, or a tank on top of a high water tower, or one on top of a hill. The pressure is then (ideally) proportional to the difference in height between the reservoir where the water originates and the faucet where it comes out. (We write "ideally" because once the water starts flowing, there also exists a pressure drop along the pipe, due to the flow). We can therefore measure pressure by the height difference ("pressure head") between the two locations, given in meters of in feet.

Pressure of water (or of any ordinary fluid) can also be measured in "atmospheres" where one atmosphere (approximately equal to a pressure head of 10 meters) is the pressure felt on the ground (at sea level) due to the weight of the layer of air ("the atmosphere") piled on top of it. We do not feel that pressure, since it is matched by the pressure of air and blood in our tissues: but if you pump the air out of a thin closed metal can, that pressure is sure to crush it! One can also use pounds per square inch (PSI), and 1 atmos. = 15.5 PSI, approximately (air pressure in car tires is measured in PSI in excess of the pressure of the surrounding atmosphere). Here we will stick to pressure heads measured in meters.

How large is the water flow F from a pipe of water? We might guess it is proportional to the pressure P (more accurately, the pressure difference P between its ends), and it also depends on the diameter and length of the pipe, etc. At least, that will be our analogy: actual water flows in pipes may behave differently. "Proportional" means that a relation exists

F  =  P  S

where S is a number depending on the length of the pipe, its cross-section area and the smoothness of its walls. We will call S the conductance of the pipe:

Flow Rate  =  Pressure  ×   Conductance

We expect the conductance of a fat pipe to be larger than that of a narrow one, and of a short pipe be larger than a long one. To pursue the analogy with electricity, we also give the name resistance of the pipe to the inverse of conductance

R = 1/S         Resistance = 1 / Conductance

The smaller the conductance, the greater the resistance, and the flow F will obey

F = P/R         Flow Rate= Pressure / Resistance

Let the unit of pipe resistance (in the above formula) be called here "ohm" (for reasons given later): if P is measured in meters of pressure head, and R is in ohms, then F is in liters per second. (If other units are used--say, gallons per second and PSI--then either different units of R are used, or else the equation needs to be always multiplied by a constant conversion factor.)

Once again: the above formulas were only developed only as an analogy to the flow of electricity. Actual water flow may not obey strict proportionality. By the way, one can also argue that for every liter of water that enters the house, about one liter must also leave it via the sewer pipes, so in a way, a closed circuit exists, as in the flow of cooling water in a car.

To remember:

 Electricity flows through wires, in a way similar to water flow through pipes. With water (at least in this analogy) the amount F of water delivered each second may be viewed as proportional to the pressure P driving it, and to the ability of the pipe to carry it. (More accurately--P is the difference in pressure between the entrance of the water and its exit.) We express this ability by the "conductance" C of the pipe, and write F = P C            or else             F = P / R Where R = 1/C is the "resistance" of the pipe

### Electric Charge--Coulombs and Amperes

All those features (and more) are mirrored in the wiring along which electric current flows. The fluid which flows along them is not water but electric charge--the stuff which on a dry day makes synthetic fabric cling, which makes xerox copiers work (laser printers, too), and which attracts bits of paper to a plastic comb, after it is rubbed against dry cloth or fur.

Static electricity can be measured, and just for completeness let it be stated that its unit is called the coulomb, after Charles Augustine Coulomb, a French military engineer in the later 1700s who invented neat ways of measuring electric charge. Its counterpart in water flow would be the liter. Just as water can be stored in jars and barrels, electric charge can be stored in devices called capacitors. Water however is much easier to store: capacitors used in electric devices will only hold a tiny part of one coulomb.

[Actually, electric charge comes in two kinds, positive (+) and negative (–), attracting each other and repelling charges of the same kind (like north and south magnetic poles!). Ordinary matter contains both in equal amounts, and as a result they cancel each other's attraction. When you rub a dry object with a cloth and make it (say) positively charged, you are removing from it some negative particles and leaving it with extra positive charge. The cloth you are rubbing with gets an equal negative charge.
In principle the same effect would be seen if instead of negative charges being removed, positive ones are deposited. Early researchers could never tell which was happening, but we now know that negative electrons are more easily removed--except in the chemistry of solutions in water, discussed later.]

In our homes, though, electricity usually comes in the form of a continuously flowing fluid, and the charge flowing in equals the charge flowing out again.

That is why circuits always use two wires--one carries the current into the home, the other carries it back. The unit of current is called the Ampére, after another French scientist (he too enters the story later). A current of one ampére carries one coulomb each second past any point in the circuit. It is thus like the flow volume F in liters/sec, except that it is customarily denoted by the letter I (or sometimes by lower case i).

### Conductors and Insulators

Not all substances can carry an electric current. Copper wire does so very well, silver even better, and most metals are not far behind. Water is also an "electric conductor," especially when substances such as salt are dissolved in it, and so is a very hot gas ("plasma") like the one inside a fluorescent light tube (where that gas is rarefied and therefore does not heat the glass). Substances soaked in water can also carry electricity, e.g. the human body, soaked in salty watery solutions such as blood. That is what makes electric shocks possible.

Most other materials are "insulators" and do not allow electric currents to flow. Ceramics, glass, rubber and most plastics, dry wood, dry paper and ordinary air are all insulators. Electric currents in the house are carried by copper wires encased in plastic insulation, while electric power lines outdoors are strung in the air between insulators made of plastic or glass. Since air is an insulator, power companies do not worry about leakage from such lines.

To remember:

 While pipes can carry water, metal wires can carry electric charge, measured in "coulombs." Charge exists in two varieties, positive and negative, attracted to each other. Not all substances can carry electricity--only electrical conductors, like metals, water with dissolved material like salt (even a small amount will do) and very hot gases ("plasmas"). Most other materials--rubber, plastic, dry wood and ordinary air--are "insulators." The analogy to water flow F (so many liters per second) is electric current intensity I, measured in amperes, with 1 ampere = 1 coulomb each second.

Next Stop: E2.   Voltage and Ohm's Law