Letters of a Radio-Engineer to His Son Part 4

In most of the electrical circuits with which you will deal you will find that electrons must be pa.s.sing along in the circuit at a most amazing rate if there is to be any appreciable effect. When you turn on the 40-watt light at your desk you start them going through the filament of the lamp at the rate of about two and a half billion billion each second. You have stood on the sidewalk in the city and watched the people stream past you. Just suppose you could stand beside that narrow little sidewalk which the filament offers to the electrons and count them as they go by. We don't try to count them although we do to-day know about how many go by in a second if the current is steady.

If some one asks you how old you are you don't say "About five hundred million seconds"; you tell him in years. When some one asks how large a current is flowing in a wire we don't tell him six billion billion electrons each second; we tell him "one ampere." Just as we use years as the units in which to count up time so we use amperes as the units in which to count up streams of electrons. When a wire is carrying a current of one ampere the electrons are streaming through it at the rate of about 6,000,000,000,000,000,000 a second.

Don't try to remember this number but do remember that an ampere is a unit in which we measure currents just as a year is a unit in which we measure time. An ampere is a unit in which we measure streams of electrons just as "miles per hour" is a unit in which we measure the speed of trains or automobiles.

If you wanted to find the weight of something you would take a scale and weigh it, wouldn't you? You might take that spring balance which hangs out in the kitchen. But if the spring balance said the thing weighed five pounds how would you know if it was right? Of course you might take what ever it was down town and weigh it on some other scales but how would you know those scales gave correct weight?

The only way to find out would be to try the scales with weights which you were sure were right and see if the readings on the scale correspond to the known weights. Then you could trust it to tell you the weight of something else. That's the way scales are tested. In fact that's the way that the makers know how to mark them in the first place. They put on known weights and marked the lines and figures which you see. What they did was called "calibrating" the scale. You could make a scale for yourself if you wished, but if it was to be reliable you would have to find the places for the markings by applying known weights, that is, by calibration.

How would you know that the weights you used to calibrate your scale were really what you thought them to be? You would have to find some place where they had a weight that everybody would agree was correct and then compare your weight with that. You might, for example, send your pound weight to the Bureau of Standards in Was.h.i.+ngton and for a small payment have the Bureau compare it with the pound which it keeps as a standard.

That is easy where one is interested in a pound. But it is a little different when one is interested in an ampere. You can't make an ampere out of a piece of platinum as you can a standard pound weight. An ampere is a stream of electrons at about the rate of six billion billion a second. No one could ever count anywhere near that many, and yet everybody who is concerned with electricity wants to be able to measure currents in amperes. How is it done?

First there is made an instrument which will have something in it to move when electrons are flowing through the instrument. We want a meter for the flow of electrons. In the bas.e.m.e.nt we have a meter for the flow of gas and another for the flow of water. Each of these has some part which will move when the water or the gas pa.s.ses through. But they are both arranged with little gear wheels so as to keep track of all the water or gas which has flowed through; they won't tell the rate at which the gas or water is flowing. They are like the odometer on the car which gives the "trip mileage" or the "total mileage." We want a meter like the speedometer which will indicate at each instant just how fast the electrons are streaming through it.

There are several kinds of meters but I shall not try to tell you now of more than one. The simplest to understand is called a "hot-wire meter."

You already know that an electron stream heats a wire. Suppose a piece of fine wire is fastened at the two ends and that there are binding posts also fastened to these ends of the wire so that the wire may be made part of the circuit where we want to know the electron stream. Then the same stream of electrons will flow through the fine wire as through the other parts of the circuit. Because the wire is fine it acts like a very narrow sidewalk for the stream of electrons and they have to b.u.mp and jostle pretty hard to get through. That's why the wire gets heated.

You know that a heated wire expands. This wire expands. It grows longer and because it is held firmly at the ends it must bow out at the center.

The bigger the rate of flow of electrons the hotter it gets; and the hotter it gets the more it bows out. At the center we might fasten one end--the short end--of a little lever. A small motion of this short end of the lever will mean a large motion of the other end, just like a "teeter board" when one end is longer than the other; the child on the long end travels further than the child on the short end. The lever magnifies the motion of the center of the hot wire part of our meter so that we can see it easier.

[Ill.u.s.tration: Fig 10]

There are several ways to make such a meter. The one shown in Fig. 10 is as easy to understand as any. We shape the long end of the lever like a pointer. Then the hotter the wire the farther the pointer moves.

If we could put this meter in an electric circuit where we knew one ampere was flowing we could put a numeral "1" opposite where the pointer stood. Then if we could increase the current until there were two amperes flowing through the meter we could mark that position of the pointer "2" and so on. That's the way we would calibrate the meter.

After we had done so we would call it an "ammeter" because it measures amperes. Years ago people would have called it an "amperemeter" but no one who is up-to-date would call it so to-day.

[Ill.u.s.tration: Fig 11]

If we had a very carefully made ammeter we would send it to the Bureau of Standards to be calibrated. At the Bureau they have a number of meters which they know are correct in their readings. They would put one of their meters and ours into the same circuit so that both carry the same stream of electrons as in Fig. 11. Then whatever the reading was on their meter could be marked opposite the pointer on ours.

Now I want to tell you how the physicists at the Bureau know what is an ampere. Several years ago there was a meeting or congress of physicists and electrical engineers from all over the world who discussed what they thought should be the unit in which to measure current. They decided just what they would call an ampere and then all the countries from which they came pa.s.sed laws saying that an ampere should be what these scientists had recommended. To-day, therefore, an ampere is defined by law.

To tell when an ampere of current is flowing requires the use of two silver plates and a solution of silver nitrate. Silver nitrate has molecules made up of one atom of silver combined with a group of atoms called "nitrate." You remember that the molecule of copper sulphate, discussed in our third letter, was formed by a copper atom and a group called sulphate. Nitrate is another group something like sulphate for it has oxygen atoms in it, but it has three instead of four, and instead of a sulphur atom there is an atom of nitrogen.

When silver nitrate molecules go into solution they break up into ions just as copper sulphate does. One ion is a silver atom which has lost one electron. This electron was stolen from it by the nitrate part of the molecule when they dissociated. The nitrate ion, therefore, is formed by a nitrogen atom, three oxygen atoms, and one extra electron.

If we put two plates of silver into such a solution nothing will happen until we connect a battery to the plates. Then the battery takes electrons away from one plate and gives electrons to the other. Some of the atoms in the plate which the battery is robbing of electrons are just like the silver ions which are moving around in the solution.

That's why they can go out into the solution and play with the nitrate ions each of which has an extra electron which it stole from some silver atom. But the moment silver ions leave their plate we have more silver ions in the solution than we do sulphate ions.

The only thing that can happen is for some of the silver ions to get out of the solution. They aren't going back to the positive silver plate from which they just came. They go on toward the negative plate where the battery is sending an electron for every one which it takes away from the positive plate. There start off towards the negative plate, not only the ions which just came from the positive plate, but all the ions that are in the solution. The first one to arrive gets an electron but it can't take it away from the silver plate. And why should it? As soon as it has got this electron it is again a normal silver atom. So it stays with the other atoms in the silver plate. That's what happens right along. For every atom which is lost from the positive plate there is one added to the negative plate. The silver of the positive plate gradually wastes away and the negative plate gradually gets an extra coating of silver.

Every time the battery takes an electron away from the positive plate and gives it to the negative plate there is added to the negative plate an atom of silver. If the negative plate is weighed before the battery is connected and again after the battery is disconnected we can tell how much silver has been added to it. Suppose the current has been perfectly steady, that is, the same number of electrons streaming through the circuit each second. Then if we know how long the current has been running we can tell how much silver has been deposited each second.

The law says that if silver is being deposited at the rate of 0.001118 gram each second then the current is one ampere. That's a small amount of silver, only about a thousandth part of a gram, and you know that it takes 28.35 grams to make an ounce. It's a very small amount of silver but it's an enormous number of atoms. How many? Six billion billion, of course, for there is deposited one atom for each electron in the stream.

In my next letter I'll tell you how we measure the pull which batteries can give to electrons, and then we shall be ready to go on with more about the audion.

LETTER 8

ELECTRON-MOVING-FORCES

(This letter may be omitted on the first reading.)

DEAR YOUNG MAN:

I trust you have a fairly good idea that an ampere means a stream of electrons at a certain definite rate and hence that a current of say 3 amperes means a stream with three times as many electrons pa.s.sing along each second.

In the third and fourth letters you found out why a battery drives electrons around a conducting circuit. You also found that there are several different kinds of batteries. Batteries differ in their abilities to drive electrons and it is therefore convenient to have some way of comparing them. We do this by measuring the electron-moving-force or "electromotive force" which each battery can exert. To express electromotive force and give the results of our measurements we must have some unit. The unit we use is called the "volt."

The volt is defined by law and is based on the suggestions of the same body of scientists who recommended the ampere of our last letter. They defined it by telling how to make a particular kind of battery and then saying that this battery had an electromotive force of a certain number of volts. One can buy such standard batteries, or standard cells as they are called, or he can make them for himself. To be sure that they are just right he can then send them to the Bureau of Standards and have them compared with the standard cells which the Bureau has.

I don't propose to tell you much about standard cells for you won't have to use them until you come to study physics in real earnest. They are not good for ordinary purposes because the moment they go to work driving electrons the conditions inside them change so their electromotive force is changed. They are delicate little affairs and are useful only as standards with which to compare other batteries. And even as standard batteries they must be used in such a way that they are not required to drive any electrons.

[Ill.u.s.tration: Fig 12]

Let's see how it can be done. Suppose two boys sit opposite each other on the floor and brace their feet together. Then with their hands they take hold of a stick and pull in opposite directions. If both have the same stick-motive-force the stick will not move.

Now suppose we connect the negative feet--I mean negative terminals--of two batteries together as in Fig. 12. Then we connect their positive terminals together by a wire. In the wire there will be lots of free electrons ready to go to the positive plate of the battery which pulls the harder. If the batteries are equal in electromotive force these electrons will stay right where they are. There will be no stream of electrons and yet we'll be using one of the batteries to compare with the other.

That is all right, you think, but what are we to do when the batteries are not just equal in e. m. f.? (e. m. f. is code for electromotive force). I'll tell you, because the telling includes some other ideas which will be valuable in your later reading.

[Ill.u.s.tration: Fig 13]

Suppose we take batteries which aren't going to be injured by being made to work--storage batteries will do nicely--and connect them in series as in Fig. 13. When batteries are in series they act like a single stronger battery, one whose e. m. f. is the sum of the e. m. f.'s of the separate batteries. Connect these batteries to a long fine wire as in Fig. 14.

There is a stream of electrons along this wire. Next connect the negative terminal of the standard cell to the negative terminal of the storage batteries, that is, brace their feet against each other. Then connect a wire to the positive terminal of the standard cell. This wire acts just like a long arm sticking out from the positive plate of this cell.

[Ill.u.s.tration: Fig 14]

Touch the end of the wire, which is _p_ of Fig. 14, to some point as _a_ on the fine wire. Now what do we have? Right at _a_, of course, there are some free electrons and they hear the calls of both batteries. If the standard battery, _S_ of the figure, calls the stronger they go to it. In that case move the end _p_ nearer the positive plate of the battery _B_, so that it will have a chance to exert a stronger pull. Suppose we try at _c_ and find the battery _B_ is there the stronger. Then we can move back to some point, say _b_, where the pulls are equal.

To make a test like this we put a sensitive current-measuring instrument in the wire which leads from the positive terminal of the standard cell.

We also use a long fine wire so that there can never be much of an electron stream anyway. When the pulls are equal there will be no current through this instrument.

As soon as we find out where the proper setting is we can replace _S_ by some other battery, say _X_, which we wish to compare with _S_. We find the setting for that battery in the same way as we just did for _S_. Suppose it is at _d_ in Fig. 14 while the setting for _S_ was at _b_. We can see at once that _X_ is stronger than _S_. The question, however, is how much stronger.

Perhaps it would be better to try to answer this question by talking about e. m. f.'s. It isn't fair to speak only of the positive plate which calls, we must speak also of the negative plate which is shooing electrons away from itself. The idea of e. m. f. takes care of both these actions. The steady stream of electrons in the fine wire is due to the e. m. f. of the battery _B_, that is to the pull of the positive terminal and the shove of the negative.

If the wire is uniform, that is the same throughout its length, then each inch of it requires just as much e. m. f. as any other inch. Two inches require twice the e. m. f. which one inch requires. We know how much e. m. f. it takes to keep the electron stream going in the part of the wire from _n_ to _b_. It takes just the e. m. f. of the standard cell, _S_, because when that had its feet braced at _n_ it pulled just as hard at _b_ as did the big battery _B_.

Suppose the distance _n_ to _d_ (usually written _nd_) is twice as great as that from _n_ to _b_ (_nb_). That means that battery _X_ has twice the e. m. f. of battery _S_. You remember that _X_ could exert the same force through the length of wire _nd_, as could the large battery. That is twice what cell _S_ can do. Therefore if we know how many volts to call the e. m.

f. of the standard cell we can say that _X_ has an e. m. f. of twice as many volts.

If we measured dry batteries this way we should find that they each had an e. m. f. of about 1.46 volts. A storage battery would be found to have about 2.4 volts when fully charged and perhaps as low as 2.1 volts when we had run it for a while.