  (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 passing 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 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. 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 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. 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. Touch the end of the wire, which is p of Fig. 14, 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 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. That is the way in which to compare batteries and to measure their e. m. f.’s, but you see it takes a lot of time. It is easier to use a “voltmeter” which is an instrument for measuring e.m.f.’s. Here is how one could be made. We know how many volts of e.m.f. are required to keep going the electron stream between n and b–we know that from the e.m.f. of our standard cell. Suppose then that we connect this new instrument, which we have just made, to the wire at n and b as in Fig. 15. Some of the electrons at n which are so anxious to get away from the negative plate of battery B can now travel as far as b through the wire of the new instrument. They do so and the pointer swings around to some new position. Opposite that we mark the number of volts which the standard battery told us there was between n and b. If we move the end of the wire from b to d the pointer will take a new position. Opposite this we mark twice the number of volts of the standard cell. We can run it to a point e where the distance ne is one-half nb, and mark our scale with half the number of volts of the standard cell, and so on for other If we connect a voltmeter to the battery X as in Fig. 16 the pointer will tell us the number of volts in the e.m.f. of X, for the pointer will take the same position as it did when the voltmeter was connected between n and d. There is only one thing to watch out for in all this. We must be careful that the voltmeter is so made that it won’t offer too easy a path for electrons to follow. We only want to find how hard a battery can pull an electron, for that is what we mean by e.m.f. Of course, we must let a small stream of electrons flow through the voltmeter so as to make the pointer move. That is why voltmeters of this kind are made out of a long piece of fine wire or else have a coil of fine wire in series with the current-measuring part. The fine wire makes a long and narrow path for the electrons and so there can be only a small stream. Usually we describe this condition by saying that a voltmeter has a high resistance. Fine wires offer more resistance to electron streams than do heavy wires of the same length. If a wire is the same diameter all along, the longer the length of it which we use the greater is the resistance which is offered to an electron stream. I can show you what an ohm is if I tell you a simple way to measure a resistance. Suppose you have a wire or coil of wire and want to know its resistance. Connect it in series with a battery and an ammeter as shown in Fig. 17. The same electron stream passes through all parts of this circuit and the ammeter tells us what this stream is in amperes. Now connect a voltmeter to the two ends of the coil as shown in the figure. The voltmeter tells in volts how much e.m.f. is being applied to force the current through the coil. Divide the number of volts by the number of amperes and the quotient (answer) is the number of ohms of resistance in the coil. Suppose the ammeter shows a current of one ampere and the voltmeter an e. m. f. of one volt. Then dividing 1 by 1 gives 1. That means that the coil has a resistance of one ohm. It also means one ohm is such a resistance that one volt will send through it a current of one ampere. You can get lots of meaning out of this. For example, it means also How many ohms would the coil have if it took 5 volts to send 2 amperes through it. Solution: Divide 5 by 2 and you get 2.5. Therefore the coil would have a resistance of 2.5 ohms. Try another. If a coil of resistance three ohms is carrying two amperes what is the voltage across the terminals of the coil? For 1 ohm it would take 1 volt to give a current of 1 ampere, wouldn’t it? For 3 ohms it takes three times as much to give one ampere. To give twice this current would take twice 3 volts. That is, 2 amperes in 3 ohms requires 2x3 volts. Here’s one for you to try by yourself. If an e.m.f. of 8 volts is sending current through a resistance of 2 ohms, how much current is flowing? Notice that I told the number of ohms and the number of volts, what are you going to tell? Don’t tell just the number; tell how many and what. |
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