Letters of a Radio-Engineer to His Son Part 5

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.

First there is made a current-measuring instrument which is quite sensitive, so that its pointer will show a deflection when only a very small stream of electrons is pa.s.sing through the instrument. We could make one in the same way as we made the ammeter of the last letter but there are other better ways of which I'll tell you later. Then we connect a good deal of fine wire in series with the instrument for a reason which I'll tell you in a minute. The next and last step is to calibrate.

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_.

[Ill.u.s.tration: Fig 15]

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 positions along the wire. That's the way we calibrate a sensitive current-measuring instrument (with its added wire, of course) so that it will read volts. It is now a voltmeter.

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.

[Ill.u.s.tration: Fig 16]

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.

You will need to know how to describe the resistance of a wire or of any part of an electric circuit. To do so you tell how many "ohms" of resistance it has. The ohm is the unit in which we measure the resistance of a circuit 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 pa.s.ses 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.

[Ill.u.s.tration: Fig 17]

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 that one volt will send a current of one ampere through a resistance of one ohm.

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.

LETTER 9

THE AUDION-CHARACTERISTIC

MY DEAR YOUNG STUDENT:

Although there is much in Letters 7 and 8 which it is well to learn and to think about, there are only three of the ideas which you must have firmly grasped to get the most out of this letter which I am now going to write you about the audion.

First: Electric currents are streams of electrons. We measure currents in amperes. To measure a current we may connect into the circuit an ammeter.

Second: Electrons move in a circuit when there is an electron-moving-force, that is an electromotive force or e. m. f. We measure e. m. f.'s in volts. To measure an e. m. f. we connect a voltmeter to the two points between which the e. m. f. is active.

Third: What current any particular e. m. f. will cause depends upon the circuit in which it is active. Circuits differ in the resistance which they offer to e. m. f.'s. For any particular e. m. f. (that is for any given e. m. f.) the resulting current will be smaller the greater the resistance of the circuit. We measure resistance in ohms. To measure it we find the quotient of the number of volts applied to the circuit by the number of amperes which flow.

In my sixth letter I told you something of how the audion works. It would be worth while to read again that letter. You remember that the current in the plate circuit can be controlled by the e. m. f. which is applied to the grid circuit. There is a relationship between the plate current and the grid voltage which is peculiar or characteristic to the tube. So we call such a relationship "a characteristic." Let us see how it may be found and what it will be.

Connect an ammeter in the plate- or B-circuit, of the tube so as to measure the plate-circuit current. You will find that almost all books use the letter "_I_" to stand for current. The reason is that scientists used to speak of the "intensity of an electric current" so that "_I_" really stands for intensity. We use _I_ to stand for something more than the word "current." It is our symbol for whatever an ammeter would read, that is for the amount of current.

[Ill.u.s.tration: Fig 18]

Another convenience in symbols is this: We shall frequently want to speak of the currents in several different circuits. It saves time to use another letter along with the letter _I_ to show the circuit to which we refer. For example, we are going to talk about the current in the B-circuit of the audion, so we call that current _I_{B}_. We write the letter _B_ below the line on which _I_ stands. That is why we say the _B_ is subscript, meaning "written below." When you are reading to yourself be sure to read _I_{B}_ as "eye-bee" or else as "eye-subscript-bee." _I_{B}_ therefore will stand for the number of amperes in the plate circuit of the audion. In the same way _I_{a}_ would stand for the current in the filament circuit.

We are going to talk about e. m. f.'s also. The letter "_E_" stands for the number of volts of e. m. f. in a circuit. In the filament circuit the battery has _E_{A}_ volts. In the plate circuit the e.

m. f. is _E_{B}_ volts. If we put a battery in the grid circuit we can let _E_{C}_ represent the number of volts applied to the grid-filament or C-circuit.

The characteristic relation which we are after is one between grid voltage, that is _E_{C}_, and plate current, that is _I_{B}_.

So we call it the _E_{C}_--_I_{B}_ characteristic. The dash between the letters is not a subtraction sign but merely a dash to separate the letters. Now we'll find the "ee-see-eye-bee"

characteristic.

Connect some small dry cells in series for use in the grid circuit. Then connect the filament to the middle cell as in Fig. 19. Take the wire which comes from the grid and put a battery clip on it, then you can connect the grid anywhere you want along this series of batteries. See Fig. 18. In the figure this movable clip is represented by an arrow head. You can see that if it is at _a_ the battery will make the grid positive. If it is moved to _b_ the grid will be more positive. On the other hand if the clip is at _o_ there will be no e. m. f. applied to the grid. If it is at _c_ the grid will be made negative.

Between grid and filament there is placed a voltmeter which will tell how much e. m. f. is applied to the grid, that is, tell the value of _E_{C}_, for any position whatever of the clip.

We shall start with the filament heated to a deep red. The manufacturers of the audion tell the purchaser what current should flow through the filament so that there will be the proper emission of electrons. There are easy ways of finding out for one's self but we shall not stop to describe them. The makers also tell how many volts to apply to the plate, that is what value _E_{B}_ should have. We could find this out also for ourselves but we shall not stop to do so.

[Ill.u.s.tration: Fig 19]

Now we set the battery clip so that there is no voltage applied to the grid; that is, we start with _E_{C}_ equal to zero. Then we read the ammeter in the plate circuit to find the value of _I_{B}_ which corresponds to this condition of the grid.

Next we move the clip so as to make the grid as positive as one battery will make it, that is we move the clip to _a_ in Fig. 19. We now have a different value of _E_{C}_ and will find a different value of _I_{B}_ when we read the ammeter. Next move the clip to apply two batteries to the grid. We get a new pair of values for _E_{C}_ and _I_{B}_, getting _E_{C}_ from the voltmeter and _I_{B}_ from the ammeter. As we continue in this way, increasing _E_{C}_, we find that the current _I_{B}_ increases for a while and then after we have reached a certain value of _E_{C}_ the current _I_{B}_ stops increasing. Adding more batteries and making the grid more positive doesn't have any effect on the plate current.

[Ill.u.s.tration: Fig 20]

Before I tell you why this happens I want to show you how to make a picture of the pairs of values of _E_{C}_ and _I_{B}_ which we have been reading on the voltmeter and ammeter.

Imagine a city where all the streets are at right angles and the north and south streets are called streets and numbered while the east and west thorofares are called avenues. I'll draw the map as in Fig. 20.

Right through the center of the city goes Main Street. But the people who laid out the roads were mathematicians and instead of calling it Main Street they called it "Zero Street." The first street east of Zero St. we should have called "East First Street" but they called it "Positive 1 St." and the next beyond "Positive 2 St.," and so on. West of the main street they called the first street "Negative 1 St." and so on.

When they came to name the avenues they were just as precise and mathematical. They called the main avenue "Zero Ave." and those north of it "Positive 1 Ave.," "Positive 2 Ave." and so on. Of course, the avenues south of Zero Ave. they called Negative.

The Town Council went almost crazy on the subject of numbering; they numbered everything. The silent policeman which stood at the corner of "Positive 2 St." and "Positive 1 Ave." was marked that way. Half way between Positive 2 St. and Positive 3 St. there was a garage which set back about two-tenths of a block from Positive 1 Ave. The Council numbered it and called it "Positive 2.5 St. and Positive 1.2 Ave." Most of the people spoke of it as "Plus 2.5 St. and Plus 1.2 Ave."

Sometime later there was an election in the city and a new Council was elected. The members were mostly young electricians and the new Highway Commissioner was a radio enthusiast. At the first meeting the Council changed the names of all the avenues to "Mil-amperes"[3] and of all the streets to "Volts."

Then the Highway Commissioner who had just been taking a set of voltmeter and ammeter readings on an audion moved that there should be a new road known as "Audion Characteristic." He said the road should pa.s.s through the following points:

Zero Volt and Plus 1.0 Mil-ampere Plus 2.0 Volts and Plus 1.7 Mil-amperes Plus 4.0 Volts and Plus 2.6 Mil-amperes Plus 6.0 Volts and Plus 3.4 Mil-amperes Plus 8.0 Volts and Plus 4.3 Mil-amperes

And so on. Fig. 21 shows the new road.