value of memorizing multiplication tables, the proper spelling of words,
the location of countries on a map, et cetera, is being questioned by
many people these days (mostly low-achieving dummkopfs) based on an
easy access to data on the Internet and other media. All such people
need to do is get fairly close to spelling topics of interest correctly
and other people who do not subscribe to the aforementioned philosophy
have seen to it that the laziness and ignorance of those who do subscribe
are duly accommodated. I'm referring to basic life skills of course,
not nuclear science or phenology. The obvious advantage gained in memorization
is developing an intuitive feel for what the entire realm of subject
entails. Strong visual clues during the learning process augment retention
of data. For instance, electronic calculators in their various forms
are great for arriving at precise numerical answers with given input
conditions. Enter an exact set of numbers and get an exact result on
the display (right or wrong, depending on the input data and the correctness
of the algorithm). Whether or not the answer makes sense and should
be believed depends on the user's familiarity with expected results.
That is where being exposed to charts, tables, nomographs, and graphs
of functions and related items is of inestimable value both to the learning
process and to the application process later in real-world situations.
On many occasions I have posted articles from publications that predate
the handheld calculator and personal computer era which include those
kinds of learning aids for readers. Here is another. As Albert Einstein
famously said*, "Any fool can know. The point is to understand."
May 1934 Radio News and Short-Wave
Wax nostalgic about and learn from the history of early electronics.
See articles from Radio &
Television News, published 1919 - 1959. All copyrights hereby acknowledged.
Modern Radio Practice in Using
Graphs and Charts
Part Nine (see
in radio design work usually can be reduced to formulas represented
as charts which permit the solution of mathematical problems without
mental effort. This series of articles presents a number of useful charts
and explains how others can be made
John M. Borst
|Any problem involving proportion can
be solved graphically without much difficulty. Such problems
occur often in a serviceman's and experimenter's life; therefore,
the chart, presented this month should prove applicable in many
For instance, one can use any milliammeter as
an ohmmeter but then it takes a little arithmetic to find the
resistance after readings are taken. This arithmetic will be
eliminated when using the chart in Figure 5. The chart can also
be applied to the slide-wire bridge, a construction is given
for an ohmmeter scale employing a milliammeter in the two popular
In the February 1932 issue of Radio News,
the formulas for the different kinds of charts were derived
and here the N-chart was introduced. It consists of three linear
scales in the form of an N or a Z and is useful in several kinds
of proportion-problems and some forms of multiplication. As
seen in Figure 1, the chart has the drawback that it is hard
to utilize the extreme end of the diagonal scale since the line,
1, does not intersect scale c within the limits of the paper.
In some cases, it will be found that nearly one fifth of the
scale b on each end cannot be used. Therefore. instead of using
the N chart, a logarithmic arrangement was used in Figure 5,
even though this meant the calculation of a special scale. It
solves the same formula as the N chart.
Now let us proceed
with the problem. The ordinary ohmmeter is usually something
like the circuit in Figure 2. The 0-1-ma. meter is the most
popular, and therefore it is used here in the examples, but
any milliammeter can be used. In fact. for low-resistance measurements,
an 0-50 m. meter is very useful. R is usually made so that the
meter shows full-scale reading when the test prods are short-circuited.
This, too, is not essential, but it is desirable since it gives
a longer scale and it simplifies computation. Suppose that we
have such an ohmmeter, in which the meter shows full-scale deflection
when the prods are short-circuited, and that it shows a lower
reading, m, when the resistance x is inserted. Then,
Here the numeral 1, represents the full-scale reading (1
ma.) If a different kind of meter is used with a full scale
reading of n ma., then,
Referring to the chart of Figure 5, connect the meter reading
on scale M (A) with the value of R on scale R and the intersection
on scale X shows the value of the unknown resistance. For instance.
if, as in our case, R is 4500 ohms and the meter went down to
.2 ma. with the resistance X inserted, then the sample line
shows that the resistance of X is 18000 ohms.
have to know is the value of R. This is the resistance which
will let just enough current flow to make the meter show full-scale
reading. It can be figured out with Ohm's law. With a 1-ma.
meter and a 4.5-volt battery, R is 4500 ohms. With a 10-ma.
meter and a 4.5-volt battery it would be 450 ohms and with a
1-ma meter and a 1.5-volt battery it would be 1500 ohms, etc.
The range of such an ohmmeter is from 1/10 R to 10 R. It is
possible to obtain some kind of reading above and below this,
but they are not accurate.
|The second type of ohmmeter has the advantage
of being especially suited to the measurement of low resistances
without drawing a very heavy current. This is illustrated in
Figure 3. The unknown resistance is shunted across the meter,
which also makes the meter go down from full-scale deflection.
For higher resistances it may be placed across the meter, plus
a resistance, a, in series with it. The sum of a, and the resistance
of the meter we shall call R. Then the value of X is
where m is the reading of the meter with X connected to
the test prods and n is the reading when the test prods do not
touch each other. The same chart (Figure 5) can be used again,
but for this type of ohmmeter use scale M (B). The sample line
shows that if the meter went down to .8 mils and the resistance
of the meter was 45 ohms, the resistance of X would be 180 ohms.
You can extend the ranges of R and X by adding or subtracting
the same number of zeros to both
A scale can be constructed
for a given ohmmeter rather easily. This is illustrated in Figure
4. Line L represents the scale on the meter. The same divisions
and numbers should be put on it. Then, in order to get the ohmmeter
divisions, draw two lines, a and b, through the ends of the
scale at any convenient angle as shown, a and b are parallel.
On a, regular divisions are set off representing ohms, on any
convenient scale. Next you should find a point P on scale B
so that OP equals R when measured in the unit employed on a.
Then draw lines from P to the divisions on a. The intersections
give the divisions for the ohmmeter scale on L. This construction
is good for the series ohmmeter (Figure 2) only. For the shunt
type, the divisions of a should be put on b instead and the
point P should be taken on a in the same manner as before. It
will be found difficult to get to both ends of the scale with
just one position of P. After some divisions have been made
with P in one position, the point can be shifted, which means
that you are using another measuring unit on both line a and
b. It will be found that the scales obtained by this method,
for the ohmmeter of Figure 2, resemble those for Figure 3 if
R is the same; only, they are mirror views of each other. When
another range is required, it can be done by making R twice
as large (or 10 times as large) and then multiplying the readings
of your previous scale.
In Figure 6, two examples of
completed scales are given. One is for a 0-1-ma. meter in the
series circuit with a resistance of R equals 4500 ohms. Its
range can be extended by employing a resistance of 45000 ohms
and a 45-volt battery. Then the scale readings should be multiplied
by 10. The other scale is designed for an ohmmeter of the shunt
type, employing an 0-1-ma. meter with an internal resistance
of 30 ohms. If your meter is somewhat less than 30 ohms you
should connect some resistance in series with it so as to make
the total 30 ohms.
Shunting the meter with a 3.3-ohm
resistor will make the scale lower, multiply all values with.1.
When your meter has a resistance of 50 ohms (such as the universal
meter) all scale values should be multiplied by 5/3 or 1.67.
Electronics Nomographs and Circuits
Figure 5 - A Millimeter as an Ohmmeter
Albert Einstein also supposedly said, "I never commit to memory
anything that can easily be looked up in a book;" however, its veracity
is in question.
February 21, 2014