February 1956 Popular Electronics
[Table of Contents
People old and young enjoy waxing nostalgic about and learning some of the history
of early electronics. Popular Electronics was published from October 1954 through April 1985. All copyrights
are hereby acknowledged. See all articles from
Fortunately, there is a constant flow of people newly interested
in electronics who are seeking information on basic principles.
Some will find an article this one on Ohm's law fundamentals and
decide maybe being just a user of electronics is good enough. Others
will, as did you and I, read this kind of material and be amazed
at how ultimately predictable electrical circuit parameters are.
If he or she continues and launches into a career in electronics
or electrical engineering, it won't be long before he or she will,
as do you and I now, look back at how simple things were at the
beginning of the journey ;-) This article was written half a century
ago, but to a word everything contained herein is as valid today
as it was then.
How to Use Ohm's Law
By E.G. Lewis
with this valuable tool will improve your ability to understand
Most electronic experimenters steer clear of anything that smacks
of theory. And with good reason, for if one gets a kick out of working
with his hands and building gadgets that do things, pushing a pencil
can be mighty boring. But there's one bit of theory that's both
easy to learn and easy to use. Best of ail, once learned, it will
provide the experimenter with a powerful mental tool that will help
him to undertake more difficult and more interesting projects, and
may even help him to save money when buying electronic parts ...
With a knowledge of Ohm's law, the experimenter can do such things
as determine what size cathode resistor to employ in an audio amplifier,
how large a dropping resistor to install in series vacuum-tube heater
strings, and what size multiplier resistor to use when converting
a milliammeter to a voltmeter. In many cases, he may be able to
combine two resistors that he has in his junk box to use in place
of one resistor that he would have to buy, thus saving money on
Ohm's law is not a man-made law like the laws against speeding
and robbery but, rather, a statement of natural or scientific law.
It is a statement of the relationship between electrical pressure
(voltage), resistance to current flow (ohms), and actual current
flow (amperes) in a closed electrical circuit. It is named after
George Simon Ohm who, in the 1820's, formulated this relationship.
The familiar unit of electrical resistance, the ohm, is named after
the same scientist.
Ohm's law itself may be expressed in many forms, both as fact
statements, and as mathematical formulas. One fact statement is
as follows: the current flow (amperage) in an electrical circuit
is directly proportional to the total electromotive force (electrical
pressure, or voltage) in the circuit and inversely proportional
to the total resistance of the circuit.
In actual practice, this fact statement of Ohm's law, as interesting
as it may be, is not used nearly as much as the mathematical relationships,
or formulas, which are derived from the law. These formulas are
given in Fig. 1 (A) in their three basic forms. The small design
at the top provides a convenient way for the beginner to remember
the relationships. In using these formulas, the numerical values
in the basic units of resistance (ohms), voltage (volts), and current
(amperes) in every case are substituted for the symbols R, E, and
Form one states that:
E = IR
or, voltage (volts) = current (amperes) multiplied by resistance
Form two states that:
I = E/R
or, current (amperes) = voltage (volts) divided by resistance
And, finally, form three states that:
R = E/I
or, resistance (ohms) = voltage (volts) divided by current (amperes).
Equipment for testing the circuit of Fig.
3(B). The same equipment may be used for checking all the circuits
which are discussed in the text.
To use any of these forms of Ohm's law, it is only necessary
to determine two of the values in the circuit, then to substitute
them in the proper formula to calculate the third value.
For example, in the basic experimental setup shown in Fig. 1
(B), the electromotive force or voltage E may be determined by a
voltmeter, current flow I by an ammeter, and the resistance R may
then be calculated by using the third form of Ohm's law, as shown
in Fig. 1 (A). But enough of general theory; let's take up some
down-to-earth practical examples.
Series Resistor: In transformerless circuits, tube heaters are
frequently connected in series across a source of fairly high voltage.
This may be done if each heater requires the same current for operation
and if the total voltage drop is equal to the source voltage. Where
the total voltage required is less than source voltage, a series
dropping resistor is connected in the circuit to provide additional
voltage drop and thus to limit current flow.
A typical circuit arrangement is shown in Fig. 2 (A). What size
resistor should be chosen for R? Let's use Ohm's law and see.
Using round figures, the total voltage drop 4n the tube circuit
proper is 35 volts (35W4) plus 50 volts (50B5) plus 12 volts (12AT7),
or a total of 97 volts. This can be determined by simple addition.
Since the source voltage is 117 volts, it will be necessary to drop
117-97 or 20 volts across the
Resistance. Current? Check the tube manual!
For these tubes, heater current is 0.15 amperes. Now, let's substitute
these values in form three of Ohm's law, as given in Fig. 1 (A).
Resistance (R) = desired voltage drop (20) /current (0.15), or:
R = 20/0.15 = 133.33 ohms
It's as simple as that!
But now a problem presents itself. If an experimenter went into
a radio parts store and asked for a 133.33-ohm resistor, the clerk
would be mighty surprised. In most cases, however, exact circuit
values are not too critical, so one should simply ask for the nearest
standard value resistor or, in this case, a 150-ohm unit.
Cathode Resistor: A common problem encountered in designing and
building audio amplifiers is shown in Fig. 2 (B). What size cathode
resistor is needed to bias this power output stage properly? As
in the case of the series heater resistor, first consult the tube
manual. Let's assume that a type 50C5 tube is being used, with B+
around 110 volts.
Referring to the tube manual, it will be seen that suggested
bias voltage is -7.5 volts for this plate voltage, and that, under
these conditions, the plate current will be 49 milliamperes, the
screen grid current 4 milliamperes. The cathode current is the total
of the plate and screen currents, or 49 plus 4 = 53 ma.
Having the voltage (7.5 volts) and the current value (53 ma.),
the resistance can be calculated using Ohm's law.
Fig. 1. (A) Three basic forms of Ohm's law.
(B) Experimental circuit for Ohm's law.
Wait a minute! When using Ohm's law, the current must be in amperes
if the values are to be determined in volts and ohms. Remembering
that 1 milliampere equals 0.001 ampere, simply take the value in
milliamperes and move the decimal point three places to the left
to convert the value to amperes. Thus, 53 ma. = 0.053 amperes. Now,
substituting this value in the formula:
R = E/I = 7.5/0.053 = 141.5 ohms
As a 141.5-ohm resistor cannot be purchased, one would then ask
the clerk for a 150-ohm unit.
Meter Multiplier: A milliammeter or microammeter may be used
as a voltmeter if it is provided with a series resistor to limit
current flow. The basic circuit arrangement is shown in Fig. 2 (C).
What size multiplier resistor should be used in the circuit? This
should be a cinch now that Ohm's law has been learned.
To measure a maximum of 100 volts, a full-scale (1-ma.) reading
on the meter should indicate that 100 volts is applied across the
entire circuit. Thus, both the voltage (100) and the current (1
ma. or 0.001 ampere) are known. Therefore:
Resistance (total) = 100/0.001 = 100,000 ohms
But this is the total resistance needed in the circuit. Since
the meter already has a resistance of 50 ohms, the multiplier resistor
(R) should have a value of 99,950 ohms. Where maximum accuracy is
desired, a special effort should be made to obtain a precision multiplier
resistor having the exact value needed. However, for practical purposes,
a 100,000-ohm resistor could be used in this circuit.
Series and Parallel Resistors
This photo shows the relative size of some
typical resistors having various wattage ratings. Units shown
are approximately life-size. Size and shape will vary somewhat
among the different manufacturers.
Suppose that a resistor is needed of a value that cannot be bought
... or, suppose there are a lot of resistors on hand, but not of
the value desired. Is there some way that two or more resistors
can be combined to obtain a special value? There is.
When resistors are connected in series, the total resistance
is simply the sum of the individual resistance values. A typical
series connection is shown in Fig. 3 (A). If the resistors shown
had values of 500 ohms (R1), 100 ohms (R2) and 50 ohms (R3), the
total resistance would be the simple sum of these values:
Rt = 650 ohms
When resistors are connected in parallel, the total resistance
is less than the value of the smallest resistor. A parallel resistor
circuit, together with the mathematical formulas used to calculate
total resistance, is shown in Fig. 3 (B). Where only two resistors
are in parallel, a special, relatively simple formula may be employed.
This formula is also given in Fig. 3 (B).
As an example, assume that a 300-ohm and 500-ohm resistor are
connected in parallel. Total resistance would then be:
Note that the value obtained (187.5 ohms) is less than that of
the smallest resistor in the parallel network (300 ohms).
Where all the resistors are of the same value, the total parallel
resistance can be determined simply by dividing the value of one
resistor by the number of resistors connected in parallel. For example,
suppose there are five (5) one-thousand-ohm (1000-ohm) resistors
connected in parallel. Total resistance would be 1000 divided by
5 or 200 ohms.
Fig. 2. Circuits for assisting in determining
the value of the unknown resistor in the following configurations:
(A) series healer string. (B) cathode bias. (C) meter multiplier.
When specifying a resistor size, not only the resistance must
be known but also the wattage rating. All the resistors which are
shown on the facing page have exactly the same resistance value,
but there is a big difference in physical size ... and in price
The wattage rating of a resistor is determined by the amount
of current it can handle, for its resistance, without overheating
or burning out. Thus, it is determined by the power that the resistor
can dissipate as heat. Naturally, a large resistor can dissipate
more heat than a smaller resistor, and - as would be expected -
the larger the wattage rating of a resistor, the larger its physical
Actual power, in watts, may be determined by the formulas given
in Fig. 3 (C). When choosing a resistor for an electronic application,
it is common practice to pick a wattage rating in a standard size
at least two to three times the actual wattage that the resistor
must dissipate as heat.
As practical examples, let's determine the wattage ratings of
the three resistors which were chosen for use as a series filament
resistor, as a cathode bias resistor, and as a meter multiplier
resistor in the previous examples.
Series Resistor: In the circuit given in Fig. 2(A), it was decided
to use a 150-ohm resistor. To determine the wattage rating, the
actual power dissipation must first be determined, using the first
formula given in Fig. 3(C) :
W = I2R = (0.15)2(150)
= (0.0225) (150) = 3.375 watts
Twice this value would be around 7 watts, and the next standard
resistor size is 10 watts. Therefore, in this application, a 150-ohm,
10-watt resistor would be specified.
Cathode Resistor: In the second example, using the circuit given
in Fig. 2(B), it was determined that a cathode resistor of 150 ohms
would be needed to give a bias voltage of -7.5 volts with a cathode
current of 53 ma. Let's round off the current figure to 50 ma. ...
the results will be close enough for practical design work. Using
the last formula given in Fig. 3(C), and changing 50 ma. to 0.050
ampere, the actual power dissipation would be:
W = EI = (7.5) (0.050) = 0.375 watts
In this case, a 1-watt resistor would be used.
Fig. 3. (A) series resistors; (B) parallel
resistors; (C) equations for calculating power.
Multiplier Resistor: In the third example discussed, Fig. 2(C),
it was calculated that a 100,000-ohm resistor would be needed as
a meter multiplier to change an 0-1 ma. meter to a 0-100 volt voltmeter.
Wattage? Let's use the second formula given in Fig. 3C.
W = E2/R = (100)2/100,000
= 10,000/100,000 = 0.1 watts
And, in this case, a 1/2-watt or even a 1/4-watt resistor would
In this discussion, the value of learning and using Ohm's law
to the average experimenter has been emphasized. Remember, however,
if these problems and examples seemed a little difficult, that they
were so only because of unfamiliarity with Ohm's law. As practice
and experience are gained, calculating resistor values with Ohm's
law becomes easier and easier ... the stage can be reached where
most of the calculations are performed mentally, with pencil and
paper seldom being necessary.
But one thing is certain! Learning to use and to apply Ohm's
law will result in a better understanding of circuit action, making
it possible to undertake and to complete successfully a greater
number of projects. It will also enable the experimenter to enjoy
his hobby a lot more!
Posted March 1, 2016