I Equals E over R
August 1932 Radio-Craft

August 1932 Radio-Craft

August 1932 Radio-Craft Cover - RF Cafe[Table of Contents]

Wax nostalgic about and learn from the history of early electronics. See articles from Radio-Craft, published 1929 - 1953. All copyrights are hereby acknowledged.

Whoa, it's a good thing I read these articles prior to publishing them, lest some soul unfamiliar with this topic be lead to the wrong conclusion! Keep in mind that this article was written in 1932, prior to the development of the quantum mechanical model of the atom, but on the other hand, Ernest Rutherford and Niels Bohr developed their model in 1913, so the relevant information was available. The Rutherford-Bohr model of the atom suggested a nucleus comprised of positive masses called protons, each of which carries a charge of +1 unit, and neutrons with no net charge. Surrounding the nucleus were orbiting masses called electrons, each of which carries a charge of -1 units. Accordingly, the net charge of an atom was the sum of protons and electrons, with unionized atoms having a net charge of 0 (zero). Neutrons, carrying no charge, have no effect on the overall atomic charge.

Modern science says quarks, three of which make up each proton and neutron, have individual charges of +1/3, -1/3, +2/3, or -2/3, thereby determining the particles' net charges (+1 for protons, 0 for neutrons). Now, take a look at Figure 3 in this article and the text description that mutually proves the drawing is not a mistake and the text is not a typo.

The author correctly believes an atomic nucleus (in this case an unionized carbon atom, N=6), which must have a net charge opposite of the number of electrons (6 for carbon), needs to be +6 charge units. However, he knows the atomic weight (mass) of a carbon atom is 12 mass units (each proton and neutron has approximately 1 mass unit). There cannot possibly be 12 protons or that would yield a net atomic charge of +12 + (-6) = +6 charge units. He resolves the quandary by proposing 6 additional protons in the nucleus along with 6 additional electrons in the nucleus. That equal set cancels out the 6 extraneous charge units, and since the mass of electrons is miniscule compared to that of protons, their presence does not upset known total atomic mass too much. I don't ever recall seeing that kind of model being proposed before.

The irony is that the raison d'être for the article is to push back the frontier of ignorance so that the reader might more fully understand what is happening in an electronic circuit. Otherwise, though, it is a useful piece.

In a very loose sense, Mr. Palmer's nucleus model is sort of accurate in that a neutron, when it decays (beta decay, mediated by the nuclear weak force), produces a proton, an electron, and an electron antineutrino (i.e, free neutron decay). That is not the same, however, as saying that a neutron is initially comprised of a proton, an electron, and an electron antineutrino. The process is not readily reversible.

I Equals E over R

A molecule of a substance is composed of positive and negative electrons - RF Cafe

A molecule of a substance, say at B Fig. 1, is composed of positive and negative electrons, such as illustrated at Fig. 2 or Fig. 3. Fig. 4 illustrates the logical sequence used in breaking down the substance. 

By C. W. Palmer

The fact that current flow in an electrical circuit depends upon voltage and resistance means nothing unless one can visualize what is actually going on. In this extremely novel presentation, the author shows not only "how" but "why."

People not familiar with electricity have the idea that little is known about this subject. This assumption is incorrect, as probably more is known about this science than about any other. Because mechanical motions and forces can be seen and felt, it is easy for the average person to understand and foretell their actions and the results ensuing. For example, few people would question the result of striking a piece of wood with the sharp edge of an axe or dropping an egg on a concrete floor; but when the problem is to visualize what is taking place in an electrical circuit, they are entirely at "sea."

If we remember that we cannot see or hear electricity directly, but can only observe its effects, the study of electricity - and its companion radio - will be much simplified.

Electricity (according to the electron theory) consists of extremely small moving particles, these particles have been named electrons and protons. These electrons and protons do not carry electricity, as some people think, they constitute electricity. In other words, an electron or proton is nothing but a small quantity of electricity. Electrons and protons are separated because they act differently; the electron is said to be a negative charge while the proton is a positive charge.

The average person usually believes an electron to be a very small particle of matter; beyond this elementary conception his ideas are vague and usually confused.

The uncharged, separated molecules cause a flow of current - RF Cafe

The uncharged, separated molecules in Fig.  5 cause a flow of current as shown in the lower part of the same figure when touched. This flow ceases in a very short time, but may be caused to flow for a longer time by the application of an E.M.F. as shown in Fig. 6.

Let us first consider "Matter." Matter is any substance having weight and volume - the air, the earth, the water, are all forms of matter.

The Atomic Structure

Consider a bar of copper (an element) as shown in Fig. 1. This bar shows certain peculiarities which identify it as copper, and even a very small piece, such as B of Fig. 1, cut from this bar will be characteristic of the whole piece. If it were possible to keep cutting down the size of the piece of copper, we would arrive at a point where a further cut would result in changing its characteristics, and it would no longer be identified as the same material as the whole. This particle containing all the peculiarities of the whole piece is called a molecule of the element.

Since the molecule has the same characteristics as the whole, it, too, must be subdivided if we are to discriminate between one substance and another. Now, since all substances have different constituents, their molecules must be different, and science has been able to break down the molecule into still smaller particles called atoms. An atom of hydrogen is different from an atom of helium; an atom of copper is different from an atom of zinc, etc. Atoms cannot exist by themselves in a normal state - at least two atoms must be combined to form a molecule.

The atoms of every substance, regardless of its nature, are composed of electrons. This means that all substances contain electricity, which seems contradictory to our general knowledge, although it is apparently true as we shall soon see.

In its normal state, an atom contains a certain number of electrons and proton arranged in a particular manner. Each substance has a different combination and grouping of the charges. Hydrogen, for example, the lightest substance known contains only one electron revolving around one proton as shown in Fig. 2. Carbon contains 12 protons grouped together with 6 electrons as a nucleus around which 6 electrons revolve as shown in Fig. 3.

The central portion of the atom is known as the nucleus and it may consist of a single proton or a group of protons and electrons. The electrons revolving around the nucleus are known as the planetary or free electrons, because they can be removed from the atom without changing its general character. These planetary electrons revolving around the nucleus may form a single ring or a number of rings around the nucleus, depending on the complexity of the atomic structure of the substance. The atomic structure is shown graphically in the form illustrated in Fig. 4 - first, there is the molecule of an element which is composed of atoms and these in turn are made up of electrons and protons.

Single elements, as described, are familiar to all, but many substances we encounter consist of chemical combinations of the atoms of two or more different elements forming another substance - a compound - whose appearance and physical properties are different from any of the elements, such as salt, water, etc.

For the sake of simplicity, we will limit our explanation to the elements and atoms.

The Charge

We have shown that atoms are composed of minute charges of electricity which, normally, are in such a form that the sum of the charges of all the electrons or negative charges equal the sum of the charges of all of the protons or positive charges. We have also explained that some of the electrons are revolving around the nucleus in orbits in a manner similar to the stars around the sun. It is to be noted that although the substance contains electricity, (electrons and protons) it is uncharged simply because the charges are equal and balanced.

If we remove one or more of the planetary electrons from an atom, the atom becomes unbalanced and lacks negative electricity (electrons). In this case, the atom is said to be positively charged. On the other hand, if we place an additional electron or electrons in one of the planetary orbits of an atom, it also becomes unbalanced - in the opposite direction - and has too much negative electricity (too many electrons). In the latter case, the atom is charged negatively.

From this it can be concluded that a substance is electrified when it has more or less than its normal number of electrons and the amount of charge is determined only by the quantity of electrons displaced. Also, it can be deducted that all electrons are the same regardless of the element or compound from which they come.

The Electric Current

Every substance has a tendency when displaced from equilibrium, to return to a state of balance as quickly as possible. Just as water will find its own level, so atoms which have lost electrons (positively charged) will attempt to attach electrons to themselves, and atoms which have excess electrons will attempt to loose them and thus become neutral.

Therefore. if we have two substances, one charged positively and the other charged negatively, and we touch them together; the excess electrons from the negative will enter the other substance in order to reach a neutral state. If the two bodies are charged equally (and oppositely) the electrons will continue to transfer until both substances are neutral.

Figure 5 shows this effect. In the upper part of the illustration the two substances are charged; and in the lower part, the excess electrons from the negative body have entered the positively charged body and neutralized the atoms lacking electrons.

If we have some means of maintaining the charges on the two balls (shown in Fig. 5.,) continuously, there would be a constant passage of electrons from the negative to the positive ball. This continual passage of electrons is what is known as an electrical current or simply a current. This follows logically from the statement we made before; that electrons are electricity.

It is not possible to add or remove electrons from a substance without the aid of some external force. This force is known as an electromotive force (E.M.F.). We will not go into the various means of maintaining an E.M.F., here. Several common sources of electromotive forces are dry batteries, storage batteries and generators.

The amount of current flowing in a circuit (for example the two balls in Fig. 6) depends on the number of electrons passing through the circuit. The number of electrons, in turn, depends (among other things) on the amount of the charge which is dependent on tile E.M.F. applied to the circuit. We may safely conclude, therefore, that the amount of current flowing in a circuit depends on the value of the E.M.F. applied to the circuit.

When visualizing the motion of electrons through a solid body, such as copper, we must remember that the electrons are very small and that there are comparatively large spaces between the atoms. As an example, if a copper cent were enlarged to be the size of the earth's diameter, the distance between atoms would be about three miles and the electrons would be only a few inches in diameter!


It is well known that certain materials such as copper, brass, silver, etc. will readily permit the passage of an electric current, while other materials such as rubber, mica, porcelain, cotton, silk etc., do not. The former materials are called conductors and the latter, insulators. The reason why metals are such good conductors of electricity is that their atoms apparently have a weak attraction for electrons and large numbers of them are either practically in a free state throughout the body of the metal or they are easily shifted by any outside electric forces. The more easily the electrons can be shifted in a metal, the lower its resistance to a flow of current, merely because a greater current flows for the same value of applied E.M.F.

This action of resistance in conductors introduces another factor in the consideration of the strength of current flow. Up to this point we have seen that the amount of current increases as the E.M.F. increases and since the opposition offered by the conductor of the current decreases the current, it may be said that the magnitude of the current flowing in any circuit depends upon the E.M.F. applied and the opposition offered by the circuit itself.

In order to facilitate the measurement and computation of electric currents, several units have been set as standards. The E.M.F. is measured in a unit called a volt; the current is measured in amperes and the opposition or resistance is measured in ohms. The first of these units is usually represented by the letter E, the second by the letter I and the resistance by the letter R.

To sum up: the current (number of amperes) flowing in a circuit depends upon the voltage applied and the resistance of the circuit. To state this in another way,

Ohm's Law 1 - RF Cafe 

A problem involving this condition is shown in Fig. 7. This involves a resistance of 5 ohms in a 10-volt circuit. Then Ohm's Law 2 - RF Cafe or 2 amperes.

Another type of problem might arise in which it is desired to know the value of the resistance in a circuit when the voltage and the current are known. Here again, Fig. 8 illustrates the conditions. This may be determined from the ratio Ohm's Law 3 - RF Cafe; or if the potential (volts) is 50 and the current is 2 amperes, the resistance will be 50/2 or 25 ohms.

The third condition of the relation considered above is one in which the resistance and the current are known and it is desired to know the applied potential. In this case. the voltage E is equal to the product of the current and the resistance (E = I x R).

If a current of 10 amperes is flowing through a resistance of 20 ohms, then the potential applied is 10 x 20 or 200 volts.

From these three examples. it is established that there are three individual conditions involving the relation of E.M.F., current and resistance. These three classifications are as follows:

When E and R are known and the current is desired:

E = I/R

When E and I are known and the resistance is desired:

R = E/I

When R and I are known and the voltage is desired:

E = R x I

The above three formulas are known as Ohm's Law in honor of the noted physicist George Simon Ohm.

Resistances in Series

We have already learned that resistance is the opposition of a substance to the flow of current. It is natural then, that the longer the substance composing the resistance, the greater will be the value of the resistance. Also, if two conductors are connected so that the current passes through each of them in succession, then the resistance of the circuit will be the sum of the individual resistances of the two conductors. This effect is illustrated at Fig. 8. The resistance of the conductor at 8A is R. Then the total resistance of the two resistors at 8B is the sum of the individual resistances.

When the area of a conductor is increased, the opposition to the flow of current will be decreased, as there are more atoms to lose and gain electrons. It also follows logically that if two conductors are connected as shown in Fig. 9, the resistance of the circuit will be less than that of either of the individual resistors R. This is known as a parallel method of connection.

The method of figuring the total resistance of the circuit for parallel resistances is different from that for series resistances. If we refer again to Fig, 9, it will be noted that the current flowing from point A to point B will be divided and part of it will pass through each resistance. If these resistances are equal, half the current will go through each, Then, if the applied E.M.F. is 10 volts and the current in each resistor is 1 ampere, the resistance of each of the resistors will be 10/1 or 10 ohms. However, the total current flowing is 2 amperes, so the resistance of the parallel circuit is 10/2 or 5 ohms.

For those readers who are familiar with the elements of algebra, the above reasoning may be expressed in the following formula:

Addition of paralel resistors - RF Cafe, etc.,

in which R is the total resistance and resistors R1, R2, etc., are the individual resistances of the parallel circuit.

The discussion of electricity and resistance given should be of assistance to many radio enthusiasts who are confused by the explanations of Ohm's Law usually given. It is suggested that the article be read over several times so that the details discussed will all be understood.

(It might be well to add that the current through a given part of a circuit will vary directly as the applied E.M.F. and inversely as the resistance, as stated by Mr. Palmer. It should be emphasized, however. that when part of a circuit is under consideration, the current, voltage and resistance of that particular part should only be considered, regardless of whatever else occurs in another part of the circuit. - Editor.)



Posted February 16, 2023
(updated from original post on 7/9/2015)