eblc1388 said:
Ok, here's my first attempt:
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“I shall now define, by the following equation, the quantity called the resistance, R, of the conductor BC:
R=V/I eq. 40.3
For some materials (for many different kinds of metallic wires, for example) and under certain conditions (at constant temperature for example) the resistance defined this way is a constant, independent of I. For other kinds of conductors (vacuum tubes, for example) the R defined in this way is not independent of I. In all cases the resistance defined by equation 40.3 is measured in ohms. Obviously, “volts divided by amperes” is equivalent to ohms. Equation 40.3 is known as Ohm’s law after Georg Simon Ohm, a German physicist (1787-1854).”
Ref: “The New College Physics, A Spiral Approach” Albert V Baez, Freeman and Company, San Francisco, 1967, pp512.
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“A German physicist named George Simon Ohm was the first to discover the relationship between current, electromotive force and resistance. The discovery is called Ohm’s law and simply expressed is - that for any circuit or part of a circuit under consideration the current in amperes is equal to the electromotive force in volts divided by the resistance in ohms. This law, mathematically expressed, is as follows:
Current = Electromotive Force/Resistance
If in the above expression we substitute the proper symbols for current, electromotive force and resistance we have the following equation:
I=V/R
This is the equation for Ohm’s Law.”
RadioRon Note: there is no mention of this Law only applying to cases where R is constant.
Ref: “Principles of Electricity applied to Telephone and Telegraph Work” A training course text, American Telephone and Telegraph Company, January, 1953 (revised from the 1938 edition), page 7.
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“One ohm is defined as the amount of resistance that allows one ampere of current to flow between two points that have a potential difference of one volt. Thus, we get Ohm’s Law, which is:
R=E/I
Where R=resistance in ohms
E= potential or EMF in volts and
I= current in amperes.”
RadioRon Note: no mention that Ohm’s Law is not obeyed when R is variable.
Ref: “The ARRL Handbook” The American Radio Relay League, Newington, CT, 2000, pp 5.2.
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“The relationship between electromotive force (voltage), the flow of current (amperes), and the resistance which impedes the flow of current (ohms), is very clearly expressed in a simple but highly valuable law known as Ohm’s Law. This law states that the current in amperes is equal to the voltage in volts divided by the resistance in ohms. Expressed as an equation:
I=E/R”
RadioRon Note: no mention in this text that this law does not hold when R is a function of I
Ref: “Radio Handbook” 22nd Edition, William I. Orr, Howard W Sams Company, Indianapolis, 1981, pp 2.6-2.7
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Now, this reference explains things in more detail and I believe explains why we are arguing.
“Over a hundred years ago, Georg Simon Ohm discovered that every time he closed a switch in a circuit such as that of Figure 4-1, the current became the same constant value. He also discovered that, providing the temperature of the conductor did not change, doubling the emf doubled the current and tripling the emf tripled the current. In other words:
*For a given circuit, the ratio of the applied emf to current is a constant*
This became known as Ohm’s Law of constant proportionality. We can express Ohm’s Law in equation form as
E/I=k eq. 4-1
Where E is the applied emf in volts, I is the resulting current in amperes, and k is a numerical constant.
Carrying this discovery a step further, Ohm found that changing the conductors or the load to some other size resulted in a different value for the numerical constant. If the current is one ampere when the emf is 10 volts, the constant becomes 10/1, or simply 10; and if the current is 0.5 ampere when the emf is 10 volts, the constant becomes 10/0.5, or 20. From these results, Ohm concluded that this constant E/I ratio for given circuit is, therefore, a property of that circuit. And since, for a given emf, the value of the constant increases as the current decreases, this constant can be thought of as representing the opposition of the circuit to the flow of current. This property then should be given a name that suggests opposition, such as resistance. Therefore:
*Resistance is the opposition of an electric circuit to the flow of current through that circuit.
The Letter symbol for resistance is R*
We can substitute the symbol R for the constant k in Equation 4-1. Since resistance is an electrical property, we require a unit of measurement for it. Although it would be quite proper to express resistance in terms of volts per ampere, it was decided to honor Ohm’s original discovery by stating that:
**the ohm is the basic unit of electric resistance. The unit symbol for ohm is the Greek letter omega**
Since Equation 4-1 has now become
R=E/I or R=V/I eq. 4-2
Where R is resistance in ohms, E is the applied emf in volts, V is the voltage drop across the resistance in volts, and I is the resulting current through the resistance in amperes, the size of the ohm is automatically established.
** An electric circuit has a resistance of one ohm when an applied emf of one volt causes a current to flow at the rate of one ampere**
Few people nowadays recall the original wording of Ohm’s law of constant proportionality which allowed us to define resistance and to establish a unit of resistance. As a result, Ohm’s law is usually stated simply by the equation
R=E/I”
Ref: “Introduction to Electric Circuits” Herbert W. Jackson, Prentice-Hall Inc, Englewood Cliffs, New Jersey, 1970, pp 70 to 71.
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Discussion:
I find the last reference to suggest that some of you may have been taught Ohm’s Law of constant proportionality in its original form, which is now effectively obsoleted by the more modern form R=E/I. It is not appropriate to believe that the original form is the most correct, because at the time Ohm was not aware of conductors whose resistance was dependent on current such as we see in semiconductors. In addition, Jackson teaches that Ohm himself realized after further study that his so-called constant of proportionality could indeed vary depending on the materials used. This lead to the definition of resistance, not the definition of constant resistance, as one of the three variables (a variable is something that can vary) that constitutes what we now call Ohm’s Law.
I also thought it might be instructive to approach this from a logical argument point of view by asking "if a diode does not obey Ohm's Law, what law then describes the resistance of the diode when a specific emf is applied and a resulting specific value of current flows?"
Your turn.
