Bulbs connected in series. Physics doesn't add up

[TimFox]

No.
Ohm found that R is constant when varying either the voltage or current for a class of materials.
One can find a ratio of any variables, but it may not be constant, just a definition of another variable without meaning.

[radiolistener]

However, with a material rather than vacuum, things get tricky due to quantum effects in the medium’s atoms, and you get “anomalous dispersion” at higher frequencies (including optical).

I don't think that topic starter can register the presence of quantum effects on his installation 

I understand what you are referring to, but it is unlikely that quantum effects could be observed in such a simple setup, even if a more stable power supply is used along with highly precise voltmeters and ammeters.

No.
Ohm found that R is constant when varying either the voltage or current for a class of materials.
One can find a ratio of any variables, but it may not be constant, just a definition of another variable without meaning.

Deriving Ohm's Law can be challenging when dealing with components that exhibit nonlinear characteristics. However, once Ohm's Law is established, its application remains valid, even in the presence of nonlinearity. In many cases, the behavior of nonlinear components can be approximated as linear within certain operating ranges, allowing for the practical application of Ohm's Law for analysis and calculations. I think it is essential just to understand the context in which the law is applied and recognize that its use may be limited for nonlinear components.

[TimFox]

Once again, Ohm's Law is a well-defined physical and electronic law that is very useful.
Your manipulation of the three terms V, I, and R is elementary algebra, without physical meaning except as a definition for the variable R

Georg Ohm did a careful series of experiments on different media in the 19th century and published his famous empirical law:  the physical content is that R is constant for a given circuit.

He tried to explain this important result, but his theoretical explanation is no longer used:  solid-state physics in the 20th century began to explain it on a physical basis.
This what the world calls "Ohm's Law":  you will find this in any reputable published source (you need not believe me).
Did you even look at that Wikipedia article?

Your discussion of the elementary algebra is not Ohm's Law.
Ohm's Law is not relevant to non-linear circuits.
Other electrical laws, such as Kirchoff's, do pertain to non-linear circuits;  perhaps you are confusing them?
My reference to quantum phenomena was not for the OP, but to show how your electromagnetic wave example also breaks down under certain circumstances (non-vacuum).

[tggzzz]

In Ohm's Law, it is permissible to consider any of the three components - voltage (U), current (I), or resistance (R) - as the constant for the relationship described by the equation \${I} = \frac{U}{R}\$. This means that, depending on the context of the analysis, one can express the law in various forms:

• \${I} = \frac{U}{R}\$.
• \${U} = {I}{R}\$.
• \${R} = \frac{U}{I}\$​.

Thus, the flexibility of Ohm's Law allows for a comprehensive analysis of electrical circuits by treating any of these components as constant, depending on the parameters of interest in the specific scenario.

Oh dog, not again.

Ohm's Law is valid for - wait for it - ohmic materials. Most materials are not ohmic, e.g. diodes. Some components even have ranges where an increase in current "causes" a decrease in voltage, i.e. negative resistance.[1]

FFI, see https://en.wikipedia.org/wiki/Ohm%27s_law especially the section on "linear approximations".

[1] For example, in this component there is 3mA flowing trough it. What is the voltage across it? What is its resistance?


I vs. V curve of 10 mA germanium tunnel diode, taken on a Tektronix model 571 curve tracer.

[radiolistener]

Ohm's Law is valid for - wait for it - ohmic materials. Most materials are not ohmic, e.g. diodes. Some components even have ranges where an increase in voltage "causes" a decrease in current, i.e. negative resistance.

And? Since diode is non-linear component, you cannot assume that R will be constant for any voltage.
But it don't prevent you to use Ohm's Law to determine it's R for specific voltage.

Some components exhibit hysteresis, which complicates the assertion that resistance will always remain constant at a given voltage. However, this does not preclude the use of Ohm's Law to measure the resistance of a component under specific conditions, once the component has been brought to a defined operating state. In such cases, you can apply Ohm's Law to determine the resistance based on the measured voltage and current, acknowledging that this value is contingent upon the specific operating point of the component and may vary under different conditions.

[tggzzz]

Ohm's Law is valid for - wait for it - ohmic materials. Most materials are not ohmic, e.g. diodes. Some components even have ranges where an increase in voltage "causes" a decrease in current, i.e. negative resistance.

And? Since diode is non-linear component, you cannot assume that R will be constant for any voltage.
But it don't prevent you to use Ohm's Law to determine it's R for specific voltage.

So, what exactly, is that tunnel diode's resistance when there  is 3mA flowing through it?

If you are to be believed, that is a trivial question to answer.

[radiolistener]

So, what exactly, is that tunnel diode's resistance when there  is 3mA flowing through it?

In Ohm's Law, three parameters are involved: voltage (U), current (I), and resistance (R). Knowing only one of these parameters makes it impossible to accurately predict the other two.

To determine the resistance of the tunnel diode at a specific conditions (operating mode) with specified current of 3 mA, it is also necessary to know the voltage drop across the diode at that moment. Only with both values (voltage and current) Ohm's Law can be applied to calculate resistance of tunnel diode. 

And given that the tunnel diode is a nonlinear component, you cannot assume that the calculated R will remain constant under varying conditions. The calculated R value will be only relevant for the specific operating mode in which it was determined.

[1] For example, in this component there is 3mA flowing trough it. What is the voltage across it? What is its resistance?

To accurately apply Ohm's Law in this scenario, you first need to establish the tunnel diode at the specific operating mode point you wish to test. Once the diode is set to this operating mode point, you can measure the voltage across it and the current flowing through it to calculate the resistance using Ohm's Law.

However, it's important to note that for the same current (3 mA), there may be multiple voltage values across the diode depending on its operating condition. If the diode is in a different operating mode, achieving the same current and voltage would require adjusting the diode's state through a different method. Therefore, the resistance value calculated will only be applicable for the particular operating mode you've established.

This distinguishes non-linear components from linear one, where R is constant, resulting in a unique voltage value for a specific current. However, you can note that Ohm's Law remains applicable in both cases.

[TimFox]

In Ohm's Law, V and I are variables, but R is a parameter.
Ohm showed that for many useful situations, R is a constant over a wide range of the two variables.
Ohm's Law (when valid) is more than a definition of the ratio R, it is an explicit statement that R is constant (for a given component).

Ohm's Law, and other uses of the word "ohm":

Meanwhile, the actual Ohm's Law (for linear ohmic materials only) has some interesting implications, only valid for linear ohmic materials.
To calculate the resistance of a long wire or similar geometry, with constant cross-section area, one can treat it as a series of short wires in series, or a series of long skinny wires in parallel.
This results in the well known formula
  R = {rho} x l / A  ,
where  {rho} is another constant (the resistivity of the material, usually given in ohm-cm),  l is the length of the wire, and A is the cross-sectional area.
Again, this only works for a linear ohmic material.

The reversal of slope in a tunnel diode is often called a negative resistance, but that is not an ohmic device.
It is straightforward to define the "ohm" unit from Ohm's Law as the ratio of volts per ampere, and use that unit for the derivative dV/dI, but that is not Ohm's Law.

As an analogy, one defines "efficiency" as the ratio of output power divided by input power.
Obviously, efficiency depends on all the variables, such as shaft rpm or power level for a motor.
It would be foolish to assume that efficiency of a practical device is constant over the useful range of the device.