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.

[tggzzz]

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.

Nonsense. Stop prevaricating and answer the question.

For example, in this component there is 3mA flowing trough it. What is the voltage across it? What is its resistance? Use numbers, not words.

For another example of a basic component which your incorrect understanding cannot explain, see https://www.eevblog.com/forum/beginners/at-nanovolts-do-resistors-still-experience-heat-at-high-amperage/msg4996246/#msg4996246

[radiolistener]

Nonsense. Stop prevaricating and answer the question.

For example, in this component there is 3mA flowing trough it. What is the voltage across it? What is its resistance? Use numbers, not words.

Your question does not have a straightforward answer as you seem to expect.

To clarify, in a nonlinear component like a tunnel diode, for a given current (in this case, 3mA), there can be more than one corresponding voltage depending on the diode's operating region. This is similar to solving an equation like \$y = b x^2 + c x^3\$, where there can be multiple valid solutions depending on the conditions.

As I previously mentioned, in order to determine the voltage and resistance accurately, it's necessary to know the exact operating point of the diode, which cannot be inferred from current value alone. The relationship between voltage and current in a tunnel diode is nonlinear, and therefore, it is misleading to expect a single answer without additional context or data.


If you'd like to explore this matter further by specifying the exact point on the graph where you're interested in determining the resistance, I'd be happy to assist.

[tggzzz]

Nonsense. Stop prevaricating and answer the question.

For example, in this component there is 3mA flowing trough it. What is the voltage across it? What is its resistance? Use numbers, not words.

Your question does not have a straightforward answer as you seem to expect.

To clarify, in a nonlinear component like a tunnel diode, for a given current (in this case, 3mA), there can be more than one corresponding voltage depending on the diode's operating region. This is similar to solving an equation like \$y = b x^2 + c x^3\$, where there can be multiple valid solutions depending on the conditions.

As I previously mentioned, in order to determine the voltage and resistance accurately, it's necessary to know the exact operating point of the diode, which cannot be inferred from current value alone. The relationship between voltage and current in a tunnel diode is nonlinear, and therefore, it is misleading to expect a single answer without additional context or data.


If you'd like to explore this matter further by specifying the exact point on the graph where you're interested in determining the resistance, I'd be happy to assist.

Please give a numerical answer in the context of your previous (false) assertion.

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.

Big hint: Ohm's law only applies to ohmic devices. Ohm's law does not apply to non-ohmic devices. That is simple and unambiguous, and I would have thought uncontroversial.

[RoGeorge]

When the filament gets hot, the resistance of the filament increases.

These are two miniature light bulbs measured with a DP832 power supply:



The plots are from https://www.eevblog.com/forum/projects/resistance-of-incandescent-light-bulbs/

Notice how the resistance (the blue trace) increases with the applied voltage.

[radiolistener]

Please give a numerical answer in the context of your previous (false) assertion.

My previous answer conveys the same point. Your question is akin to asking for a single solution to a cubic equation. When informed that it is impossible to provide a unique solution because there may be multiple valid answers, you assert that this is a false claim and request a single numerical value. What you expect? 

Big hint: Ohm's law only applies to ohmic devices. Ohm's law does not apply to non-ohmic devices. That is simple and unambiguous, and I would have thought uncontroversial.

It is true that a tunnel diode is not an Ohmic device, and thus it would be technically incorrect to describe the relation \${R} = \frac{U}{I}\$ as Ohm's law in the case where \${R}\$ is not a constant Ohmic resistance. However, this equation can still be applied to determine the dynamic or differential resistance of the diode at a specific point on its I-V characteristic curve.

Notice how the resistance (the blue trace) increases with the applied voltage.

Yes, as I mentioned earlier, for a non-linear component, it is essential to set the component to a specific operating point on its I-V curve in order to accurately measure its resistance by considering the values of voltage and current.

[Andy Chee]

Big hint: Ohm's law only applies to ohmic devices. Ohm's law does not apply to non-ohmic devices. That is simple and unambiguous, and I would have thought uncontroversial.

What is an ohmic device?  A device that behaves according to ohm's law.

Seems like a circular argument to me.

https://yourlogicalfallacyis.com/begging-the-question

[tggzzz]

Big hint: Ohm's law only applies to ohmic devices. Ohm's law does not apply to non-ohmic devices. That is simple and unambiguous, and I would have thought uncontroversial.

What is an ohmic device?  A device that behaves according to ohm's law.

Seems like a circular argument to me.

https://yourlogicalfallacyis.com/begging-the-question

Not an argument, simply a statement of the obvious.

The key point is that not all devices/materials are ohmic, and for such devices/materials V is not linearly proportional to R, as implied by V=IR.

[DimitriP]

If you fill two of these buckets half-way, you'll have less water than a single full bucket.
Lightbulbs are like these buckets.

Resistors on the other hand are more like this bucket below (yeah , it's not perfect, but it illustrates the point :


and most importantly, if you fill two six gallon buckets half-way, how many buckets do you have ?

[radiolistener]

The key point is that not all devices/materials are ohmic, and for such devices/materials V is not linearly proportional to R, as implied by V=IR.

To clarify, I did not assert that all components are Ohmic. Nonlinear components cannot be classified as such.

However, Ohm's law equation can still be applied to determine the dynamic resistance at a specific operating point. It is important to note, though, that this resistance will not necessarily remain the same at other specific operating points. Therefore, the calculated value will be valid only for the specific mode of operation of the nonlinear component.


It is also important to consider that nonlinear components may exhibit hysteresis. Therefore, for accurate resistance measurements at a specified operating point, it is crucial to establish the component in the desired mode correctly, as the measured resistance may differ depending on whether the voltage was increased or decreased to reach that point.

[tggzzz]

Please give a numerical answer in the context of your previous (false) assertion.

My previous answer conveys the same point. Your question is akin to asking for a single solution to a cubic equation. When informed that it is impossible to provide a unique solution because there may be multiple valid answers, you assert that this is a false claim and request a single numerical value. What you expect? 

I don't expect that! You expect that from your insistence that V=IR.

Big hint: Ohm's law only applies to ohmic devices. Ohm's law does not apply to non-ohmic devices. That is simple and unambiguous, and I would have thought uncontroversial.

It is true that a tunnel diode is not an Ohmic device, and thus it would be technically incorrect to describe the relation \${R} = \frac{U}{I}\$ as Ohm's law in the case where \${R}\$ is not a constant Ohmic resistance. However, this equation can still be applied to determine the dynamic or differential resistance of the diode at a specific point on its I-V characteristic curve.

You are on the right track, but the equation is wrong.

The relevant equation is R_dynamic=^dv/_di . R_dynamic is also termed the differential resistance, as implied by the differential equation familiar in calculus.

Notice how the resistance (the blue trace) increases with the applied voltage.

Yes, as I mentioned earlier, for a non-linear component, it is essential to set the component to a specific operating point on its I-V curve in order to accurately measure its resistance by considering the values of voltage and current.

Almost. The operating point is required to determine the dynamic resistance.

Of course you don't even need a cubic equation to become aware of why dynamic resistance is important; a simple y=mx+c equation is sufficient. It is possible to have negative V/I and positive ^dV/_dI, e.g. a cell/battery.


(from https://en.wikipedia.org/wiki/Negative_resistance )

[MrAl]

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.

Hello there,

This discrepancy about Ohm's Law comes up from time to time on the web.  This might be the fifth time or more that I've seen people try to claim that "Ohm's Law" holds for every single situation no matter how obscure.

You probably do not realize it yet, but what the equivalent to what you are saying is that:
c=a/b

is Ohm's Law.  That's not a Law, and just because we change the lettering that does not make it what we usually refer to as Ohm's Law either.  In fact, Ohm's Law is not a true Law either.
Let me list a few here:
c=a/b
d=g/f
a=b*c
m=diddly/tweedly
r=v/i

Which of those is Ohm's Law?
None of them, not even the last one, because OL involves constant quantities not variable quantities.
To be more succinct, we might write in upper case:
R=V/I
and maybe we can take that to be Ohm's Law because it helps us SOLVE something without any more information.  If you need more information about the current or voltage, then what you are implying is something like this:
r=v(t)/i(t)

or even:
r=v(t)/i(x)

and what this tells us is that both 'v' and 'i' are functions that must be defined before we can calculate r.

Like some of the other examples posted by others in this thread but I'll add one more:
y=r*sin(angle)

Now this might look like:
y=R*sin(angle)

but it's not.  It's entirely different.  The second means we have a constant radius so 'y' will plot out a half circle if we span the angle from 0 to pi.  However, the first is not the same as the second because 'r' is a variable also, and that means it could be a function:
y=r(t)*sin(angle)

and notice now we have two independent variables not just one (which was the angle previously).

Now as to the constraints on the formula:
r=v/i

if we constrain 'v' and 'i' to stay within certain limits, we still don't have Ohm's Law.  I bring this up because you said that sometimes we can calculate Ohm's Law at a point if we limit the span of the variables.
That's still not Ohm's Law.  That's called "Linearization" about a point.  We then go about to 'pretend' that it obeys what we refer to as Ohm's Law.

I really like the example of the negative resistance though.  That really kicks this thing in the butt.  There's no way we can call that Ohm's Law.  If we try to say that we can get a negative resistance R with R=V/I we would have to say that one of the variables V or I is negative, as in:
R=-2/3

or:
R=2/(-3)

and this makes little sense also because it does not matter what the polarity is, the resistance is always positive.  For example, if we apply +5 volts with a current of 5 amps, R=1 Ohm, but if we apply -5 volts with 5 amps, the resistance is still R=1 Ohm.

It is also noteworthy to mention that 'resistance' is not the same as 'Ohm's Law' just because we use units of "Ohms" for resistance.  Ohm's Law and resistance are two different things.  We can have a resistive element that does not follow what we call Ohm's Law.  This has been demonstrated many times in the past with the diode equation.
In other words, if Ohm's Law holds for diodes just because they exhibit Ohmic behavior about a certain operating point, then why do we need the Diode equation?
The diode equation looks something like this:
id=is*(e^(qv/nkT)-1)

and if we lump some constants and use an approximation based on 'is' always being much smaller than 'id' we can come up with this:
v=log(id)*K  (where K is just some of the constants lumped)
and this shows us that the voltage is proportional to the natural log of the current, not proportional to the current.  And this is even after using an approximation that makes the expression even simpler than it was originally.
This shows that this:
v=log(id)*K
is certainly not the same as:
V=I*R

they are two different relationships.  If we could call the first one as the second one then we might as well say we have one formula:
v=i*r

for everything in the universe.  Why not?  If we "just have to know more about the current or voltage" (or whatever else) then we can use Ohm's Law to describe anything we want to use it for.
What is the temperature of the sun?  It's v=i*r of course.
What is the rotation of the earth around the sun?  It's also v=i*r, what else could it be.
What is the quantum state at the second location when we use teleportation to transmit the state to the that second location?  Why, it's v=i*r, naturally!


I think this happens because we use formulas regularly without really knowing or remembering the mysteries behind some of them.  We all do this at some point.  Also, we use the word "Ohms" for resistance and so we can start to believe that everything that has resistance follows Ohm's Law.

[MrAl]

Big hint: Ohm's law only applies to ohmic devices. Ohm's law does not apply to non-ohmic devices. That is simple and unambiguous, and I would have thought uncontroversial.

What is an ohmic device?  A device that behaves according to ohm's law.

Seems like a circular argument to me.

https://yourlogicalfallacyis.com/begging-the-question

An ohmic device is a device that follows Ohm's Law 'almost' everywhere.
We have to say 'almost' because nothing holds for Ohm's Law everywhere because it's not a true Law.

[MrAl]

Dear community

I am a beginner learning the basics of electronics. Currently I read "Easy Electronics" by Charles Platt. I am making the experiments from the book to make sure I get the same results. I am on the page 9 and already have a question I cannot answer myself.
The book says when two identical components are in parallel, then the current doubles. Consequently, when two identical components are in series, they create twice as much resistance for the current and there will be half as much current. Sounds logical.
I have proved experimentally that "when two identical components are in parallel, then the current doubles" and I have no problems with that. However, something weird happens "when two identical components are in series", because they actually do not create twice as much resistance as promised. In fact, the resistance increases less than 50%!
In other words, the question is: Why is the resistance not doubled when I put two identical cmponents in series?

Below are details of the experiments, images and drawings. Although I tried to be as thorough as possible, I imagine there may be some gaps, so any relevant questions and comments are welcome.

Equipment used
DC Power Supply
2x 2.5V bulbs
2x bulb holders


Notes
For unknown reason the resistance if the same type bulbs significantly differs -  from 1.3 to 4 Ω. I selected 2 bulbs with 1.9 Ω.
Bulb holders are identical.

Experiment 1
One 2.5V bulb consumes 178mA. Verified with both bulbs.

Experiment 2
Two 2.5V bulbs in parallel consume 353mA. 176.5mA per bulb which is pretty close to the current for one bult from Experiment 1(178mA)!

Experiment 3
What will happen if bulbs put in series? 175mA as half of the current? Half of that like 87.5mA? Wrong! The current is 127mA. And this figure puzzles me. How is it possible?

Hi,

As you are finding out, incandescent light bulbs do not follow the rule that "two identical components in series" must show twice the resistance.  That's mostly only at a constant temperature, even for regular resistors, which I'm pretty sure even the man Ohm even knew at the time he did his experiments.

Sometimes books tend to generalize a little too much in order to simplify the explanations.  This is one of those cases, and it's not a rare thing to see.  It's because providing the entire story in one book means using many pages of words which would take up too much room and even partly deride from the main topic which is "basic electricity".

The reason light bulbs do not follow this rule is because the filament gets very hot, and that means it draws a lot less current than when it is cold.  The ratio when cold to when hot is roughly 8 to 1.  That means that a bulb that measures 80 Ohms when hot may only measure around 10 Ohms when cold.
When the temperature is somewhere between hot and cold, the resistance can be anything between 10 and 80 Ohms approximately.  The relationship is exponential and that means that it is not what we call "linear".  There are many, many devices like this like the diode, and we have different formulas for all those devices.  We can't use what we call Ohm's Law because as soon as we change the voltage the filament changes temperature, and that changes the relationship between current and voltage.

I can post one of the formulas for the light bulb but it might not help much.  It would show the approximate relationship between current and voltage for a filament bulb, and it's not Ohm's Law by any stretch of the imagination

One thing you may find interesting is if you measure the resistance of one bulb with an Ohm Meter (no applied voltage yet) and then connect two of them in series and measure them both with the Ohm Meter, you will see twice the resistance.  Why is that working now.  It's because the temperature of the filament did not change in this experiment like it did with the original experiment.
Likewise, with the filaments hot, you should see twice the resistance of one hot bulb although you cannot measure it with an Ohm Meter unless you had a way to very quickly remove the voltage and quickly make a resistance measurement, which is kind of hard to do.

[radiolistener]

It is possible to have negative V/I and positive ^dV/_dI, e.g. a cell/battery.

I don't see anything wrong with the concept of negative resistance. This phenomenon occurs in certain non-linear components. Negative resistance is a behavior in devices like tunnel diodes and certain oscillators, where it can facilitate signal amplification or self-oscillation. While it may seem counterintuitive compared to conventional resistive behavior, it is a well-established concept in electronics.

[MrAl]

It is possible to have negative V/I and positive ^dV/_dI, e.g. a cell/battery.

I don't see anything wrong with the concept of negative resistance. This phenomenon occurs in certain non-linear components. Negative resistance is a behavior in devices like tunnel diodes and certain oscillators, where it can facilitate signal amplification or self-oscillation. While it may seem counterintuitive compared to conventional resistive behavior, it is a well-established concept in electronics.

That's not the point.  Read some of the other replies just before yours.  There's a full explanation of what Ohm's Law is all about, and what it is not.

[tggzzz]

It is possible to have negative V/I and positive ^dV/_dI, e.g. a cell/battery.

I don't see anything wrong with the concept of negative resistance. This phenomenon occurs in certain non-linear components. Negative resistance is a behavior in devices like tunnel diodes and certain oscillators, where it can facilitate signal amplification or self-oscillation. While it may seem counterintuitive compared to conventional resistive behavior, it is a well-established concept in electronics.

Good to see you acknowledge the existence and properties of tunnel diodes

There is no such thing as "conventional resistive behaviour". There are measured V-I curves, and several mathematical models are used to explain aspects of the measurements.

Different mathematical models are useful in different situations, as is typical with any kind of model of physical behaviour. Many people have a naive mis-understanding of the models' applicability.

[BeBuLamar]

Unlike a diode which conducts when the forward bias voltage reaches a certain value the resistor (yes the bulb filament of an incandescent bulb is a resistor too) changes its value depending on temperature. This happens with all resistors but for most applications the value only changes slightly. For example a heater when it's hot the resistance is higher, not by much but enough that I can tell if it's hot by measuring the resistance. For the light bulb the resistance changes signficantly because its temperture changes a lot in off to on condition. At half voltage the filament isn't as hot and the resistance is lower.