Bulbs connected in series. Physics doesn't add up

[Electrump]

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?

[Grandchuck]

Incandescent lamps are non linear.  The resistance goes way up when they are lit.

[BrokenYugo]

You have independently discovered light bulbs are not nice linear resistors.

Tungsten (the filament material) has a pretty high positive temperature coefficient, the hotter/brighter it gets the higher the resistance, so the bulb conveniently sort of finds it's own operating point for a given voltage across it and requires no driver/ballast.

With identical bulbs in series the voltage and current will be equally divided, but as you've run into the current/resistance value is very dependent of the filament temperature. You'll note they don't glow as brightly in series.

This is slightly outside of your question but do also keep in mind measuring low ohm values accurately is tricky business. With a basic DMM at least check for zero (short test probes together, observe zero or note the offset) and make sure you can get a repeatable reading.

[Sorama]

Your experiment proves that the resistance of the bulbs when the voltage is halved (bulbs in series) is 19,7 ohms, so not linear in function of voltage.

You better take 2 resistors (watch the power dissipation): they are lineair.

Edit: yugo was quicker than me…

[TimFox]

Ohm's Law is an approximation that is accurate for "ohmic" devices, i.e. those that obey Ohm's Law.
Devices sold as "resistors" obey the equation closely.
Other conductive devices (e.g., diodes) disobey this "Law".
In your experiment, at equilibrium, there is a large deviation from the linear relationship V = I R for each bulb in your different connections.

[BeBuLamar]

Ohm's Law is an approximation that is accurate for "ohmic" devices, i.e. those that obey Ohm's Law.

The light bulbs obey ohm's law just as the resistors do. Just that the temperature of the light bulb changes so much from room temp to over 4000F when it's lighted.

[Electrump]

It came as a surprise to me that not all components strictly obey the Ohm's law. I will repeat the experiment with a two and maybe even three resistors to see how obedient they are. Thanks to everyone for the quick and comrehencive replies!

[TimFox]

Ohm's Law is an approximation that is accurate for "ohmic" devices, i.e. those that obey Ohm's Law.

The light bulbs obey ohm's law just as the resistors do. Just that the temperature of the light bulb changes so much from room temp to over 4000F when it's lighted.

If the "resistance" parameter depends on the current in a strong way, then the object does NOT obey Ohm's Law.
If it did obey Ohm's Law, you could predict directly the current as a function of voltage (or vice-versa).
There is a weaker law, where you have a differential parameter R_AC = dV/dI, where R_AC is reasonably constant over a narrow range of current (and therefore temperature) that allows you to calculate small changes of current or voltage for small changes of the other variable.

[TimFox]

It came as a surprise to me that not all components strictly obey the Ohm's law. I will repeat the experiment with a two and maybe even three resistors to see how obedient they are. Thanks to everyone for the quick and comrehencive replies!

A component that obeys Ohm's Law is called "ohmic".  Wires, good resistors, etc. are examples of such components.
As an elementary example of a two-wire device that is far from ohmic, consider a normal silicon diode.
Even normal resistors, operated at a constant temperature, will show a small non-linear effect, called "voltage co-efficient of resistance".
Wirewound and metal film resistors have small voltage co-efficients (sometimes found on a datasheet), but carbon resistors and thick-film resistors can have measurable co-efficients, even when the temperature does not change.
The physics behind Ohm's Law is complex, and part of "solid-state physics" in the scientific textbooks.
This is a page from a good manufacturer of high-resistance resistors that we used before I retired for critical applications:  https://srt-restech.de/pdf/eng/TD_VCR_En.pdf

[radiolistener]

In other words, the question is: Why is the resistance not doubled when I put two identical cmponents in series?

2x 2.5V bulbs

The resistance of an incandescent lamp is temperature-dependent. When connected in series, the voltage across each lamp is reduced, leading to lower power output and consequently a lower operating temperature compared to parallel connections, where each lamp receives the full supply voltage. This variation in temperature results in corresponding changes in the lamps' resistance.

It came as a surprise to me that not all components strictly obey the Ohm's law.

No, Ohm's Law is a fundamental principle, and it applies universally. However, the effect that you see is due to the fact that the properties of certain components, such as resistors or incandescent lamps, can change with varying voltage or temperature. For instance, in components like incandescent lamps, the resistance increases with temperature, which in turn affects the current and voltage relationship. This can give the impression that they do not strictly follow Ohm's Law, but in reality, the law is still valid - it’s the component parameters that are changed dynamically.

[RJSV]

   Now, you see, you have obtained a very good and hopefully lasting memory, of this.   If others mention 'non-linearity' your memory system will recall all this, and you can be emphasizing that, if you answer, with confidence.   You understand the other person's question quite well,... maybe even making comment about the wrong assumption, led you astray a bit as well!

   By the BTW, I'm 70 now, and often 'pleased' to learn some, simple, technicality that I'd never heard.   So questions, and learning really should be at any age, any level of knowledge.
It's the ones that have finished learning, that are missing out,  especially if complacent.  (Those folks are in government, seemingly everywhere).
Thanks for good question !
Any EEVBLOG member can always message me, with question.

[tooki]

Ohm's Law is an approximation that is accurate for "ohmic" devices, i.e. those that obey Ohm's Law.

The light bulbs obey ohm's law just as the resistors do. Just that the temperature of the light bulb changes so much from room temp to over 4000F when it's lighted.

If the "resistance" parameter depends on the current in a strong way, then the object does NOT obey Ohm's Law.
If it did obey Ohm's Law, you could predict directly the current as a function of voltage (or vice-versa).
There is a weaker law, where you have a differential parameter R_AC = dV/dI, where R_AC is reasonably constant over a narrow range of current (and therefore temperature) that allows you to calculate small changes of current or voltage for small changes of the other variable.

Well, I mean... strictly speaking, the incandescent lamps do obey Ohm's Law. The fact that their self-heating changes their resistance doesn't mean Ohm's Law doesn't apply. If you heated the tungsten filament with a directed acetylene torch flame, its resistance would rise just as much as if it reached that temperature through self-heating. Conversely, if you used highly effective cooling to prevent the filament from warming up, its resistance would remain low even with current flowing through it.

[RJSV]

   The explanation, in physics and molecular terms, is that increased temperature activity consists of faster and likely more widespread movements, of each particular particle, and that creates a kind of opposition to other particle (electrons) travel or out of the more active region.
Can think of it like passing through a 'party' of dancers, vs a quiet library where everyone is passive and more stationary.   The odds of collision are less, in the library, as you make your way through, to other side.
   That's thermal energy.

[TimFox]

In other words, the question is: Why is the resistance not doubled when I put two identical cmponents in series?

2x 2.5V bulbs

The resistance of an incandescent lamp is temperature-dependent. When connected in series, the voltage across each lamp is reduced, leading to lower power output and consequently a lower operating temperature compared to parallel connections, where each lamp receives the full supply voltage. This variation in temperature results in corresponding changes in the lamps' resistance.

It came as a surprise to me that not all components strictly obey the Ohm's law.

No, Ohm's Law is a fundamental principle, and it applies universally. However, the effect that you see is due to the fact that the properties of certain components, such as resistors or incandescent lamps, can change with varying voltage or temperature. For instance, in components like incandescent lamps, the resistance increases with temperature, which in turn affects the current and voltage relationship. This can give the impression that they do not strictly follow Ohm's Law, but in reality, the law is still valid - it’s the component parameters that are changed dynamically.

No.  Ohm's Law is not a fundamental principle, and does not apply universally.
It is a good approximation for many useful situations.
If the constant parameter "R" is not a constant, then the equation is not linear, and Ohm's Law is linear.
Note that my discussion of voltage co-efficient of resistance is not due to temperature changes:  in my work with precision analog electronics, we had to be careful with physically small 50 megohm resistors, with voltage < 10 V, because at that voltage gradient (V/mm) in small sizes standard SMT resistors had too much deviation from linearity, but the 2 microwatt power dissipation did not change the temperature.
Remember:  Ohm's Law (for engineering) states V = I R, where R is a constant parameter.
In physics, it is usually stated as a vector equation:  J = s E, where J is the current density (vector),  E is the electric field vector, and s (usually lower-case Greek sigma) is the conductivity.  More generally, s can be a tensor if the two vectors are not parallel (in an anisotropic medium).

[IanB]

It came as a surprise to me that not all components strictly obey the Ohm's law. I will repeat the experiment with a two and maybe even three resistors to see how obedient they are. Thanks to everyone for the quick and comrehencive replies!

A very nice experiment you can do, is to take a single bulb and vary the voltage across it in increasing steps, and record the current each time. Then plot a graph of the results.

V		mA
0.0		0
0.5		?
1.0		?
1.5		?
2.0		?
2.5		178
3.0		?

[RJSV]

   Since there is discussion of thermally related nonlinearities, maybe your next question concerns transistors ?
   With BJT or bipolar type, PNP or NPN;   they have non-linear inputs, base to emitter.   Because that type transistor responds to the Bas Emitter current, and fairly complicated effects of voltage, there are 'regions' that change, accordingly:
   Voltage applied one way (direction) or the other way, will alter these regions, within the block of silicon.   That's what give the BJT type the ability to control a larger change in output,...even if 'temperature' never changes.

   A capacitor might have changing values as well, depending on applied voltage, and not on temperature.   So in extreme cases a capacitor might have a slight amount of nonlinearity.

[TimFox]

I can't quote my solid-state physics textbooks here, since they are not available online, but Wikipedia's article is pretty good.
https://en.wikipedia.org/wiki/Ohm%27s_law
Specifically, it notes near the beginning:  "More specifically, Ohm's law states that the R in this relation is constant, independent of the current.  If the resistance is not constant, the previous equation cannot be called Ohm's law, but it can still be used as a definition of static/DC resistance.   Ohm's law is an empirical relation which accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However some materials do not obey Ohm's law; these are called non-ohmic."
When measuring a material, it is practical to keep its temperature constant, for example a thin or thick film deposited on a ceramic substrate can have its temperature externally controlled, or lab-standard resistors are often kept in a circulating constant-temperature oil bath.  If the ratio between voltage and current, at constant temperature, deviates from a constant, that can be considered a voltage co-efficient.
For an ohmic material with a substantial temperature co-efficient (e.g., carbon), if you maintain the temperature (or the self-heating is not large enough to matter), then the resistor is ohmic with a temperature-dependent parameter R(T), where T is the temperature.
A "light bulb" is more than its filament, since it is mounted in a bulb, and it is difficult (not impossible) to maintain the filament temperature (around 1000 to 3000 K) in its normal operating range, therefore the component is non-linear.

[TimFox]

   Since there is discussion of thermally related nonlinearities, maybe your next question concerns transistors ?
   With BJT or bipolar type, PNP or NPN;   they have non-linear inputs, base to emitter.   Because that type transistor responds to the Bas Emitter current, and fairly complicated effects of voltage, there are 'regions' that change, accordingly:
   Voltage applied one way (direction) or the other way, will alter these regions, within the block of silicon.   That's what give the BJT type the ability to control a larger change in output,...even if 'temperature' never changes.

   A capacitor might have changing values as well, depending on applied voltage, and not on temperature.   So in extreme cases a capacitor might have a slight amount of nonlinearity.

Many popular ceramic capacitor dielectrics (such as Z5U) are very non-linear over their safe voltage range.
A good manufacturer will graph the capacitance as a function of voltage, and the effect is huge.
That value is useful to estimate the AC current at a given DC bias voltage.
NP0/C0G ceramic capacitors have both very low voltage and temperature co-efficients of capacitance.

[IanB]

Dear community

I am a beginner learning the basics of electronics...

Dear Electrobump,

I just wanted to mention that this is one of the best first post, beginner questions we have seen on this forum! 

It contains all necessary information about the question, presented in a well organized manner, and you followed up promptly in response to the answers.

Please do stick around!

[Ice-Tea]

Two additional pointers:

- You could have had a sniff already that something is different than expected even with a single bulb. You measured 1.9 for a single bulb and measured 0.18A or so with 2.5V. If you plug those values in Ohms law you'll notice a few minor issues 
- I noticed your supply is at 2V. Make sure to check all your variables ;-)

You've stumbled on the difference between textbook and beginners approaches and real life. You'll encounter much more of this, and some of it will bite you in the ass from time to time.

Other examples: a textbook wire is perfect zero  . Often that approximation is good enough, sometimes it's not. A diode is, as a first approximation, equivalent to a check valve. Untill you figure out it won't open in the pass direction untill you have 0.7V. And then you figure out before 0.7V it already leaks a very little bit. And then you notice that that 0.7V will increase slightly with increased current. And then you figure out that...

Electronics is the art of choosing the right abstraction level ;-)

[radiolistener]

Here are the calculated values based on your experiments.



As you can see, Ohm's law holds true in all cases. The variation in results is due to the change in the lamp's resistance as its temperature changes.

You can verify this with a digital multimeter by measuring the voltage across the lamps. The measured values may differ slightly from the calculated ones, as I assumed both lamps have identical parameters, whereas in reality, there may be slight variations. The exact values can be confirmed with the DMM.

You can also verify this through an additional experiment: connect a single lamp and set your power supply to 0.9995 V. The current should read 127 mA, and the power should be 127 mW, as calculated from your experiment with two lamps in series. This will further confirm that Ohm's law is still valid.

[TimFox]

In your table, the calculated parameter R differs between the two circuits, and is not constant if you change the applied voltage.
See my quotation above on applicability of Ohm’s Law.
Ohm discovered his empirical relationship for a wide range of practical conductors and configurations, but there are many exceptions, as I have already discussed.
If V is an arbitrary function of I, then the ratio V/I is not constant and Ohm’s Law where R is constant, is not obeyed.

[radiolistener]

In your table, the calculated parameter R differs between the two circuits, and is not constant if you change the applied voltage.

Yes, you're correct that the R can vary with changes in applied voltage, especially for components like incandescent lamps, where resistance is temperature-dependent. However, R can still be accurately calculated from the voltage drop across the component.

To confirm the calculated value of R, you can perform an additional experiment with a single lamp by applying the same voltage drop as observed in the series experiment. If the measured resistance matches the calculated value, this will confirm that the calculation of R based on Ohm's Law is correct, despite the temperature variations affecting resistance.

The same principle of Ohm's Law applies to electromagnetic waves, where the magnetic field, electric field, and wave impedance of the medium are interrelated in a similar manner. Just as in electrical circuits, the relationship between voltage, current, and resistance can be seen in the context of electromagnetic waves, where the electric field (E), magnetic field (H), and wave impedance (Z) are connected through the equation:

\${Z} = \frac{E}{H}\$

This demonstrates that Ohm's Law is not only applicable to conductive materials but also holds true in the propagation of electromagnetic waves through different media.

[TimFox]

If I slowly increase the current through the bulb, and the voltage does not change proportionally, then the bulb is not linear, the resistance is not constant, the device is not ohmic, and Ohm’s Law does not apply.
Yes, you can calculate the non-constant ratio V/I as a function of current or voltage, but the actual Ohm’s Law states that the ratio is constant.
This is well-described in the Wikipedia article I cited.
In electromagnetic waves in vacuum (an ideal medium) the basic laws from Maxwell give a constant ratio as you stated, the characteristic impedance of free space.
If you replace vacuum with a linear dielectric, this value changes to a different constant.
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).
Many physical and engineering problems require only linear equations, such as Ohm’s empirical equation, but one needs to know when they are applicable to the required accuracy.

[radiolistener]

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.