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I have started recently on the study of electronics.

One of the most basic statements that I learned about electricity is the relationship between the voltage and the current across a conductor. I did some experiments and I found that it isn't always 100% accurate, though it is pretty precise with resistors.

Some components like LEDs, transistors, and diodes, don't have this linear relationship.

When I started studying electronics I thought I could mathematically predict what would happen in every circuit but some components are impossible to predict precisely.

I found some graphs on the web and I started wondering if things like this are purely empirical.

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    \$\begingroup\$ Honestly, consider your title. Take a step back. Do you seriously think anybody will ever say "no, you should not take the most basic thing they're teaching seriously"? \$\endgroup\$ May 21 at 12:19
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    \$\begingroup\$ Ohms Law is absolute, it's just that not everything has a fixed resistance. \$\endgroup\$
    – Finbarr
    May 21 at 12:23
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    \$\begingroup\$ also, you're meandering about how things can't be precisely described, but that's just not true: Ohm's law is precise when it comes to resistors. Many things just aren't perfect resistors. Does it mean Ohm's law is wrong: no, not at all. It just means that for some purposes the model of "this component is a perfect resistor" isn't good enough. Learn Ohm's law. It's really the most fundamental thing. \$\endgroup\$ May 21 at 12:23
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    \$\begingroup\$ ... but also learn where you can apply it. \$\endgroup\$
    – Transistor
    May 21 at 12:24
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    \$\begingroup\$ If a measurement disagrees with a standard model, it's quite likely that you've made a measurement error .. \$\endgroup\$
    – pjc50
    May 21 at 16:36

14 Answers 14

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Yes, you should take Ohm's law seriously.

You do, though, need to keep in mind that it applies only to simple resistors and conductors.

Ohm's law is a simplification of some complicated math. It applies only to linear resistive circuits. If you stay in that area, then Ohm's law will give you correct results.

The other elements you mention (LEDs, transistors, diodes) are not linear resistive elements. Those parts have a very different relationship between current and voltage.

For diodes, you can refer to the Schockley diode equation for the relationship between current and voltage. It also applies to LEDs, which are light emitting diodes.


The simplification given by Ohm's law is often times all you need.

Take an LED as an example. A typical task is to calculate the value a series resistor in order to safely operate an LED from a given voltage.

If you just connect an LED to a voltage source, you'll destroy the LED.

What you do then, is to look up the maximum safe operating current for the LED as well as its nominal forward voltage (both given in the LED datasheet) then use Ohm's law to calculate a minimum resistance.

Say you want to operate a blue LED from a 5V source. You look in the datasheet of the LED and find that it can tolerate a maximum of 20mA and that it has a nominal forward voltage of 3.3V.

That is to say, when given 20 mA a voltage of about 3.3V will appear across the LED.

The difference between 3.3V and 5V is 1.7V. At 20 mA, Ohm's law says you need an 85 ohm resistor in series with the LED.

That won't be perfectly correct, but close enough. You will then usually find that you need a resistor with a larger value because that 20mA maximum is really bright with modern LEDs.

If you actually measure the voltage across the LED or the current through it, then you will find differences to the calculated values. The voltage drop across the resistor will obey Ohm's law, though.

Keep in mind that a lot of what you learn in the beginning when studying pretty much any subject will be simplifications.

If you were to start studying electronics, and your instructor pointed you at Maxwell's equations and told you to calculate the current through a resistor for a given voltage, you'd probably just quietly leave the classroom and never come back.

Ohm's law itself is empirical, and only applies to purely resistive circuits. Purely resistive circuits don't exist - every conductor and every circuit has inductive and capacitive effects, as well as depending to some extent on temperature.

Learn Ohm's law, use it. It gives usable results over many common conditions with many common materials. Just keep in mind that is doesn't cover all conditions or materials.

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    \$\begingroup\$ These have been called lies to children. \$\endgroup\$ May 22 at 14:33
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    \$\begingroup\$ "All models are wrong. Some models are useful." \$\endgroup\$ May 23 at 0:48
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    \$\begingroup\$ @ColonelThirtyTwo That quote is from George Box. Let's give him credit. \$\endgroup\$ May 23 at 13:23
  • \$\begingroup\$ "If [..] your instructor pointed you at Maxwell's equations and told you to calculate the current through a resistor for a given voltage" the instructor would have mentioned ony the easier part and have omitted the more important and difficult one: solid state physics (based on quantum mechanics). Maxwell's equations are by far not sufficient to explain or derive Ohm's law. That's why Ohm's law is so useful: in very many cases it can be applied extremely accurately without knowing about the details of its solid state physics foundations. \$\endgroup\$
    – Curd
    May 25 at 12:45
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The big problem with your statement is that it seems you haven't understood what Ohm's law is actually about. I'm not saying it's your fault (maybe it depends on how it was taught to you).

Ohm's law, in its basic form, is fairly simple and extremely general:

It states that voltage across a "conductor" and the current in that same "conductor" are proportional.

The problem is that it applies only to a specific class of conductors, those called ohmic conductors, which are a specific type of conductors (e.g. pure metals or metals alloys).

It doesn't apply so easily (or at all) to components made of semiconductors, especially doped ones, such as diodes or to other materials (e.g. gasses).

For more details see the relevant wikipedia page.

As far as basic components are concerned, the only one that follows "exactly" Ohm's law is the resistor. I said "exactly" beacuse you have to neglect temperature increase and electrical limits. E.g.: if you apply a 1V across a 1ohm resistor and get 1A, you shouldn't expect the same reisistor to endure a 10kV voltage producing a 10kA, unless that resistor is REALLY big (e.g. an high-voltage cable).

And if you feel adventurous, you could explore how a real resistor really behaves and to which extent it is "linear" (another way to say that it follows Ohm's law), by reading a datasheet of resistors from some manufacturer, like this one.

The so-called "voltage coefficient of resistance" (VCR) tells you the extent of non-linearity in following Ohm's law at increasing voltages.

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    \$\begingroup\$ Usually the expected deviation from ohms law of a specific resistor is usually stated in the datasheet. \$\endgroup\$
    – lalala
    May 23 at 17:44
  • \$\begingroup\$ I'll point out that Ohm's Law is also only true in DC circuits; in AC circuits, even some circuits that would follow Ohm's Law in DC don't do so (e.g. if they include a coil of wire that acts as an inductor), because you need to take capacitance/inductance into account. \$\endgroup\$
    – nick012000
    May 24 at 4:20
  • \$\begingroup\$ @nick012000 That's a completely different matter. A coil of wire is not simply a "resistor". For slowly varying signals Ohm's law is still valid. As many have pointed out, Ohm's law is in itself an approximation. It's limits must be known, and they are numerous. That's doesn't mean it is applicable only at DC, which in itself is also an idealization. In the real world there is no such thing as DC as long as you take it mathematically, because at least when you switch it on it is a "step function" ... \$\endgroup\$ May 24 at 11:40
  • \$\begingroup\$ @nick012000 ... If you take a common 1kohm 1/4 W resistor and apply a 1V RMS 100Hz sine wave you get an 1mA RMS current sine wave. That's ohm's law and parasite L and C of the resistor are completely negligible at that frequencies (as is radiation, skin effect and proximity effect). Bottom line: Ohm's law is valid also with varying signals, as long as their frequency is low enough. \$\endgroup\$ May 24 at 11:40
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    \$\begingroup\$ @nick012000, Actually, you can use Ohm's law (and Kirchoff's laws, etc.) in a network of passive resistors, inductors, and capacitors if the network is driven by a single sinusoidal frequency. The trick is to compute the complex impedance of each component at the given frequency, and then do all of the math using complex numbers. \$\endgroup\$ May 24 at 13:50
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A man named Georg Ohm started empirical tests in 1825 to find what laws there exists in electric circuits. The tests were difficult because there was no proper understanding of the concepts of electricity and what material actually is. Think of making measurements in the era when the proper measure for a phenomena was not established, there were only different vague and possibly contradicting ideas. In addition respected philosophers said that no experiments are needed nor should be believed, because only a reasoned fact is a fact.

Ohm's law was an empirical finding. It bound together the quantity of the electricity, the intensity of the electricity (see NOTE1), the dimensions of a metal conductor and a materiel property of metals which varied from metal to metal. Today that material property is called resistivity.

Ohm's law can today be derived from electromagnetic field theory and the atomic and molecular structure of materials and it's validity range can be predicted with these theories. Resistors are specially made so that Ohm's law is good enough model in practical applications. Metal wires made of single homogenic alloy obey it, too. Semiconductor joints, many gases and liquids for example do not obey it as you have found by measuring with leds.

I suggest you to keep your both ears open during lectures. A competent teacher surely tells also something of the validity range of his formulas.

NOTE1: As said the concepts of the electricity were not established as names nor how they should be measured.

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When I started studying electronics I thought I could mathematically predict what would happen in every circuit but some components are impossible to predict precisely.

There is an old saying that all models are wrong, but some models are useful.

We build mathematical models of components based on a combination of our understanding of the underlying physics and our empirical observations. We simplify those models so that we can use them to design circuits.

Then we build the circuits and test if they behave the way we expected them to, or if we ignored something that actually turned out to matter. Some people use simulation between design and physical testing.

Taking for example a diode:

The simplest model we might use is a component that acts as a short circuit in one direction and an open circuit in the other direction.

The next step up (and the model used in many introductory electronics courses) is to assign a fixed voltage drop in the forward direction.

The next step up would be the Shockley diode equation, \$I=I_\mathrm{S} \left( e^\frac{V_\text{D}}{n V_\text{T}} - 1 \right)\$

Beyond that the next steps would depend on what we were trying to model, for a high frequency application junction capacitance (which varies with DC bias voltage) is likely to be important. For a high current application series resistance may be important.

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You can define the "resistance" as the ratio between voltage and current across a dipole. R=U/I.

Just like speed is defined as distance per time.

Some special components have the odd characteristic of having a constant "resistance" over a wide range of voltage (or currents)...

And actually having a mostly constant resistance is what occurs with most conducting materials : a piece of metal, the graphite inside a pencil, many examples. But, some devices don't have a constant resistance, that's the case, of course, of semiconductors. And the resistance of most materials can depend on other aspects, most notably temperature.

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Ohm law should be taken seriously, it is a pretty good mathematical approximation of what is happening in a resistive material and is good enough for most purposes.

It is however only that, an approximation, if you look at the behaviour of the material the resistance will vary with other factors most particularly with temperature.

As you have already discovered other components do not behave in the way a simple resistor does. The relationship between current and voltage is much more complex than the simple relationship you have tested for a resistor.

These relationships can also be expressed mathematically and there are a number of different equations for each component. As the equation or model becomes more precise, or closer to reality, it becomes more complex taking into account more variables.

This means that trying to work this out for combinations of components gets very complex very quickly and so we use computer tools or simulators to work it all out for us.

Part of the skill of an engineer is to decide how close to reality you need to get in order to do what you are trying to do and select the appropriate model.

Ohms law is good enough for most purely resistive components.

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Some components like LEDs, transistors, and diodes, don't have this linear relationship.

But they aren't resistors. Ohm's Law only applies to resistors and components that are 'resistive'.

I did some experiments and I found that it isn't always 100% accurate, though it is pretty precise with resistors.

The reason it's 'pretty precise' with resistors is that they are deliberately made to have a precise resistance. But why bother? Why not just make of use of whatever property a device has, 'resistive' or not? In some cases we do, but the property of having a linear relationship between voltage and current is very useful in electronic circuit design - particularly in analog circuits where we often want to accurately set voltages and currents and/or maintain proportionality.

But not always. Digital circuits generally don't need resistors, and where they do use them the resistance often doesn't have to be very accurate or linear. When you see a 'resistor' in the internal circuit of a digital IC it is often actually a MOSFET connected as a current source.

So the reason resistors follow Ohm's Law almost perfectly while other components don't, is that we want them to. That's why we call them 'resistors'.

When I started studying electronics I thought I could mathematically predict what would happen in every circuit but some components are impossible to predict precisely.

A basic principle of electronic design is that if a component's characteristics are precisely defined then you can precisely predict its performance. Components with unpredictable behavior are generally avoided (unless you want that property in eg. a noise generator) in favor of components that do allow us to mathematically predict what will happen.

Designing electronic circuits would be much harder if all the components behaved in ways that were hard to predict, which is why component manufacturers put a lot of effort into making parts with well defined characteristics. It's also one reason many circuits have far more parts in them than they could have if components were custom made to match the requirements of that particular circuit. Designers often prefer to use 'generic' parts such as resistors, capacitors etc. which have simpler behavior that is easier to calculate.

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Ohm's Law is not a law of physics, but rather, it is a constitutive relation for an electrical element called a linear conductor/resistor.

The concept of a constitutive relation for elements of mechanical, electrical, thermal, fluid, or magnetic systems is well developed in the broad field of engineering system analysis.

See the entry in Hyperphysics:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html

If the resistance is constant over a considerable range of voltage, then Ohm's law, I = V/R, can be used to predict the behavior of the material. Although the definition above involves DC current and voltage, the same definition holds for the AC application of resistors.

Whether or not a material obeys Ohm's law, its resistance can be described in terms of its bulk resistivity. The resistivity, and thus the resistance, is temperature dependent. Over sizable ranges of temperature, this temperature dependence can be predicted from a temperature coefficient of resistance.

When applying models for electrical elements the conductance or resistance of a circuit element depends on other specified factors that we recognize as (1) geometry; (2) properties of materials; and (3) operating conditions.

This is the Hyperphysics entry for resistivity (conductivity) as a property of material, its geometric shape, and temperature:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html#c2

This four page application note shows the I-V characteristic curve of a typical diode (non-linear resistor) that might be observed when using an instrument called Source-Measure Unit (SMU) to plot the I-V characteristic curve of a device under test (DUT):

https://www.mouser.com/pdfdocs/IVChrzDIodes2450_AN1.PDF

This 22 page reference shows the I-V characteristic curve for an ideal resistor (which is a straight line through the origin) on nominal pages 4-6:

https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-071j-introduction-to-electronics-signals-and-measurement-spring-2006/lecture-notes/03_kirchhoff1.pdf

Ohm's law in general refers to the constitutive relation R = V/I for any linear or non-linear resistive/conductive element. However Ohm's law may also refer to the linear I-V characteristic curve depending on the context.

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  • \$\begingroup\$ I don't see how calling Ohm's Law a "constitutive relation" makes any difference whatsoever. The sources you link repeat Ohm's Law, whether they call it that or not. And no one is claiming that Ohm's Law, as commonly used in circuit theory, is a "law of physics". Ohm's Law is simply the relationship between current and voltage for an ideal resistor...it is essentially the definition of an ideal resistor. \$\endgroup\$ May 21 at 22:42
  • \$\begingroup\$ If you want to engage in semantics calling it a "Constitutive Relation" is the custom in studies of signals and system analysis. I don't see how calling it "Ohm's Law" makes it anything other than the linear relation between voltage and current for something that you are calling an "ideal resistor". Constitutive Relations is the group or class to which Ohm's Law is a member. \$\endgroup\$ May 21 at 22:51
  • \$\begingroup\$ Well, you have changed your wording a great deal. Originally you said "No, do not take Ohm's Law for granted, since it is not a law of physics, and when we apply Ohm's law in system models it is typically described as a Constitutive Relation." This suggests that because Ohm's Law is not a law of physics and because you call it a constitutive relation that somehow its usefulness is lessened. \$\endgroup\$ May 22 at 0:09
  • \$\begingroup\$ I posted sources that describe the meaning of constitutive relations in engineering and scientific context. Ohm's law is just one type of constitutive relation that relates voltage to current for an ideal element. So no one should take Ohm's law for granted. It is not a law of physics and it is a constitutive relation. In fact a person who studies unified system models will recognize that this is the most useful way to understand Ohm's law for a resistor element or Hooke's law for a linear spring constant. \$\endgroup\$ May 22 at 2:06
  • \$\begingroup\$ @ElliotAlderson: The notion of "resistance" isn't really a physical quantity. Given two points, one can describe the potential difference between them without regard for why that potential difference exists. Likewise, one can describe the amount of charge that crosses a surface without regard for why the charge is moving. If at some moment in time a coulomb per second of charge is moving from one side of an object to the other, and potentials at the sides of the object differ by one volt, Ohm's Law defines the "resistance" of the part as one ohm. \$\endgroup\$
    – supercat
    May 23 at 20:48
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There's another implied question here, that might be what is actually being asked:

When I started studying electronics I thought I could mathematically predict what would happen in every circuit but some components are impossible to predict precisely.

I think that implies the question, "can you precisely mathematically predict what would happen in every circuit?" The answer to that is "yes," with varying amount of accuracy and complexity. You can mathematically model the quantum interactions of electrons in materials, abstract it away to device level equations, abstract that away to circuit level models.

Ohm's Law describes resistors only, so you need other models for other devices. Once you have the other models, your can mathematically predict how a circuit works. You'll learn them as you study electrical engineering some more.

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@Lorenzo Donati -- Codidact.com already got it correct and with great thoroughness. I'm simply going to reiterate an important point: the statement V=IR is always correct under all conditions, all voltages, all temperatures, whatever. But that's not Ohm's Law. Ohm's "Law" states that R is constant under all conditions. Of course that's not completely true 100% of the time or even 100% true any of the time. But it is approximately true for some devices over a limited range of conditions. Those devices are said to be "Ohmic."

So yes, you should take Ohm's Law seriously, but understand that it's not really a Law at all, it's just a simplifying assumption. If you understand when the assumption is applicable then it can make your work a lot easier.

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Should I take Ohm's law for granted?

Ohm's Law states, 'At a constant temperature, the current 'I' through a conductor is directly proportional to the potential difference 'V' applied across its ends.'

I α V

V/I = R

where 'R' is a constant, known as the resistance of the conductor at that temperature.

Ohm's Law is applicable to any conductor, with the exception of semiconductors and superconductors.

There should be no doubt on the veracity of Ohm's Law as it is easily verified.

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    \$\begingroup\$ "Ohm's Law is applicable to any conductor, with the exception of semiconductors and superconductors." Only in DC circuits. Things get more complicated in AC circuits, including some circuits that follow Ohm's Law in DC, because you need to take inductance/capacitance into account. Also, capacitors don't follow Ohm's Law in DC, either. \$\endgroup\$
    – nick012000
    May 24 at 4:24
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    \$\begingroup\$ @nick012000, Yes, it would be applicable to an AC circuit were the 'conductor' to be purely 'resistive'. By the way, the term 'resistance' was an offshoot of Ohm's Law. \$\endgroup\$
    – vu2nan
    May 24 at 5:25
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VU2NAN was onto something: "at constant temperature". Here are some lab experiments: Connect a 100 watt incandescent light bulb to a power supply and measure the voltage and current. From these you can calculate the resistance. Start with 1 volt. Then 10 volts. Then 100 volts. Do not be surprised if the resistance changes with the temperature of the filament.

Next, do the same thing with a 100 ohm 1 watt resistor. Start with 1 volt. then 10 volts. Then at 100 volts, you might find that the resistance suddenly increases to infinity! (Accompanied by a flash and a wonderful smell that says, "Welcome home, brother electronics experimenter.")

Then put a 10k resistor in series with a small neon lamp. You will find that the total resistance starts out at infinity, and then drops to a lower value at 100 volts. Almost the opposite of the 100 ohm resistor.

Finally, note that something like ohm's law applies to many things in physics, not just electric current. For example, in magnetism, ampere-turns = flux * reluctance. (And reluctance can change, just like electrical resistance) There are more examples in fluid dynamics, heat flow in solid objects, strain in a structural member under load, etc.
. . . K6YVL

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Ohm's Law is as fundamentally important to EE's as Einstein's Relativity equation (E = mc²) is to Physicists.

This was created 200 yrs ago by Georg Ohm, a Bavarian Physicist in 1824.

Later Maxwell's 20 Equations were unified from many other Physicists' Laws into the complete Theory of Electromagnetics. These are based on Laws of Physics upon which all linear electronics follow. Later Oliver Heaviside unified them into 4 equations which are mathematically still relevant today.
I recall we solved Ohm's Laws in class from these equations in Electromagnetic Theory classes.

These equations also inspired Einstein to develop his Laws of Relativity.

Does that make Ohm's Law true for every material? No

Scaling depends on the constant conductive property of materials.

Nonlinearity materials may be caused by insulator leakage, semiconductor exponential characteristics but have linear bulk resistance in saturation, thermal coefficients (tempco's), breakdown voltage, avalanche effects, magneto-resistive materials and RF loss effects such as skin effects and Eddy Current effects.

With experience on these above, you can predict these behaviours too and in some cases make constant assumptions for R on leakage of caps rated at max voltage but understand thermal and aging may affect this. Leakage leakage current are based on Arrhenius Laws of Chemistry and double for every 10 deg C rise. But the apparent collector-emitter resistance, Rce, is fixed from the "Early Effect" ( a high resistance ) as the Vce drops towards saturation reaches the bulk resistance between the metal-to-semi interface Rce bulk resistance as a switch. (1 to a few ohms for a small signal switch)

ESR is the effective Series Resistance of insulators which are dielectrics as in Capacitors. This is due to the metal-insulator interface and affects heat loss in caps using Ohm's Law. The same is true for coils at DC rated resistance or DCR which causes start current in motors.

You can even use Ohm's Law from DC to AC to RF as long as you understand the nonlinear contributions, the rules for reactive impedance as a function of f and the nonlinear material properties..

The combination of resistance, R and reactance,X equals impedance, Z(f)=R+X(f). These are orthogonal qualities based on Euclidean Vector geometry and Pythagoras's Law for the hypotenuse of the R and X.

But Ohm's Law still applies on each axis. For example, the reactance of 2 capacitors becomes an AC voltage transformer, just as 2 couple coils transforms voltage. But coils conduct heat far better, so capacitor transformers must be limited to small currents, such as reducing 100kV down to 100V monitors or 330V down to 6V offline converters.

Does that mean you cannot empirically predict any component? Yes, because you have not learned the dependencies for conductivity in nonlinear resistance. They teach the basics of linear and exponential semiconductor material in school, then you learn the non-linear properties of materials from direct experience, either in labs or on the job.

Does this mean your measurements were invalid? Not necessarily, but maybe. Often linear models of conductors are too simple as metal has a positive resistance increase with temperature (1:10 for a light bulb) or you overlooked secondary effects sharing bulk resistance or something else.

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You have hit the spot!

This is a long and interesting story. It is the heart of electronics. Crudely speaking, the name of the game is to make and use gadgets that have interesting and useful I-versus- V characteristics.

From Horowitz, Hill, "The Art of Electronics", page 3. :-)

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  • \$\begingroup\$ Why the downvote? \$\endgroup\$
    – Antonio
    May 26 at 9:41

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