Resistance: Definition & Difference Explained

[Sho Kano]

Handwaving the concern away.. Add a trivial slope to each step.

Meaning if you drop a ball straight down on a step, it will bounce off horizontally?

 

[jbriggs444]

Meaning if you drop a ball straight down on a step, it will bounce off horizontally?

It's an analogy. It is not meant to be taken literally. The hypothetical bowling ball falls down, loses its kinetic energy in an inelastic collision with the next stop down, gently rolls to the edge of the step and falls again. The cycle repeats.

 

[Dale]

Is that because of the small mass?

Yes. It is a worthwhile exercise to actually calculate the KE.

So if there is no change in kinetic energy, the potential energy must be the one contributing to the heat? I thought heat was from collisions of the electrons

It is a needless complication. Electrons are not little billiard balls coliding with bigger billiard balls, and actually modeling their behavior is fairly complicated. All of the energy transfer can be understood purely classically in terms of the fields, which is my preference.

 

[David Lewis]

...the current into and out of the cap is initially 1A and falls rapidly as the capacitor is energised (reaches equilibrium)

We don't know how rapidly the current falls. Not enough info was provided under the scenario I outlined to calculate it.

The definition for resistance must specify by what mechanism current is impeded (or V/I ratio is affected) in order to distinguish it from reactance.

 

[jfizzix]

Does that mean V/I will always be the value of resistance at that particular moment?

I believe so, yes

 

[Dale]

The definition for resistance must specify by what mechanism current is impeded (or V/I ratio is affected) in order to distinguish it from reactance.

No, it doesn't. A component with reactance simply has a non constant resistance. There is no need to specify the mechanism.

 

[ZapperZ]

I find it rather amusing that after 2 pages of discussion on this, not once did I see anyone suggesting that the origin of "resistance" or "resistivity" in a material arises out of the concept the Drude model, which is really the microscopic derivation of Ohm's Law. In it, the origin of the presence of "resistance" for an ideal conductor is clearly laid out.

Maybe this is not considered since the level of knowledge appears to be in First-year physics. But considering all that has transpired here, and how things are going around in circles as people tried to figure out what caused what, maybe it is necessary to go to a more fundamental level.

Zz.

 

[David Lewis]

ZapperZ, Would it be fair to say then resistance arises when electrical energy is converted to heat or radiation?

 

[ZapperZ]

ZapperZ, Would it be fair to say then resistance arises when electrical energy is converted to heat or radiation?

You are mixing the cause and effect. The presence of resistance LEADS to heat (i.e. Ohmic heating), not the other way around, i.e. the conversion of electrical energy into heat leads to resistance.

At the simplest level, resistance is the collision between electrons and (i) other electrons (ii) lattice ions (iii) impurities.

Zz.

 

[nasu]

No, it doesn't. A component with reactance simply has a non constant resistance. There is no need to specify the mechanism.

You mean the resistance (R) of a coil which has reactance as well (X_L) is not constant? It varies in time? Or you mean some other type of "non-constant"?
Maybe you are trying to simplify thing more they can be. :)

 

[Dale]

You mean the resistance (R) of a coil which has reactance as well (XL) is not constant? It varies in time? Or you mean some other type of "non-constant"?

It is not constant wrt time and wrt frequency.

 

[nasu]

How does the resistance changes in time?
Or even the reactance component?

 

[jbriggs444]

You agree that if one divides the instantaneous voltage drop across the coil by the instantaneous current across the coil, the quotient is not fixed, right?

 

[nasu]

Sure. But the the resistance of the coil is not defined as that ratio. Neither the inductive reactance of the coil.
They are both constants, for a given coil and frequency. Saying that resistance is not constant implies a different definition of resistance and may create confussion rather than clarifying the subject.

I think that Introducing reactance in the discussion about resistance is not useful anyway.

 

[jbriggs444]

Sure. But the the resistance of the coil is not defined as that ratio.

Then that is the disagreement at hand.

 

[Dale]

Sure. But the the resistance of the coil is not defined as that ratio.

Yes, it is. By definition R=V/I. That ratio is the definition of resistance, and it is not constant wrt time for an inductor as jbriggs444 showed above.

If you disagree with that definition, then can you please provide a reference that defines it differently? There may very well be alternative definitions, as happens often.

I think that Introducing reactance in the discussion about resistance is not useful anyway.

I agree. It should not have been introduced.

 

[nasu]

Well, you say "by definition". Do you have a reference for that?
I am not just trying to bounce back the question to you. But it is not so easy to find a definition for the resistance for the general case.

Maybe could just specify what will you call the quantity labeled by R in many RLC circuits, and which is given as 4 Ohms, for example.
Do you call this resistance or something else?

Of course, for an inductive coil, the resistance is not a separate component and it may be the question what u do you consider in u/i.
If you take the overall u, over the coil, what you get depends on bot R and L and frequency. The voltage across the resistive part of the coil's impedance cannot be measured directly, I suppose. But we can model the coil as an RL circuit where R is what you measure in a DC (constant current) regime.

 

[Dale]

Well, you say "by definition". Do you have a reference for that?
I am not just trying to bounce back the question to you. But it is not so easy to find a definition for the resistance for the general case.

The definition is easy to find. $R=V/I$. It is not always useful, but it is clearly defined.

Wikipedia uses that definition as does my old introductory physics text (Serway, Physics for Scientists and Engineers, P 759, 3ed, 1990). A lot of texts introduce Ohm's law without explicitly defining resistance.

 

[nasu]

I was talking a bout a general definition, one that can be applied to AC circuits, including the resistance of an inductive coil.
What is the meaning of these symbols (V,I) for circuits with non-constant voltage and current?
In my books capital letters are usually used for either constant values (DC circuits) or RMS values (AC circuits). In both cases their ratio is constant in time.

 

[Dale]

I was talking a bout a general definition, one that can be applied to AC circuits, including the resistance of an inductive coil.

The definition certainly can be applied to AC circuits and inductive coils.

When you apply the definition for certain elements or circuits the result is not constant. So what? Why should the result of all definitions be preordained to be constant?

 

[nasu]

By what definition is not constant? R=V/I gives a constant for both AC and DC circuits, as V and I are constants even for AC circuits. (with notations used in Serway in the chapter about AC circuits).

You did not say what would you call the R quantity in an RLC (or just RL) circuit. As used in the Serway text which you mentioned, for example. Is that dependent of time?

 

[leright]

The definition of resistance, more precisely than R = V/I is R = dV(I)/dI. As the others have pointed out, resistance is really the instantaneous slope (derivative) of the V vs. I curve. The resistance is not constant for materials that are not ohmic. It varies with current...meaning the V vs. I curve is not a straight line. It is not even constant for resistors. It's just an approximation we use. Resistors have increased resistance at higher currents because the temperature increases as current increases.

There can be negative differential resistance as well with some devices.

 

[leright]

Also, make sure to be clear with terminology. Resistance is generally frequency independent but impedance is frequency dependent. For inductors the magnitude of the impedance increases as frequency increases whereas for capacitors the magnitude of the impedance decreases as frequency increases.

Also, resistance is purely a real number, whereas impedance is a complex number, consisting of both a resistance (real) and a reactance (imaginary). Resistors are generally only resistive (real) and inductors/capacitors are generally only reactive (imaginary). When you combine resistors with inductors or capacitors then you get a combination of real and imaginary components of impedance. But to say a capacitor or inductor exhibits a resistance (other than parasitic effects) is incorrect, I'd say.

 

[stevendaryl]

Well, you say "by definition". Do you have a reference for that?
I am not just trying to bounce back the question to you. But it is not so easy to find a definition for the resistance for the general case.

The relationship between voltage and current for a circuit may be extremely complicated. To me, it is only useful to talk about "resistance" in the case where the voltage is (approximately) linearly proportional to the current.

We can define an ideal resistor to be a linear circuit element such that the voltage drop across the element is proportional to the current through the element. If a circuit element is a resistor, then we can define the resistance to be R = V/I.

We can define an ideal capacitor to be a linear circuit element such that the voltage drop across the element is proportional to the charge on the element (the charge being the time integral of the current flowing into the element). If a circuit element is a capacitor, then we can define the capacitance to be C = Q/V.

We can define an ideal inductor to be a linear circuit element such that the voltage drop across the element is proportional to the time derivative of the current. If an element is an inductor, then we can define the inductance by: L = V/\frac{dI}{dt}.

For non-ideal circuit elements (which means any actual circuit element), we can often approximately describe them as a combination of ideal elements, where R, C and L may be nonconstant. But this is only a heuristic description---there is nothing fundamental about it. There is no absolute answer to the question: "What is the resistance of this actual, nonideal, circuit element?" You can model the circuit element as a combination of time-dependent, or current-dependent, or frequency-dependent resisters, inductors or capacitors, but I don't think that the question "What is the element's resistance?" makes any sense outside of the particular way you've chosen to model it.

 

[Dale]

By what definition is not constant? R=V/I gives a constant for both AC and DC circuits, as V and I are constants even for AC circuit

Please provide a reference for this claim as well as for any alternative definition of resistance that you would like to use.

 

[Dale]

The definition of resistance, more precisely than R = V/I is R = dV(I)/dI. As the others have pointed out, resistance is really the instantaneous slope (derivative) of the V vs. I curve. The resistance is not constant for materials that are not ohmic. It varies with current...meaning the V vs. I curve is not a straight line.

That is another suitable definition for resistance. A circuit textbook of mine did not explicitly define resistance in the text, but when it introduced Ohm's law it drew a picture of the V/I curve for a resistor with a little graphic indicating that the slope was R. I actually prefer that definition since it is easier to apply to things like voltage and current sources.

The Wikipedia article calls it "differential resistance" to distinguish it from "chordal resistance". I am not sure where that terminology came from so I am not sure I trust it.

 

[David Lewis]

R=V/I is a perfectly good definition for resistance, with two caveats:

1. Since reactance also equals V/I, the definition only applies when electrical energy is converted to heat or radiation.

2. V/I defines resistance in the particular sense (how much you have, or would have, in particular cases). Whenever a physical quantity is defined in the particular sense, it's conveyed as a formula, with physical quantities represented by algebraic variables.

In the general sense, resistance is the property of a circuit or circuit element that opposes current in the process of converting electrical energy to heat or electromagnetic radiation. Whenever a physical quantity is defined in the general sense (what it is) it's expressed rhetorically, i.e. numbers are not put to it.

 

[leright]

The relationship between voltage and current for a circuit may be extremely complicated. To me, it is only useful to talk about "resistance" in the case where the voltage is (approximately) linearly proportional to the current.

Not unless you use the more general definition of resistance, R = dV/dI, which reduces to R = V/I for devices with linear V vs. I characteristics.