Resistance: Definition & Difference Explained

AI Thread Summary
Resistance in electrical circuits is defined by the formula R = V/I, which describes the relationship between voltage (V) and current (I). However, resistance is not a constant value; it varies with factors such as temperature, pressure, and applied voltage. The equation R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area, provides a more comprehensive understanding of resistance as a material property. The distinction between definitions and equations is important, as definitions establish conventions while equations calculate specific values. Overall, resistance is a physical concept that impedes current by converting energy, and the behavior of components like capacitors and inductors introduces additional complexities in AC circuits.
Sho Kano
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My professor says resistance depends on,
R\quad =\quad \frac { \rho L }{ A }

And is defined as,
R\quad =\quad \frac { V }{ I }

What does she mean? What is the difference?
A definition is denoted by \equiv, what is the difference between that and an ordinary equal sign?
 
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Electrical resistance is a physical concept like force, and not a mathematical one (so we wouldn't necessarily use the triple equals sign here).
In a related example, kinetic energy has been at times defined as half the mass times the square of the velocity, but this an equation that doesn't work when you're going near the speed of light. There are other definitions of kinetic energy that work well with special relativity, and reduce to the usual formula at low velocities.
The amount of resistance (as far as I know) is always equal to voltage over current, so you could define electric resistance by that ratio, but it's important to consider that that resistance is not just one constant for a given material. It depends on temperature, pressure, and applied voltage, among other things.
 
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R=V/I is not the definition of resistance. It's a formula to calculate its value.

Resistance is the property of a circuit or circuit element that impedes current by converting the current's kinetic energy to heat.
 
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David Lewis said:
R=V/I is not the definition of resistance. It's a formula to calculate its value.

Resistance is the property of a circuit or circuit element that impedes current by converting the current's kinetic energy to heat.
I disagree. Resistance is defined by ##R=V/I##, and the KE is negligibe, it is the PE in the field which is converted to heat.
 
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Sho Kano said:
My professor says resistance depends on,
R\quad =\quad \frac { \rho L }{ A }

And is defined as,
R\quad =\quad \frac { V }{ I }

What does she mean? What is the difference?
A definition is denoted by \equiv, what is the difference between that and an ordinary equal sign?
A definition in physics serves the same purpose as in ordinary language, it establishes a convention for the meaning of a given word or symbol. So ##R\equiv V/I## says that whenever we say ##R## we mean ##V/I##.

We can then use other information and definitions to deduce the relationship between ##R## and other quantities. Those deduced relationships are identified using the usual equals sign.
 
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Dale wrote: "Resistance is defined by R=V/I."

David Lewis wrote: You apply 1V to a capacitor, the initial current is 1A, so the resistance of the capacitor at that moment is 1 ohm?
 
David Lewis said:
Dale wrote: "Resistance is defined by R=V/I."

David Lewis wrote: You apply 1V to a capacitor, the initial current is 1A, so the resistance of the capacitor at that moment is 1 ohm?

the apparent resistance of the capacitor is 1 Ohm, Yes
the current into and out of the cap is initially 1A and falls rapidly as the capacitor is energised ( reaches equilibrium)
NOTE: NO current flows through the capacitor tho.

and another note ... please learn to use the reply button so as to quote people ...
doing the "he wrote, she wrote" etc thing can get very confusing to read :wink:

Regards
Dave
 
David Lewis said:
You apply 1V to a capacitor, the initial current is 1A, so the resistance of the capacitor at that moment is 1 ohm?
That isn't the way that capacitors work, but in principle, yes. In a capacitor I is not proportional to V so it's resistance is not constant. Materials for which I is proportional to V are called "Ohmic".
 
  • #10
Tom.G said:
The International Standard for resistance is based on the Hall Effect. Here is a link, but beware, it's dense reading.

http://www.bourbaphy.fr/jeanneret.pdf
Thanks, that is an excellent paper!
 
  • #11
ohms.jpg


Dale is right, resistance is merely the relationship between voltage V and current I. Components do not need to be linear, nor passive, so that many relationships are possible. The picture attached illustrates a few. (The one labeled battery represents a battery with internal resistance.).

The arbitrary curve is not impossible. R could be defined as the slope of a line connecting any two points on the arbitrary curve. The value could be positive, negative or zero.
It is only when we have approximately linear materials, that R becomes nearly constant (see the black line in the chart). That is what your professor had in mind, but it is not the only possibility.

The international standard defines the ohm, not resistance. ohm is to resistance as a meter is to distance.
 
  • #12
It would be more accurate to say the reactance of the capacitor is 1 ohm. Resistance is not the only physical quantity that can impede current or influence voltage/current ratios.
 
  • #13
David Lewis said:
It would be more accurate to say the reactance of the capacitor is 1 ohm.
ONLY when dealing with AC, not DC

Capacitive reactance XC and Inductive reactance XL
are very different beasts to plain resistance. Yes they are both measured in Ohms
but that is where the similarity ends

You cannot use Ohms Law, R = V/I, to determine resistance in an AC circuitD
 
  • #14
davenn said:
You cannot use Ohms Law, R = V/I, to determine resistance in an AC circuit

That's true davenn in that form, but Ohms Law comes in several forms. See the Insights Article, AC Power Analysis: Part 1, Basics for the complex form.

AC Power Analysis: Part 1 said:
DC Ohm’s Law ##V=I\cdot R## becomes AC ##\bar V=\bar I\cdot \bar Z## where ##\bar Z## is the complex impedance. ##\bar Z## includes resistance, inductance, and capacitance.
 
  • #15
anorlunda said:
That's true davenn in that form, but Ohms Law comes in several forms. See the Insights Article, AC Power Analysis: Part 1, Basics for the complex form.

which is what I said :wink:

if capacitive and inductive reactances are followed up with some research by David Lewis
he's going to come across the term impedance pretty quickly :smile:
 
  • #16
This is a graphical illustration of resistance:


http://cdn.pjmedia.com/instapundit/wp-content/uploads/2016/04/Screen-Shot-2016-04-02-at-8.10.41-PM.png
 
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  • #17
davenn said:
(A capacitor exhibits reactance) ONLY when dealing with AC, not DC
It may be AC or DC. The only requirement is that the voltage is changing.
 
  • #18
David Lewis said:
It may be AC or DC. The only requirement is that the voltage is changing.
If it is DC then the voltage is not changing, by definition.
 
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  • #19
David Lewis said:
It may be AC or DC. The only requirement is that the voltage is changing.

this is incorrect ... so you just contradicted yourself
see Dale's response
 
  • #20
Dale said:
If it is DC then the voltage is not changing, by definition.
DC voltage can change as much as it wants it just can't change polarity from pos/neg...or neg/pos.
 
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  • #21
David Lewis said:
David Lewis wrote: You apply 1V to a capacitor, the initial current is 1A, so ...
You invented a fictional value of 1A here, to illustrate your example. How did you decide on that particular value?
 
  • #22
Sho Kano said:
My professor says resistance depends on,
R\quad =\quad \frac { \rho L }{ A }
##\rho## is [/color]resistivity[/color], it's a property of the material, and the unit of
resistivity is the ohm-meter :wideeyed:

R is resistance [/color]and has units of ohms; we can measure resistance
using an ohmmeter :woot:
 
  • #23
houlahound said:
DC voltage can change as much as it wants it just can't change polarity from pos/neg...or neg/pos.
The term DC is quite maleable, it can accommodate changes in polarity as well as changes in magnitude. For this reason, it is usually important to more precisely describe what you are talking about, instead of leaving it up to people to guess or assume.
 
  • #24
Dale said:
I disagree. Resistance is defined by ##R=V/I##, and the KE is negligibe, it is the PE in the field which is converted to heat.
Is that because of the small mass?
 
  • #25
jfizzix said:
Electrical resistance is a physical concept like force, and not a mathematical one (so we wouldn't necessarily use the triple equals sign here).
In a related example, kinetic energy has been at times defined as half the mass times the square of the velocity, but this an equation that doesn't work when you're going near the speed of light. There are other definitions of kinetic energy that work well with special relativity, and reduce to the usual formula at low velocities.
The amount of resistance (as far as I know) is always equal to voltage over current, so you could define electric resistance by that ratio, but it's important to consider that that resistance is not just one constant for a given material. It depends on temperature, pressure, and applied voltage, among other things.
Does that mean V/I will always be the value of resistance at that particular moment?
 
  • #26
davenn said:
which is what I said :wink:

if capacitive and inductive reactances are followed up with some research by David Lewis
he's going to come across the term impedance pretty quickly :smile:
This isn't learned in a typical 2nd semester college physics class right?
 
  • #27
Sho Kano said:
Is that because of the small mass?
If you roll a bowling ball down a flight of stairs, it gets a fair bit of kinetic energy at each step. It picks up kinetic energy at each step and stops cold as it hits the next one down.

If you shrink that bowling ball [retaining its original mass] and drop it down a stairs with the same total height but with steps that are at the size scale of atoms then it will lose the same total amount of potential energy. But the kinetic energy that it gains between each step and the next becomes nearly negligible.

It's not mass -- it's step size.
 
  • #28
jbriggs444 said:
If you roll a bowling ball down a flight of stairs, it gets a fair bit of kinetic energy at each step. It picks up kinetic energy at each step and stops cold as it hits the next one down.

If you shrink that bowling ball [retaining its original mass] and drop it down a stairs with the same total height but with steps that are at the size scale of atoms then it will lose the same total amount of potential energy. But the kinetic energy that it gains between each step and the next becomes nearly negligible.

It's not mass -- it's step size.
If you drop a bowling ball or any ball down a flight of stairs, it does stop moving right at the instant it reaches the next step, but how does it keep on moving down? Is it because there is some kind of elastic potential energy stored in the ball's compression?
 
  • #29
Dale said:
I disagree. Resistance is defined by ##R=V/I##, and the KE is negligibe, it is the PE in the field which is converted to heat.
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
 
  • #30
Sho Kano said:
If you drop a bowling ball or any ball down a flight of stairs, it does stop moving right at the instant it reaches the next step, but how does it keep on moving down? Is it because there is some kind of elastic potential energy stored in the ball's compression?
Handwaving the concern away.. Add a trivial slope to each step.
 
  • #31
jbriggs444 said:
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?
 
  • #32
Sho Kano said:
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.
 
  • #33
Sho Kano said:
Is that because of the small mass?
Yes. It is a worthwhile exercise to actually calculate the KE.
Sho Kano said:
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.
 
  • #34
davenn said:
...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.
 
  • #35
Sho Kano said:
Does that mean V/I will always be the value of resistance at that particular moment?
I believe so, yes
 
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  • #36
David Lewis said:
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.
 
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  • #37
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.
 
  • #38
ZapperZ, Would it be fair to say then resistance arises when electrical energy is converted to heat or radiation?
 
  • #39
David Lewis said:
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.
 
  • #40
Dale said:
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 (XL) 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. :)
 
  • #41
nasu said:
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.
 
  • #42
How does the resistance changes in time?
Or even the reactance component?
 
  • #43
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?
 
  • #44
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.
 
  • #45
nasu said:
Sure. But the the resistance of the coil is not defined as that ratio.
Then that is the disagreement at hand.
 
  • #46
nasu said:
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.

nasu said:
I think that Introducing reactance in the discussion about resistance is not useful anyway.
I agree. It should not have been introduced.
 
  • #47
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.
 
  • #48
nasu said:
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.
 
  • #49
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.
 
  • #50
nasu said:
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?
 
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