Resistance: Definition & Difference Explained

[Sho Kano]

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?

 

[jfizzix]

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.

 

[David Lewis]

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.

 

[Dale]

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.

 

[Dale]

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.

 

[David Lewis]

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?

 

[Tom.G]

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

 

[davenn]

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

Regards
Dave

 

[Dale]

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".

 

[Dale]

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!

 

[anorlunda]

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.

 

[David Lewis]

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.

 

[davenn]

It would be more accurate to say the reactance of the capacitor is 1 ohm.

ONLY when dealing with AC, not DC

Capacitive reactance X_C and Inductive reactance X_L
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

 

[anorlunda]

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.

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.

 

[davenn]

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

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

 

[SteamKing]

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
​

 

[David Lewis]

(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.

 

[Dale]

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.

 

[davenn]

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

 

[houlahound]

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.

 

[NascentOxygen]

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?

 

[NascentOxygen]

My professor says resistance depends on,
$R\quad =\quad \frac { \rho L }{ A }$

$\rho$ is resistivity, it's a property of the material, and the unit of
resistivity is the ohm-meter

R is resistance and has units of ohms; we can measure resistance
using an ohmmeter

 

[NascentOxygen]

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.

 

[Sho Kano]

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?

 

[Sho Kano]

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?

 

[Sho Kano]

which is what I said

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

This isn't learned in a typical 2nd semester college physics class right?

 

[jbriggs444]

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.

 

[Sho Kano]

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?

 

[Sho Kano]

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

 

[jbriggs444]

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.

 

[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