# B What is resistance?

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1. Apr 2, 2016

### 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?

2. Apr 2, 2016

### 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.

Last edited: Apr 2, 2016
3. Apr 2, 2016

### 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.

Last edited: Apr 2, 2016
4. Apr 2, 2016

### Staff: Mentor

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.

5. Apr 2, 2016

### Staff: Mentor

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.

6. Apr 2, 2016

### 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?

7. Apr 2, 2016

8. Apr 3, 2016

### davenn

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

9. Apr 3, 2016

### Staff: Mentor

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. Apr 3, 2016

### Staff: Mentor

Thanks, that is an excellent paper!

11. Apr 3, 2016

### Staff: Mentor

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. Apr 3, 2016

### 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.

13. Apr 3, 2016

### davenn

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 circuit

D

14. Apr 3, 2016

### Staff: Mentor

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.

15. Apr 3, 2016

### davenn

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

16. Apr 3, 2016

### SteamKing

Staff Emeritus
This is a graphical illustration of resistance:

Last edited by a moderator: May 7, 2017
17. Apr 3, 2016

### David Lewis

It may be AC or DC. The only requirement is that the voltage is changing.

18. Apr 3, 2016

### Staff: Mentor

If it is DC then the voltage is not changing, by definition.

19. Apr 3, 2016

### davenn

this is incorrect ... so you just contradicted yourself
see Dale's response

20. Apr 4, 2016

### houlahound

DC voltage can change as much as it wants it just can't change polarity from pos/neg...or neg/pos.

Last edited: Apr 4, 2016
21. Apr 4, 2016

### Staff: Mentor

You invented a fictional value of 1A here, to illustrate your example. How did you decide on that particular value?

22. Apr 4, 2016

### Staff: Mentor

$\rho$ 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

23. Apr 4, 2016

### Staff: Mentor

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. Apr 5, 2016

### Sho Kano

Is that because of the small mass?

25. Apr 5, 2016

### Sho Kano

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