"Chuck Harris" wrote in message
...
Hi Ratch,
No one has said all materials are ohmic.
L&M do not say it directly, but they imply it. See below
What I understand L&M to be saying is that if j is proportional to E,
the material is ohmic. Proportionality requires j and E to be
related by a CONSTANT (constant relative to j and E, that is).
If rho is a constant, the material is ohmic. If rho is not constant,
the material is not ohmic.
What you say above is true, but I don't see L&M saying that. Read
further.
In quoting L&M, I left off the first paragraph where they discuss rho
being constant, to wit:
[4. OHM's LAW
If there is no electric field in a conductor, there is also no
electric current; the mean velocity (v) of the charge carriers
(electrons) vanishes. In many, although by no means all, materials the
current density is proportional to the electric field:
j = (1/rho) * E (9-16)
The quantity rho is called the resistivity of the material; its inverse
1/rho is usually called the conductivity. It is a property of the
material; in addition, it will vary with the temperature of the
conductor.
So far so good. L&M agrees that not all materials have a proportionate
relationship between E and j.
Eq. (9-16) describes the current density in terms of the electric
field at a point in a conductor (Fig. 9-11). It is called Ohm's law.
materials that obey Ohm's law are usually called ohmic conductors. This
relation enables us to calculate the current flowing through a wire of
length L which is connected to two terminals - points between which
there is a potential difference V....]
Now here is where they crash. They first give equation (9-16) and call
it Ohm's law. Then they say that all materials that obey equation (9-16)
are ohmic. Well, all materials obey the resistivity equation (9-16).
Therefore by their reasoning, all materials are ohmic. They go on to say
that Ohm's law can be used to show the relationship between resisitivity,
current density, and electric field. That is certainly true for Equation
(9-16), but that is the resistivity equation and it stands on it own
independent of Ohm's law. The resistivity (9-16) is used to determine
whether a material has the Ohm's law property, but it is not Ohm's law per
se.
L&M could have said a bit more about what they meant about a material
not following Ohm's law; how they meant that a material that has a non
constant rho is non ohmic. However, I caught the meaning the first time
I read it, so it cannot have been too badly worded.
You were primed to understand it because of your exposure to this
discussion.
The trip from (9-16) to: V = RI is just a straight forward
rearrangement, and substitution. It still states the same thing as
(9-16). A material is non ohmic if R is not a constant.
I don't see L&M saying anything that corresponds to the last sentence
above. Again, the resistance equation V=IR can be used to determine if a
material has the Ohm's law property, but V=IR stands on its own and is not
Ohm's law per se. Look at
http://maxwell.byu.edu/~spencerr/websumm122/node50.html again. Ratch
-Chuck
Ratch wrote:
Yes, rho and R are proportional to each other, but that does not
answer
the question I asked before (see the first paragraph above). How does
L&M
define something as nonohmic when according to what they say, everything
is
ohmic because it follows V=IR (which they say is Ohm's law).
So, as a result, if R is some function of I, the material is non ohmic.
I agree with that, but according to what you said about what L&M
writes, that never happens because all materials follow V=IR. Does L&M
mention
nonohmic materials? Ohm's law cannot be both V=IR and constant
resistance
as current varies. Which one does L&M say it is? Ratch
There is no inconsistency.
Yes, according to what L&M says there is. Ratch