Proportionality And Its Consequences

[MrAl]

Both R and V are variables. There isn't anything special about V that gives it some special status over R. In any real cirucit, you can vary V AND R to affect the current, which is also a variable. Constants are things like the Universal Gravitation Constant, Avogrado's Number and Boltzmann Constant, as in the previously mentioned, PV=nRT. In the case of Ohm's law, the constant of proportionality is unity.

If R was a constant, they it wouldn't be included on the little triangle that noobs use to calculate these quantities. Do you ever see anyone calculating Boltzmann's constant from pressure and temperature?

Hi again,


That's funny, because i posted that "you have to know the variables
from the constants" and you go right ahead and try to say that a
constant is again a variable!
If you want to keep asserting this go right ahead, but why didnt you
then answer the question about whether A,B,C, and D are constants
or not?

So now lets see what you know about mathematical equations...
In the equation again:

y=A*x^3+B*x^2+C*x+D

are A,B,C, and D constants or variables?

 

[BrownOut]

A, B, C and D are irrelevant.

 

[MrAl]

A, B, C and D are irrelevant.

Hello again,


I think you are copping out of the question. I am asking this question
for a good reason: knowing what are constants and what are variables
in equations is a very important concept to understanding the basic
nature of what is being stated by the equation itself. That is, knowing
this helps to clarify and even define just what kind of relationship we
are dealing with.
BTW, i am happy that you are interested in this. Many people dont
care one way or the other

So again, are A,B,C, and D constants or variables?

I'll be waiting for your answer...

 

[BrownOut]

I think you're getting off-track with your irrelevant questioning. I've given you 3 good examples of constants, so why continue to pursue this? In all of the equations we've discussed, we can easily define the constants and variables:

F = Gm1m1/R^2; G is constant m1, m2, and r are variables

PV = nRT; R is constant, P, V, n, and T are variables.

E = IR; E, I and R are variables.

See? I can tell a constant from a variable.

But I'll answer your question. A, B, C and D are simply coefficients. They can be constants, vaiables or functions. If you don't believe me, look at the insert. These lines are described by the equation: (rearranged to look like your equation)

-1/2uCoxW/LVds^2 + 1/2uCoxW/L(Vgs-Vth)Vds - id = 0

Notice how the first order coefficient is allow to change? If it were strictly a constant, that would not be allowed.

 

[shimniok]

shimniok:
Then i guess you should argue with the writers of those definitions because they all say proportionality exists in the Ohm's Law. R is a CONSTANT.

If you define R as a constant for a given circuit, then yes, I agree proportionality exists---and I said as much in my last post.

So in the special case of Ohm's law applied to a constant resistance (or, for that matter, a constant voltage; or, for that matter a constant current), then Ohm's law describes proportionality, defined as a constant ratio between two variables.

To help with the terminology, here's an excerpt from Wikipedia

----8<----
A constant in mathematics is an amount that does not change, over time or otherwise: it is a fixed value. In most fields of discourse the term is an antonym of "variable", but in mathematical parlance a mathematical variable may sometimes also be called a constant. [emphasis mine]

More particularly, the term constant has several uses:

* In mathematics and computer science:
o Mathematical constant, a number that arises naturally in mathematics, such as π and e
o A coefficient or other parameter in a formula; given as a number or as a variable, but not being considered one of the arguments
...
In physics and chemistry:
* Physical constant, a physical quantity that is generally believed to be both universal in nature and constant in time, such as c, the speed of light, or h, the Planck constant

 

[MrAl]

I think you're getting off-track with your irrelevant questioning. I've given you 3 good examples of constants, so why continue to pursue this? In all of the equations we've discussed, we can easily define the constants and variables:

F = Gm1m1/R^2; G is constant m1, m2, and r are variables

PV = nRT; R is constant, P, V, n, and T are variables.

E = IR; E, I and R are variables.

See? I can tell a constant from a variable.

But I'll answer your question. A, B, C and D are simply coefficients. They can be constants, vaiables or functions. If you don't believe me, look at the insert. These lines are described by the equation: (rearranged to look like your equation)

-1/2uCoxW/LVds^2 + 1/2uCoxW/L(Vgs-Vth)Vds - id = 0

Notice how the first order coefficient is allow to change? If it were strictly a constant, that would not be allowed.

Hi,


Yes, they are coefficients but those coefficients are almost always
constants. They are not functions unless written as A(...), etc.

But, let me be a little more succinct for you...

-------------------------------------------------------
In my application i need to use the equation:

y=A*x^3+B*x^2+C*x+D

where
A, B, C and D are predetermined constants.
--------------------------------------------------------

Now, the question is, in the above application, are A, B, C and D
constants or not?

I'd very much like to hear your answer now TIA.

 

[BrownOut]

You're wasting space and time with trival questions. I've already answered your question, and coefficients are, in genreal, not constants.

If you have any non-trivial questions, I'll answer. Otherwise, we're done here.

 

[shimniok]

-------------------------------------------------------
In my application i need to use the equation:

y=A*x^3+B*x^2+C*x+D

where
A, B, C and D are predetermined constants.
--------------------------------------------------------

You have defined them as constants, so they are constants, obviously.

Are you saying that A, B, C, and D MUST ALWAYS be constants in that equation whether or not you explicitly define them as constants?


Here's another example:

In my application I have a thermistor attached across an ideal voltage source of fixed value (9V). The resistance of the thermistor is (heheh) proportional to temperature given by the function, say, Fr(t) = 2t

In the case of this particular circuit:

V = IR
where V=9V, R=Fr(t)=2tΩ

Is R a constant, coefficient or variable? Why?

Is V a constant, coefficient or variable? Why?

What about I?

Michael

 

[MrAl]

You're wasting space and time with trival questions. I've already answered your question, and coefficients are, in genreal, not constants.

If you have any non-trivial questions, I'll answer. Otherwise, we're done here.

Hi,

That's your opinion. Even when it is predetermined that A,B,C,D are
constants ahead of time for a given application you can not admit
that they are constants. That was my point. Once you get past
that, we can move on.

 

[MrAl]

You have defined them as constants, so they are constants, obviously.

Are you saying that A, B, C, and D MUST ALWAYS be constants in that equation whether or not you explicitly define them as constants?


Here's another example:

In my application I have a thermistor attached across an ideal voltage source of fixed value (9V). The resistance of the thermistor is (heheh) proportional to temperature given by the function, say, Fr(t) = 2t

In the case of this particular circuit:

V = IR
where V=9V, R=Fr(t)=2tΩ

Is R a constant, coefficient or variable? Why?

Is V a constant, coefficient or variable? Why?

What about I?

Michael

Hi Michael,

I was just trying to see if the person arguing a point could see the
difference between something that is arbitrarily defined and something
that is defined very specifically.

When it is *stated* that A,B,C, and D *are* constants (for an application)
there is no way around it...they have to be constants...because they
are defined that way beforehand. In other words, we know a certain
physical process and it can be defined very concisely only when A,
B,C, and D are contants. I could show examples but this should be clear.

I think what is happening is that just because resistance is measured
in 'ohms' they think all resistance is somehow defined by Ohm's Law.
Ohm's Law is a very specific relationship between v and i, and without
R being constant there is no relationship to speak of.
For example, if we define:
y=x*r
we have an equation, but *just* an equation, but when we define:
y=x*R
we have defined a very specific relationship, not just an equation.
It's a relationship that links many many values of x and y together,
not just one single pair.

Lets take a quick look at another common equation...

v=v(0)*(1-e^(-a*t))

Now if we define a to be a constant, we have a nice equation that
tells us the way a regular capacitor charges, for example. If we
instead define a to be a variable, we loose that uniqueness. Now
we may choose to modify that to make 'a' a variable for some other
type of problem, but for our simple capacitor we have to make it
a constant or else the equation doesnt match up with the physical
phenomenon anymore.

This isnt about equations, it's about the physics of things where
the relationship already exists and we want to be able to describe
that relationship using mathematics.

It is important i guess that we dont take anyones word for it one way or
another, but at least the reader should try to understand why this is so.

Ask the question, "Why would R have to be constant in Ohm's Law",
and then seek to find out what could possibly make so many web sites
and so many professors all state R as a constant.

The key to understanding this is in the phrase "in direct proportion to",
that's why i started this thread talking about that unique relationship.

 

[BrownOut]

Hi,

That's your opinion. Even when it is predetermined that A,B,C,D are
constants ahead of time for a given application you can not admit
that they are constants. That was my point. Once you get past
that, we can move on.

It's not about an admition or a lack thereof, it's about a trivial question that doesn't warrent an answer, ie "If it's a constant, is it a constant." Being a constant means it never changes. What's so hard about that? I've answered your question about the linearity of coefficients. Time to move on.

 

[BrownOut]

so many web sites

Yeah, all those websited are written by physicits. NOT!

so many professors all state R as a constant

You'll only find Commumity College professors making claims so clearly wrong. You'll never hear a claim like that in advanced physics lectures.

 

[MrAl]

Yeah, all those websited are written by physicits. NOT!


You'll only find Commumity College professors making claims so clearly wrong. You'll never hear a claim like that in advanced physics lectures.

Hello again,


Nope, universities.
This is FAR too simple for that kind of requirement anyway.

Let me ask you this then...

Why exactly don't you believe that in Ohm's Law that R must be constant?

Before you answer, please be aware that if you make R a variable as in:
y=x*r

then you have just allowed x and y to be any point on the xy plane, and that is
no more a statement of what this 'Law' is then stating what the xy plane itself is.
It wont help if we say, "pick any value for R you feel like picking, and that
is the law", because gee i could make y anything i want it to be for any x.
What kind of physical phenomenon could that possibly describe?
I guess we could say F=m*a right?

When we limit the 'Law' to R being a constant, we say something very
unique about all the possibilities of x and y.

So maybe i dont understand why you think R should be a variable to begin with,
so i ask you the question then:
"Why exactly don't you believe that in Ohm's Law that R must be constant?"

If you like, you can also tell me what law this is:
c=a*b
I would be very interested to hear your opinion about this too.

I also have taken the time to graph both v=i*r and v=i*R in the attachment.
Notice how the pic on the right seems to describe something very particular,
while the left side takes up the whole first quadrant.

 

[BrownOut]

Heh, you're trying to show a 3 dimential quantity on a 2-D graph. That's a very basic error, so it calls into question all your other mathamatical assertions. Look at the graph I provided earlier, that's the only reasonably you can graph that quantity, unless you use 3-d modeling software.

In physics, there are many, many, many phenomona that can't be graphed. That doesn't mean they are invalid.

It's clear you're trying every dodge you can think of. You might want to ask yourself why this takes to much to prove? A proff should be simple.

 

[MrAl]

I can see you dont truely want to discuss this, just assert your (wrong)
opinion. You make assertion after assertion, yet dont answer the questions
you are asked. You wont even state exactly why you dont believe that
R has to be constant, because you know that will show exactly how and why
you are wrong.

We dont need 3d graphing because what we are talking about is much much
simpler than that. You're still just trying to complicate in order to avoid
commitment to any one argument.

You said r was a variable, and i showed you what happened when we allowed
it to be a variable. We end up saying something like F=m*a or c=a*b
rather than stating what Ohm's Law really is.
Yes, there are other relationships we might look at like v=i*r^2 or whatever,
but it again will not be Ohm's Law.

For the last time...

Ohm's Law is a very very SPECIFIC rule, that states the relationship between
current and voltage in a conductor, and that that relationship isnt just any ol'
relationship, it is the relationship of PROPORTIONALITY.
What is is not is: it is not a more general relationship like c=a*b, or F=m*a.

BTW i asked myself why this takes so much to 'prove', and i realized that first
of all i am not trying to prove anything because it has been proved long ago,
and second that it takes longer to get through to people who have closed
minds.


"In physics, there are many, many, many phenomona that can't be graphed.
That doesnt mean they are invalid"

Yes, and Ohm's Law isnt one of them because it can be graphed quite easily
for v and i, that's the whole point!

Answer some questions for a change? How do you think R varies if it is a variable?

 

[BrownOut]

Ohm's law can be graphed for vaiablble V and R. It does requre a 3_D graph to see this correctly. But I posted a good approximation for this relationship on an earlier post. You want to just ignor that, so you are the one who clearly doesn't want to discuss this issue. I don't need to answer your questions; I already have. Just because you write an upper-case letter in an equation, that doesn't make it a constant. A constant is a quantity that doesn't change, and we all know that R changes, in fact, there are infinite values for R that Ohm's law is valid for. V, I and R are all variables. All of those quantities can vary in an electric system. It's so elementary. It's been proven over and over in this thread, as well, it's been proven over and over that proportion does not requre that only one quantity be a variable. Also, it's been proven that each quantity of Ohm's law affects the other two, thus all are variables. You decide to ignor all of this and just continue to ask trivial or irrelevant questions. Look the thread over, man, all has been answered. You just keep asking after the answers have been provided.

 

[Tesla23]

In an earlier thread we managed to reach agreement by not referring to 'Ohm'. we seemed to be able to agree on:

The facts are:
1. in most homogeneous materials (i.e. no junctions), for all practical purposes V = IR where R is a function of temperature only
2. For any two terminal device with a voltage V across it and a current I flowing through it, you can calculate a quantity R = V/I that has the dimensions of resistance. Once you have determined R in this way, then V=IR and I=V/R hold as long as you don't change V or I.

It seems that some folk learnt that (1) is Ohm's law and others learnt it as (2).

 

[shimniok]

I think what is happening is that just because resistance is measured
in 'ohms' they think all resistance is somehow defined by Ohm's Law.
Ohm's Law is a very specific relationship between v and i, and without
R being constant there is no relationship to speak of.
...
The key to understanding this is in the phrase "in direct proportion to",
that's why i started this thread talking about that unique relationship.

Thank you for the very cogent, clear, explanation of your thoughts. I see what you're getting at, now. Will continue pondering...

In terms of physical relationships... I guess "one of these things is not like the other" -- resistance is a physical *property* of the circuit, thus a coefficient (like coefficient of drag for a car, say), whereas voltage and current represent, well, a sort of energy state of the system ... or something.

So you're essentially saying that the most important focus of Ohm's Law is describing the relationship between electron flow and electric potential in a circuit? I'll buy that.

 

[MrAl]

Hi again,



It's a little harder to respond to three people with the same post, but
it's nice to see that some people are still interested in the real truth
behind Ohm's Law. I've answered the replies one at a time here.


BrownOut:
Well my friend feel free to show us your 3d graph. I'd be happy to see
what you are trying to say. If you are trying to say that R changes
in a conductor then sure, we all know it does, but that is not what
Ohm's Law is all about. Ohm's Law is about an idealized condition and
not only that, for some currents the law holds over several orders of
magnitude too. If we pump 3000 amps through a 10 foot piece of 22 gauge
wire it wont take long before its resistance shoots up to a million megohms
or more (he he) but that is not what Ohm's Law is about.
Still, if you feel that a 3d graph would help then sure post one for us.

BTW just to clarify, we know that R can change if we force it to change
on purpose. If we swap a 10 ohm resistor for a 20 ohm resistor certainly
things are going to change and we can claim that R had indeed changed,
but that is not what Ohm's Law is trying to say either. It is more about
using the SAME resistor during the experiments.

This might provide a clearer picture...
Ohm's conclusion went something like this:

1. Take a length of wire, pump 1 amp through it.
2. Measure the voltage across the wire ends from end to end. Lets say 3v this time.
3. Now if you increase the current to 2 amps which is 2 times the original current,
the voltage across the two ends will change by the same proportion: 2 times. Thus,
if we increase the current to 2 amps the voltage will rise to 6v for that piece of wire.
4. So the conclusion was that if you increase the current by 2 times the voltage
will also increase by 2 times, and if you instead increase the voltage by 2 times the
current will increase by 2 times.
5. The only way this can happen is if R of the wire is constant.
6. This also leads to the term "ohmic" which is used to describe objects that obey
this law of proportionality.

The converse, making r a variable, would mean 'ohmic' would have no meaning because
everything under the sun could be called ohmic.

A really good geometric analogy i think would be a circle. When R is constant
in the equation for a circle we get a really nice, perfect circle. If R was allowed
to vary however we would get everything BUT a circle, with many resulting shapes
totally unrecognizable. If we did experiments with v=i*r, we would find that
we could not recognize what kind of device we were experimenting with in some
cases, but if v ended up being proportional to i we would know right then and there
that we were working with a resistance like a wire (an ohmic conductor).


Tesla23:
What happens is some people learn the law by looking at V=I*R or similar, and never
get the real truth behind the experiment that led to the result of proportionality.
They are given the math first rather than the experiment first.
Please see the above 6 steps of Ohm's Law and see what you think about that.

shimniok:
Well, the most important part is that current and voltage are proportional.
This is why i tried to reach people through the door of proportionality rather
than trying to argue about Ohm's Law at first, which they have learned through
mathematics rather than outright understanding of the nature of the experiment
that led to the law. This is something that requires 'understanding' BEFORE
'mathematics', not mathematics before understanding. Mathematics can get us
very lost in space while understanding can lead to some wonderful mathematics.
I believe that reading over those 6 steps outlined above can help anyone gain
the understanding they need to get past the 'math before fact' paradox.

Objects that do not obey this rule are said to be 'non ohmic'.

Please take a look at those 6 steps outlined above and see if this makes
more sense after that.


Take care all...

 

[BrownOut]

Haveing a material that's 'ohmic' is not what the law is about. Here is a very simple illustration:

Take a regualted, adjustable power supply and connect a variable resistor.
Set up the power supply for constant volts.
Vary and volts and observe the current meter varying with the voltage.
Vary the resistance and observe the current meter varying inversly with resistance.
Ohm's law holds for both cases, hence Voltage, Current and Resistance are variables.

Now, set up the source for constant current.
Vary the current and observe voltage changes with current.
Vary the resistance and observe voltage changes with resistance (proportionally)
Ohm's law holds for all cases, hence Voltage, Current and Resistance are all variables.