Originally Posted by BrownOut

You're mistating Ohm's Law.



Resistance, given by the symbol R, is not the constant of proportionality.

i=v*(1/R)

1/R can still be said to be the constant of proportionality. In other words,
i is proportional to v.

I do prefer to call R the constant of proportionality too however as in:

v=i*R

where we would then have to say that i is inversely proportional to R.

You can call it the Sultan of Arabia; that won't make it so. V and R are both varaibles.

Originally Posted by MrAl

The law stating that the direct current flowing in a conductor is directly proportional to the potential difference between its ends.

For a specific conductor? Or any conductor? I guess you could say that for a given conductor, where R is fixed (constant), the current is directly proportional to the voltage for that specific situation.

But you can't (correctly) say the same when you generalize to any conductor or resistor(s) in the circuit. Do you see the distinction?

Ohm's law doesn't describe a directly proportional relationship anymore than the ideal gas law (PV=nRT) describes a directly proportional relationship between pressure and temperature. With Ohm's law, current depends on voltage and resistance. All three are variables. With the I.G.L., pressure depends on volume, temperature, and the number of moles of the gas.

When x varies proportionally to y, by definition, there can't be any other variables in the equation.

There are in Ohm's Law and the ideal gas law.

Therefore they are not equations describing direct proportionality.

Michael

Originally Posted by BrownOut

You can call it the Sultan of Arabia; that won't make it so. V and R are both varaibles.

Hello again,


It's not 'me' that is calling it anything...it's the way that law is written.
If you want to mess with Ohm's Law then you have to first mess with
proportionality and what it means when two variables are proportional.


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. You have to know
when 'variables' are really constants and when they are not. Just because R is a
letter like v and i that doesnt automatically make it a variable in an equation.

I suppose that you would also want to say then that in the equation:
y=A*x^3+B*x^2+C*x+D
that A,B,C, and D are variables?

You have to know
when 'variables' are really constants and when they are not. Just because R is a
letter like v and i that doesnt automatically make it a variable in an equation.

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?

A, B, C and D are irrelevant.

Originally Posted by BrownOut

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...

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.

Originally Posted by MrAl

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

Originally Posted by 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.

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.

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.

Originally Posted by MrAl

-------------------------------------------------------
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

Originally Posted by shimniok

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.