# What is ohms law (was Ic=C x dv/dt)

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#### Laplace

Apr 4, 2010
1,252
If he could just learn to differentiate the voltage equation, then he would not have to get involved with reactance.
The reason we get involved with reactance is to avoid dealing with differential equations. Reactance is easy, differential calculus is hard.

By the way, Ohm's law is not R=V/I and all its variations, like most folks believe. That formula is the definition of resistance or impedance. Ohm's law is a property of a material, specifically its resistive linearity.
I'll go with what most folks believe, because we can honor Georg Simon Ohm for his contribution by naming anything we want as Ohm's Law; not necessarily what he proposed in the 1820's. Back then nobody knew what galvanic electricity even was, not even Ohm who used Fourier's heat diffusion equations to explain his experimental results (because everyone back then recognized Fourier as a smart guy.)

I can show you quotes in a couple of good physics books that show that my statement to be true.
There is no reason to refer to some crackpot physicists when we can read any introductory textbook on Electric Circuits to learn everything anyone would ever need to know about Ohm's Law. Or possibly, it is not the author of the physics textbook who is the crackpot.

If a capacitor allowed current to pass, it would instead be a resistor.
Current flows into one terminal, the same current flows out the other terminal. Current flows through whatever is between those terminals. And the capacitor obeys Kirchoff's current and voltage laws just like any resistor must. If there is a capacitor in a branch of a circuit network, will mesh current flow through the capacitor? How would it be a useful concept for circuit analysis if current did not flow through a capacitor? Or do you propose changing the notation for mesh currents when they reach the capacitor terminals to show that the mesh current does not flow through the capacitor? How would that be more useful?

#### Ratch

Mar 10, 2013
1,098
The reason we get involved with reactance is to avoid dealing with differential equations. Reactance is easy, differential calculus is hard.

Reactance only applies to sinusoidal steady state. Transient behavior requires differential equations. Linear differential equations like those found in most circuits are not too bad.

I'll go with what most folks believe,
Good thing we don't live in Columbus's time, or you would believe the Earth is flat. Similarly, in Galileo's time. a lot of folks believed the Earth was the center of the universe.

because we can honor Georg Simon Ohm for his contribution by naming anything we want as Ohm's Law; not necessarily what he proposed in the 1820's.
Where is the honor in naming a definition a law? We define speed as distance/time. Ever heard of Newton's speed law? I haven't.

Back then nobody knew what galvanic electricity even was, not even Ohm who used Fourier's heat diffusion equations to explain his experimental results (because everyone back then recognized Fourier as a smart guy.)
It doesn't matter how the electrical energy was obtained. They had to know right away that certain materials conducted current better than others. Ohm noticed the linearity was a property of the material. If Fourier helped Ohm out, no problem. Scientists often make advances based on the work of others.

There is no reason to refer to some crackpot physicists when we can read any introductory textbook on Electric Circuits to learn everything anyone would ever need to know about Ohm's Law.
No, you can learn everything you need to know from a textbook about the definition of resistance or impedance. Even if they mistakenly call it Ohm's law.

Or possibly, it is not the author of the physics textbook who is the crackpot.
Until you read the textbook and refute it, you cannot legitimately say that. Until you do the foregoing, that is just a wild accusation.

For you edification, there are some materials that are ohmic and others that are non-ohmic. That is one of the properties of a material. This link explains what that property is and how to determine it. http://physics.kuniv.edu.kw/phys107/Exp1.pdf

Current flows into one terminal, the same current flows out the other terminal.
That is TTT. Charge flows, current is already defined as charge flow. Current flow literally means "charge flow flow". The current into the terminal has the same value as the current leaving the opposite terminal. That is because the same amount of charge accumulating on the capacitor plate per unit time is the same as the amount of charge leaving on the opposite plate per unit time. That does not mean that current exists through the capacitor. If it did, the capacitor would be a resistor.
Current flows through whatever is between those terminals.
No it doesn't. There are two circuits involved. One circuit accumulates the charge, the other depletes the charge. The two circuits are isolated from each other by the capacitor's dielectric. The charges that enter a capacitor are not the same charges that leave.

And the capacitor obeys Kirchoff's current and voltage laws just like any resistor must.
No it doesn't. Circuitwise yes, but on the capacitor itself, no. Kirchoff's law does not apply to a capacitor, because a capacitor stores and dispenses charges.

If there is a capacitor in a branch of a circuit network, will mesh current flow through the capacitor?
No, for the reason already given.

How would it be a useful concept for circuit analysis if current did not flow through a capacitor? Or do you propose changing the notation for mesh currents when they reach the capacitor terminals to show that the mesh current does not flow through the capacitor? How would that be more useful?
Mesh analysis works because the capacitor stores and dispenses charge by equal amounts per unit time. This fools a lot of folks into thinking that the current exists through the capacitor. The mathematics of mesh analysis does not know the difference, but those who understand how a capacitor works know what is really happening.

Ratch

#### ElectronicPotatoe

Dec 17, 2016
24
You are fighting over technicalities that do not matter in this situation. Ohm's law is a property, yes, but that doesn't change anything.

Many electronic books focus on the practical stuff and just throw the equations towards you without proving them, unlike physics books. If you read an electronic book, you'll get this:

Ohm's law: V=IR and 20000 excercises using that equation, and you don't know what you are doing, you just do it. I don't like that much but it doesn't matter now.

In a physics book you'll get the whole current density and conductivity story, crap for the one that doesn't care:

J=σE, this being Ohm's law.

The famous equation is obtained by replacing E for V/L and J for I/A, which is not Ohm's law, just a consequence.

Last edited:

#### Ratch

Mar 10, 2013
1,098
You are fighting over technicalities that do not matter in this situation. Ohm's law is a property, yes, but that doesn't change anything.

Many electronic books focus on the practical stuff and just throw the equations towards you without proving them, unlike physics books. If you read an electronic book, you'll get this:

Ohm's law: V=IR and 20000 excercises using that equation, and you don't know what you are doing, you just do it. I don't like that much but it doesn't matter now.

In a physics book you'll get the whole current density and conductivity story, crap for the one that doesn't care:

J=σE, this being Ohm's law.

The famous equation is obtained by replacing E for V/L and J for I/A, which is not Ohm's law, just a consequence.

The technicality is that Ohm's law is mostly represented and taught incorrectly as a relationship when it is really a definition. Naming something as one thing when it is really something else makes it a misnomer. Voltage and current have to be evaluated to determine if Ohm's law is being followed.

Ratch

#### ElectronicPotatoe

Dec 17, 2016
24
The technicality is that Ohm's law is mostly represented and taught incorrectly as a relationship when it is really a definition.

Mmmh not really. It is a relationship, only not of V, I and R.

#### Ratch

Mar 10, 2013
1,098
Mmmh not really. It is a relationship, only not of V, I and R.
I should have been more clear in saying Ohm's law is a material property defined by a linear relationship between V and I, not a definition of resistance or impedance as mostly taught today.

Ratch

#### ElectronicPotatoe

Dec 17, 2016
24
I should have been more clear in saying Ohm's law is a material property defined by a linear relationship between V and I, not a definition of resistance or impedance as mostly taught today.

Ratch

J=σE, this being Ohm's law.

The famous equation is obtained by replacing E for V/L and J for I/A, which is not Ohm's law, just a consequence.

Correct me if I'm wrong, but I was sure that one was Ohm's law.

#### Ratch

Mar 10, 2013
1,098
Correct me if I'm wrong, but I was sure that one was Ohm's law.
No, that is the definition of conductivity, or the reciprocal of conductivity which is resistivity.

Here is a quote from a physics book by Halliday and Resnick, 1967 p. 780 .

"We stress that the relationship V = i R is not a statement of Ohm's law. A conductor obeys Ohm's law only if its V - i curve is linear, that is, if R is independent of V and i. The relationship R = V/i remains as the general definition of the resistance of a conductor whether or not the conductor obeys Ohm's law.

The microscopic equivalent of the relationship v=i R is Eq. 31-7, or E = j * rho . A conducting material is said to obey Ohm's law if a plot of E versus j is linear, that is, if the resistivity rho is independent of E and j. Ohm's law is a specific property of certain materials and is not a general law of electromagnetism, for example, like Gauss's law."

I can provide a quote from another physics book that says pretty much the same thing.

Ratch

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,510
"We stress that the relationship V = i R is not a statement of Ohm's law. A conductor obeys Ohm's law only if its V - i curve is linear, that is, if R is independent of V and i. The relationship R = V/i remains as the general definition of the resistance of a conductor whether or not the conductor obeys Ohm's law.

And area = 1/2 base x height only works for a triangle with straight edges.

#### ElectronicPotatoe

Dec 17, 2016
24
No, that is the definition of conductivity, or the reciprocal of conductivity which is resistivity.

Here is a quote from a physics book by Halliday and Resnick, 1967 p. 780 .

"We stress that the relationship V = i R is not a statement of Ohm's law. A conductor obeys Ohm's law only if its V - i curve is linear, that is, if R is independent of V and i. The relationship R = V/i remains as the general definition of the resistance of a conductor whether or not the conductor obeys Ohm's law.

The microscopic equivalent of the relationship v=i R is Eq. 31-7, or E = j * rho . A conducting material is said to obey Ohm's law if a plot of E versus j is linear, that is, if the resistivity rho is independent of E and j. Ohm's law is a specific property of certain materials and is not a general law of electromagnetism, for example, like Gauss's law."

I can provide a quote from another physics book that says pretty much the same thing.

Ratch

Serway´s book does not say that.

This is what it says:

"More specifically, Ohm’s law states the following: For many materials (including most metals), the ratio of the current density to the electric field is a constant s that is independent of the electric field producing the current"

7th edition, Vol 2, page 756.

It's kind of surprising actually. Resnick and Halladay's book is a very respected book amongst the universities here. So is Serway's. Even though Halladay's is old, that part of physics didn't change much, if anything at all.

Later, in Serway's book it clarifies this:

"Ohm’s law is related to a proportionality of J to E (Eq. 27.6) or, equivalently, of I to V"

So I guess after all the are not contradicting each other. I don't know which one is the original though.

Edit: The relation of J to E is Ohm's law though, not the definition of conductivity.

#### Ratch

Mar 10, 2013
1,098
Serway´s book does not say that.

This is what it says:

"More specifically, Ohm’s law states the following: For many materials (including most metals), the ratio of the current density to the electric field is a constant s that is independent of the electric field producing the current"

7th edition, Vol 2, page 756.

It's kind of surprising actually. Resnick and Halladay's book is a very respected book amongst the universities here. So is Serway's. Even though Halladay's is old, that part of physics didn't change much, if anything at all.

Later, in Serway's book it clarifies this:

"Ohm’s law is related to a proportionality of J to E (Eq. 27.6) or, equivalently, of I to V"

So I guess after all the are not contradicting each other. I don't know which one is the original though.

Edit: The relation of J to E is Ohm's law though, not the definition of conductivity.

J and E define the resistivity and therefore the conductivity. The following is from Wikipedia.

Ratch

#### Laplace

Apr 4, 2010
1,252
Instead of consulting physics textbooks to understand Ohm's law, it may be more fruitful referring to Ohm's original treatise from 1827 on the Galvanic Circuit, specifically its 1891 English translation. Attached is a partial extract of said document, specifically the last few pages reviewing the principal points revealed by Ohm's theoretical investigations. These points lead directly to the Ohm's law that electrical engineers are familiar with:

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• galvanic_circuit.pdf
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#### Ratch

Mar 10, 2013
1,098
Instead of consulting physics textbooks to understand Ohm's law, it may be more fruitful referring to Ohm's original treatise from 1827 on the Galvanic Circuit, specifically its 1891 English translation. Attached is a partial extract of said document, specifically the last few pages reviewing the principal points revealed by Ohm's theoretical investigations. These points lead directly to the Ohm's law that electrical engineers are familiar with:
View attachment 33481

Yes, he is talking about the linearity of ohmic materials like metallic wires. Those results would not be true if measurements were made on non-ohmic substances, would they?

Ratch

#### Laplace

Apr 4, 2010
1,252
Those results would not be true if measurements were made on non-ohmic substances, would they?
What would be the purpose of discussing non-ohmic materials in a discussion of Ohm's Law?

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,510
Those results would not be true if measurements were made on non-ohmic substances, would they?

And area = 1/2 base x height only works for a triangle with straight edges.

For example A = 2.pi.r/2 * r

Because a circle has straight edges when you look at a sufficiently small segment.

#### Laplace

Apr 4, 2010
1,252
...when you look at a sufficiently small segment.
For a non-linear V-I characteristic we can find the corresponding dynamic resistance, and the dynamic resistance does obey Ohm's Law - over a small segment.

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,510
For a non-linear V-I characteristic we can find the corresponding dynamic resistance, and the dynamic resistance does obey Ohm's Law - over a small segment.

My point exactly.

#### Ratch

Mar 10, 2013
1,098
What would be the purpose of discussing non-ohmic materials in a discussion of Ohm's Law?

The discussion is past. Ohmic and non-ohmic materials are defined. It only remains to determine if a material follows Ohm's law.

Ratch

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,510
The discussion is past. Ohmic and non-ohmic materials are defined. It only remains to determine if a material follows Ohm's law.

Most materials are, or can be considered to be ohmic at a single point.

#### Ratch

Mar 10, 2013
1,098
And area = 1/2 base x height only works for a triangle with straight edges.

For example A = 2.pi.r/2 * r

What is that supposed to mean?

Because a circle has straight edges when you look at a sufficiently small segment.

And each almost straight segment has a different slope, so the whole line curves.

Ratch

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