Is an ideal capacitor a resistor then?

Interesting question. An ideal capacitor would mean its dielectric would be a perfect insulator (infinite resistance), so I expect that would mean it would only have reactance and no series resistance.

 

The point is that a capacitor is defined as passing zero direct current.

As to the maths.

Why is what I wrote more useful than limits?

Because physicists rely on mathematicians to get the logic correct and prove that the formulae they use are correct.

For instance we use sets because we want to be able to guarantee that the rules we set down are followed.

It is very important that a+b leads to a known result.

In fact we want our set S to have the property that every member can be added to any other member to produce another member of S

For any p,q, r in S p+q = a unique r in S that is different from p or q.

That way we can blythely add things without worry that we might be generating something that is not a number (is S is a set of numbers).

That way we can develop an algebra, confident that we can always guarantee an answer.

But k + ∞ = and k * ∞ = ∞ which is a problem from the get-go.

This spectre actually occurs in Fourier analysis where if we add sufficient terms of a continuous function we leave the set of continuous functions and enter something else. The phenomenon is called Gibbs phenomenon,, and is usually omitted in courses because it breaks the rules. But the spike can be seen on a good oscilloscope.

 

Hmmm,

I'm not sure I buy that voltage is analogous to mechanical force and that resistance is analogous to mass. Yes, I am aware voltage is often referred to as EMF and that the F in EMF is 'Force'. However, I contend that that is just a convenient misnomer. Sure, voltage across and electrical field can apply a mechanical force on charges, but that is crossing over from an electrical system to a mechanical one. In the final analysis, I don't think you can really compare electrical systems to mechanical systems

Let me briefly explain why. I will stipulate ideal systems and the use (of the) term 'force' to apply only to mechanical force.

When (a) voltage (is) applied to a resistor and current flows, the energy is converted to heat and lost. When you take the voltage off the resistor(,) that energy cannot be regained, no(t) matter how you slice it, from the resistor as a voltage and current. Whereas, if you apply a force to a mass and acceleration occurs, energy is retained by the mass and increase in velocity. That energy can be retrieved as a force and acceleration.

I contend then that resistance is more like mechanical friction than mass. I also contend that a better electrical analogy to mechanical force is dV/dt and a better electrical analogy to mass is inductance. Not perfect, but in my opinion a bit better.

(blue means strikeout)

Edit: finger foul edits

 

Hello, Bill, long time no speak.

Hopefully those remarks were not addressed towards myself since the title of this thread is the difference between electrics and mechanics.

 

Sorry t_n_k, just being picky here, but outer space is not at absolute zero temperature, it is actually about 3 Kelvin above absolute zero.

Matt

That's why I said "approaching", rather than stipulating at absolute zero. I thought someone would pick me up on that point. Anyway, wasn't it clear I was writing with a proverbial tongue in cheek.

 

That's why I said "approaching", rather than stipulating at absolute zero. I thought someone would pick me up on that point. Anyway, wasn't it clear I was writing with a proverbial tongue in cheek.

Ah, ok. I looked back at your post to see if that's what you might have meant, but I couldn't read it that way. Oh well, that was my fault

 

.When voltage applied to a resistor and current flows, the energy is converted to heat and lost...

Yes, and we know how useless heat energy is. I mean, you can't even cook a steak with it or move a freight train. Oh, wait...

 

Hello, Bill, long time no speak.

Hopefully those remarks were not addressed towards myself since the title of this thread is the difference between electrics and mechanics.

No. Just general discussion on the subject. It came up in my academic past frequently. The disciplines are really different, was the net of those past discussions. Not all of us agreed on the 'closest approach'.

 

Yes, and we know how useless heat energy is. I mean, you can't even cook a steak with it or move a freight train. Oh, wait...

Yeah.




But since that reply is 2 short...

Mmmm...steak....

 

The point is that a capacitor is defined as passing zero direct current.

As to the maths.

Why is what I wrote more useful than limits?

Because physicists rely on mathematicians to get the logic correct and prove that the formulae they use are correct.

For instance we use sets because we want to be able to guarantee that the rules we set down are followed.

It is very important that a+b leads to a known result.

In fact we want our set S to have the property that every member can be added to any other member to produce another member of S

For any p,q, r in S p+q = a unique r in S that is different from p or q.

That way we can blythely add things without worry that we might be generating something that is not a number (is S is a set of numbers).

That way we can develop an algebra, confident that we can always guarantee an answer.

But k + ∞ = and k * ∞ = ∞ which is a problem from the get-go.

This spectre actually occurs in Fourier analysis where if we add sufficient terms of a continuous function we leave the set of continuous functions and enter something else. The phenomenon is called Gibbs phenomenon,, and is usually omitted in courses because it breaks the rules. But the spike can be seen on a good oscilloscope.

Did you ever get the opportunity to speak with Lord Russel? You seem to share some thought patterns.

 

Did you ever get the opportunity to speak with Lord Russel? You seem to share some thought patterns.

It's like your response (and that of Chad Orzel's dog) to steak.

I wish.

Though I was first introduced to his paradox and then read his book when I was fourteen.

 

BillO,

Here is a more physically useful example.

The resultant of two coplanar vectors is another vector in the same plane.

Imagine what what happen if you could not guarantee that was always the case.

How much physics that we take for granted would fall apart?

 

Okay.

I'll assume you mean adding two coplanar vectors.

If the result was at least predictable, and the projection of the result in the original plane, given a suitable transformation, was the same as things 'are now', then nothing, other than the mathematics, should change.

I may be putting too much stipulation on reaching that conclusion, but this reminds me a little of such things as complex numbers, tensors and other tools of non-euclidean space.

If adding the two coplanar vectors were unpredictable as to which direction and magnitude the result took, as your statement may suggest, and the universe still held itself together, we'd a new physics.