I Hate Capacitors
Hi guys,
Some thing has been eating me for days. Its about capacitors and may sound trivial but I wil assure u it is not so. The question is: "what will be the capacitance of a parallel plate plate capacitor when it is filled with a conductor touching both plates."
All books I have seen so far say it will be infinite or tends to infinity, but i dont agree. I will put my view point.
let us go to the grassroots and define capacitance. The ability of a capacitor(or any object for that matter) to 'store' charge at a given pottential difference. Now once both the plates are connected the whole assembly is nothing but a conductor. Two statements here:
(i) Any conductor except a superconductor has some resistance, no matter how small, it is non zero. Thus there will be some pottential drop. V not= 0
(ii) No part of a conductor can accumulate any net charge, because of the presence of charge carriers (electrons). Q = 0
Thus the capacitance C = Q/V = 0/non zero = 0
Now some thing very very absurd(funny rather) is written in one of the books (Arihant Electricity and magnetism). It say since a conductor can allow infinite amount of charge 'though' its plates, Q>>>>V. So C tends to infinity. Wah bhai !! Listen to my analogy. Take a bucket, cut off its bottom and say u have a bucket of infinite capacity !! LOL !!
Intrestingly and disgustingly nearly all physics trachers disagree with me. i am the lone fighter for my cause. I have ddecided to conduct an extensive experiment on this starting from 25 Sept after the FIITJEE exam ;) So what do you people think? Am I wrong ?
Saurya Time
13 comments:
If u hate capacitors u must hate optics, gravitation and thermodynamics where we approximate sin by tan, neglect small heights(compared to radius of earth), and assume an idealised world(no friction) respectively.
That is why we assume a conductor as a superconductor.Yes, a bucket with it's bottom cut will have infinite capacity in an idealised world without gravity and friction.
You have picked the most important drawback of Physics-"Approximations and suppositions". It pinches and it pinches right at the centre of mind that how can we utilise this idealised Physics in this real world? If we have to analyse, why don't we analyse the true world?!
What is the need of these suppositions and approximations? It only makes a student loose his confidence in Physics. It might sound familier to the post 'Where are we going?' by Arun.
Man, I like ya flo. But seriously, I've had a lot of tough time with stuff like this (refer my Where... post) But what Rajat says is true, we truly assume that the R = 0, not tending to 0 (which is the superconductor (even they don't have equality)). Remember the assumptions you take before you make contradicting statements, because it generally contradicts an assumption. There's a lot more pain in assuming something and without straying from assumptions disproving the possibilty of ever using that assumption, and then blindly using the very assumption that started the mess. I've found dozens of such loopholes in chemical equillibrium/kinetics/ionic equilibrium.
And at Rajat, we too aren't fools to assume that we CAN compute anything meaningful related to the real world. We just like to take it to the next step of reality, but still ignore a large number of unrelated effects.
Here's a lovely one:
If you remember the derivation for "self-energy" for a spherical shell with a charge 'q', we considered to bring charges in dq installments from inf to the shell and re-distribute charges (which requires no work), and we continued.
BUT, by mathematical definitions, dq can be used ONLY if there exists no number between 0 and dq (which is an interpretation of dq -> 0). BUT, by the laws of physics, q is quantised in by 'e' (1.619E-19). Sooooo, how the heck do we use calculus here? In large cases, where the actual charge is large, then we can ignore quantum effects, but here we can't.
There was a similar q on what would happen if you released an electron on a conducting charged sphere. I came up with an idea, but I'd like to hear you all's first. I kinda got my phy teacher to agree with my reasoning, (but can't get most of my class-mates to do the same).
Ok Arun signing off
TIME WHERE'S YOUR POST???? (I'm desperate)
Hey friends.
I feel a little lagged behind in the blog(find a good sunday morning to fix things up).
As far as the current problem is concerned - capacitance is the ability to hold charge(not the charge that is left behind on leaving it alone).ok lets put it this way, u can load a capacitor plate with a greater amount of charge if it is connected to a good conductor.if the conductor is perfect the charge is infinite.An alternate approach is using permittivity but i hope the argument above is good enough.
Talking about school teachers, you cannot expect them to be great thinkers or reasoners(nice word). A good teacher(open to ideas and ques.) can give you that extra decisive bit of knowledge which might help u to end up with something resonable.
Talking about approximations, we use them to understand things.Its easy to critisize the system, the syllabus.But telling us certain wrong things in the lower classes and then contradicting it at this stage is not the worst option after all. It is the use of approximations which teaches and enables us to go against them at a later stage. We analyse the true world, leaving out facts which are unnecessary and repetetive. In mechanics we are not interested in the motion of the wedge, we only want to know how our laws(newton's, not ours) work and the problems set to develop and test these skills.
Ok, now the dq issue. Calculus is a theoretical subject, don't question it because very surprisingly and strangely it perfectly agrees with practical works.Arun, I got ur point there. I dont agree with quantization of charge at the e level .We still dont know about the constituents of an electron(of its charge) so may be we have smaller units. But that does not solve the problem. Even if e charge is the smallest- we use a hypothetical smaller charge ->0 to prove the result and it agrees with reality.
What we (all physicisians, scientists) have been trying to do is to justify things we see around us.And if any of our theories violates a physical observation its our job(or happens with time) to change our theories to suit it.
I hope I was clear enough to let u know what i feel.I'll come back to u guys in a few days (maybe some of u agree with me).Till then, Enjoy!!
Ankit
Quoting from Ankit...
"What we (all physicisians, scientists) have been trying to do is to justify things we see around us.And if any of our theories violates a physical observation its our job(or happens with time) to change our theories to suit it."
Thats right. Look at Organic Chemistry (Ok mayb I'm writing it coz I DONT LIKE CHEM!!) U take some organic compounds, do particular reactions and suggest a mechanism. But then u find exceptions, and start giving different logics for them... They might be right, but the point is that the theories are not made first, the real world is.
So while our approximations allow us to Simplify the Problem, or Works in nearly all cases we want to consider,
Some cases are still left out...
Waiting for another Theory to be found...
Waiting for another Genius to think about them...
Waiting for another Fused Bulb to light up!!
So light up Buddies!!
--
PS: I wanted to know if Rajat should b added as a memeber (So that he can post) He's enthusiastic and much more intelligent than I am (Maybhe would have been a KVamPY had he given the Test) This would also allows us to increase the scope of our blog.. not "Just for KVamPYs 2005" but anyone who is witty and wanna join...
Plz leave a comment.. or mail me!
@Rash I think why not? We really need enthusiastic ppl to carry on this blog, and well the KVamPY's have ditched us in a large majority. So sure.
@ankit: I know perfectly well that calculus works everywhere (I bow to thee o calculus), but nonetheless, as a student, I can not convince myself that we can apply laws of continuous functions (calculus) to discrete functions (quantised physics). On a larger scale, sure we can ignore effects, but at that small scale, we can't.
I remember thinking of physics maths like this:
We construct a mathematical model to represent the PHYSICAL situation (I like to say this): we give MEANINGLESS symbols meaning by saying that this and this aspect is ALSO shown by the physical reality, and then (and only then) do we say that the model is a satifactory one.
BUT if the model DOESN'T satisfy the necessary criterion, then back to the drawing board again.
Quantizedness is a necessary criterion at those small levels, but calculus doesn't satisfy it. As far as I know, they make some modifications to calculus to make it satisfy the above.
to Rasagy(gr81)-You should surely add Rajat to the list. Its good to have different viewpoints.
to Arun-i was going through ur comment and i saw this :- "Quantizedness is a necessary criterion at those small levels" - i still wonder what makes it necessary. I dont know why, but i cannot convince myself that its obvious. I think the only reason we say charge is quantized is because we haven't been able to find smaller charges.(Since charges flow in the form of e).
I dont say that the correctness of calculus to the problem(what was it? oh yes, energy stored in a shell) necessarily proves that we can apply it here, but i cannot see any strong reasons to think otherwise.Waiting for your comments Arun(I admit that u have a unique style of writing)........
And obviously i would like the others to join in too.
A vague thought - A lot of people seem to be holidaying these days(the members list features a lot of names i have never seen any contribution from).I guess they are working towards the jee. Its a good thing to know that any exam at such a level actually requires a lot of learning(memory based stuff) and just concentrating on good things(i mean the real science) would not be a very smart thing to do.But hey, what are the coaching institutes for-they'll get you the iit while you get physics. The next eight months(infact just less) are crucial and i dont expect a lot of bloggers during this time. I hope we still manage to keep ur love for the subject alive and running.Bye
Ankit- Your words couldn't be more true. Sadly because of the race, i've lost a lot of love for the subject. Every time I come across one of these things, I wonder why we're doing the wrnog stuff. The reason is simple, we can't do the perfectly right stuff anyway, so this is an approx. which we can deal with at this level. But atleast that much should be told to us, so that we can satisfy our inner conscience.
As for the 'quantizedness', it's a law in physics. At first, I too had a similar doubt. But then I understood Heisenberg's Uncertainity Principle. I had always (since 9th or so) thought that it was just that WE couldn't do it, but not that it couldn't be done. But the HUP (sounds interesting doesn't it) is a FUNDAMENTAL LAW. It say no matter what you do, your certainity can not invaildate this, because to receive data, you atleast have to use light, as it is the least criminal (that's a math concept I think).
Another such law is the second law of thermodynamics, i.e. entropy of the universe can never decrease (I keep feeling guilty every time I open my fridge that I'm saping way some of the universes precious useable energy).
So looking at this, I felt that the fact that quantum is FUNDAMENTAL isn't so invisionable.
To everyone out there, PLEASE post as much as you can. It just takes like 5-6 minutes a week (since most of us post on sundays anyway).
Hey guys …
the discussion began from what and is ending on what … my view .. take in rajat (nice guy) … by the way to tackle my problem on capacitance I have been doing an experiment .. The capacitance of a capacitor as u all will agree is just a matter of definition … how we define it … Now, be it ideal situation or not , I found one experiment that can point at the capacitance of a conductor … This is the experiment in brief
U all know that the current in an RC circuit is given by the equation,
i=i0e-t/T
u know tis decay of current expression … now without using very sophisticated equipments (my college lab was enough) I tried to plotted a I ~ t graph and from it I tried to calculate the time constant T. First I used a normal capacitor available at electronics shops and then the one I made … two metal plates filled with a metal block ….(bit crude but served the purpose) … As expected the fall of current in the second case was very sharp … ie T 0 … So RC 0 but R not = 0 hence C=0 or at least C 0…
Its nowhere near to infinity … what most physics books suggested …
Now that I have an experiment to back me up not only have I convinced myself but my friends and teachers here as well.
Ok now about the calculus thing and the quantization of charge … I believe calculus is only a tool … Don’t believe in what it does to your concepts of quantization … If u believe u will land up no where … It gives u accurate results … Every thing in out world is quantized … even space (read loop quantum gravity) so what will u do ? Dump calculus ?
Saurya Time
Ok time. I just would like to argue about my statement here. I agree calculus is a tool, like a wrench. But you can't always use a wrench now can you? Suppose you want to hammer in a nail, you could try to use a wrench, and though it would work, it wouldn't be very appropriate to use it.
My main argument is that maths is a tool, and physics is a way of applying the right tool. If the tool/statement doesn't satisfy the properties of the problem, you should be using it right?
For example, suppose your a bit looney and start to consider current as a vector. Now that's a very easy thing to disprove, because if you put two wires, if i was a vector, then the resultant current will DEPEND on the angle you put it in.
Now consider a more subtle case like using cylinder with height dy instead of lenght dl for integrating to find surface area of a sphere/cone/etc. You KNOW the answer, and hence can say it's wrong. You could also experiment, but I have no idea how to measure surface area, please enlighten me. My basic point is that using this here is WRONG. It doesn't satisfy the case, and hence is a bad model.
I'd like to try your experiment, but I have a good feeling that experimental error for such a crude (no offense intended) might make the results less valid. Anyway, good job at keeping the spirit of science (exprimentation and observation) alive. I raise a toast to you.
@ Arun
About the experiment, I could very well have done a Gedanken experiment, but i did the practical one just for the sake of the sprit of science .. ya right ..(i almost expected the result and would have had a heart attack if i would have got some other result..lol)
lets get to the application of calculus. certainly i agree with u that we cannot use a wrench to hammer a nail ... but u know what ? calculus is a Swiss Knife ...
Time
Man, I don't want to start a flame war, but the thing is that calculus can only be used over continuous spaces, atleast in the continuous result ones. i.e. For integration of sin[x], you would end up getting a sum, not a function that satisfies the same. So my point is not that calculus is a wrench. I love calculus, and think it's the greatest thing in the world, but that doesn't change the fact that it shouldn't be used in discontinous spaces. Why don't you integrate [x^2]^2 as a general value, and tell me the value (I was about to put in sin[x], but that can be evaluated (not using calculus) then e^[x] which had the same argument (again not using calculus). I repeat, I have no prob's with calculus, I simply believe that your tools have to satisfy the physical parameters,
A swiss knife can't drill a hole in our intuition like Q.M. can.
Certainly Arun,
u cannot apply calculus over discontinuous space. But then tell me one thing in this universe which is perfectly continuous? Mass energy? charge? Space time? Nothing is continuous. Does that mean we should abandon calculus?
The quantised units of all of these are so so so small that ambiguity arises in the order of 10^-39 (I am talking about plank scale in space time singularity)
The error in our mesurments are so much that we can stop bothering about the 10^-39 things and so. Thus we can use calculus over such discontinuos things. Certainly QM provide the best results, but first try to teach QED to a class 11 student to calculate evergy stored in a isolated spherical capacitor.
In that case tell me why at all do we take mass to be constant for small velocities?
In the end what u say is absolutely correct, but we will consider it once we find very very accurate mesuring instruments.
Saurya Time
gagagoodado, (martian for [expletive]). Man Time, I never said we have to apply it every where. My specification further wasn't for plank lenght, but for the charge of an electron. When we calculated the self energy for a sphere. Here the total charge itself is quite small (lets say 1 nC), and e is 10 ^-19. There's a diff in 10^-10. All I'm saying is when we DO consider the quantisation. When we WORK at orders of Plank length, e,etc, then shouldn't we consider this is calculus. AGAIN, NOT ALWAYS, just at this lenghths. I DON'T HAVE ANY PROBLEM WITH CALCULUS, OR APPROX. but at these scales, we CAN'T approx.
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