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Express Laplace transform of voltage across a capacitor in terms of charge

I'd be interested to hear folks' opinions.

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    $\begingroup$ +1 because this is a discussion which I think we (the community) need to have. $\endgroup$ – sammy gerbil Mar 2 '17 at 8:42
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Disclaimer: I have written an answer to the question discussed here, so one might consider my opinion in this matter biased. I did not vote on the closure of the question in any way.

I think the question should have the tag, but should not be closed. Clearly, this is essentially an exercise in computing the behaviour of a specific circuit in a specific situation, and the question asks to understand a specific step in the derivation, clearly not because it is interested in the end result since the end result is already known. So "primarily for educational value" applies as well as being about a specific exercise, and therefore I think the tag should be applied.

However, I don't think it should be closed - it shows some effort to work through the problem (the equation it asks about in the end was derived by that effort in the first place) and the question of why the voltage is computed in this way is conceptual. There is no straightforward "plug-and-chug" derivation that yields eq. ($\star$), it must be arrived at mainly by physical reasoning about the circuit, not computation.

As supporting evidence that this is not (or should not be) off-topic as homework-like, consider the 3:0 Leave Open review this question received in the queue. Homework-like questions that are clearly off-topic usuaslly receive quick and almost always unanimous close reviews, so this at least shows it is not clearly off-topic.

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  • $\begingroup$ "The end result is known" is a slippery metric to use. Known to whom? To the OP? Then it misses half the questions that should get the tag, because OP doesn't have the solutions. To Science in general? Then it applies to all of this site. To the textbook author? To some fraction of authors in the literature? It's a nice heuristic, but I don't think it can be sharpened into anything meaningful. $\endgroup$ – Emilio Pisanty Mar 5 '17 at 13:20
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As our current policy says, the tag should be applied to questions which arise in the context of doing "educational exercises". The defining property of an educational exercise is that the purpose of solving the exercise is learning to use (or gaining further practice with) the method by which it is solved.

I don't believe that is the case in this question. It's been claimed that this is the exercise:

Consider a circuit consisting of a capacitor $C$, an impedance $\tilde{Z}(\omega)$, and a constant voltage source $V$ connected in a loop. Suppose in equilibrium the charge across the capacitor is $Q_e$. Now at time $t=0$ we drop some charge on the capacitor, making the total capacitor charge $Q_0$. We'd like to solve for the time dependent charge $Q(t)$ on the capacitor.

The purpose of solving this problem is not for you to learn the method by which it can be solved, I presume. If I understand correctly, the entire purpose of this problem is to provide context for the underlying conceptual question,

The paper I'm reading writes an equation which leads me to believe that $$\hat{V}(p) = \frac{Q_e}{pC} - \frac{\hat{Q}(p)}{C} \, , \tag{$\star$}$$ but I don't understand why that's the case.

Why is equation $(\star)$ correct?

It's completely irrelevant (again if I understand correctly) whether you actually make any further progress in solving the exercise. That would not be the case if your purpose were to learn the method of solution. Therefore, I conclude the tag is inappropriate for this question.

As further justification, another property of almost all educational exercises is that you get them from some other source: a textbook, a homework assignment, an old contest, a problem book, or so on. As I understand it, this is not the case here. Now, it is possible to have a question which does not include an exercise from an external source but is nevertheless a question, e.g. if the poster has made up an exercise for themselves to get practice with a certain technique. But this is quite rare. Rare enough that, when a question is not based on an exercise from some external source, we should probably avoid applying the tag unless we know that the poster's intent is to practice the method. I certainly don't believe that is the case here.

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    $\begingroup$ I agree with you opening definition, but disagree that this question is not caught by it. Isn't it obvious that DS is teaching himself how to apply transforms to solve AC circuit problems? And since when has the source of the exercise been material? Some other source than what? Often a user says he made up the question himself, but that is no defence against closure under your definition. What makes the question in the 2nd box conceptual? What is the difference between that and asking "why the answer is X?" ? $\endgroup$ – sammy gerbil Mar 2 '17 at 5:40
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    $\begingroup$ No, it is not obvious. Not to me, anyway, not unless you make the definition of "teaching" to be so broad that it encompasses every good question on the site. And as I said, the source of the exercise is not what makes a question a homework-and-exercises question, but it is a good heuristic. Yes, people can lie, but there are other heuristics that are not so easily defeated. ("Other source" means other than the person who is trying to solve the exercise.) $\endgroup$ – David Z♦ Mar 2 '17 at 6:18
  • $\begingroup$ Also, you're right that what Daniel is asking here is not all that different from asking "why is the answer X?" Questions of this nature are, in most cases, conceptual. They ask about the concept that one should use in the process of finding that the answer is X. Note the difference between that and "what is the answer?", "is X the answer?", or "how do I get the answer?", which are examples of non-conceptual questions. $\endgroup$ – David Z♦ Mar 2 '17 at 6:21
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    $\begingroup$ I am not claiming anyone lies about the source of a problem; I am claiming that the source is irrelevant, just as whether an exercise is self-teaching or imposed by a teacher is irrelevant (if I understand the policy correctly). ... It seems contradictory to me that "what concept will enable me to get the answer X?" is conceptual but "how do I get the answer X?" is non-conceptual. The same answer could be given to both. $\endgroup$ – sammy gerbil Mar 2 '17 at 6:39
  • $\begingroup$ You're right that the HW policy says that the source of a problem is irrelevant. It's the purpose that matters. But what I'm saying here is that source is fairly well correlated with purpose. If you have doubts about the purpose, you can consider the source to help you resolve those doubts. Also, if someone literally asked "what concept will enable me to get the answer X?", that is also not a conceptual question. But that is not what I referred to in my previous comment. I was talking about questions about a concept, not asking for a concept (that's the gist, anyway). $\endgroup$ – David Z♦ Mar 2 '17 at 6:45
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    $\begingroup$ DS has not identified a concept, has he? It seems to me that he is asking "what is the concept which will explain why equation star is true?" He explained in a comment : The kind of conceptual answer that would satisfy me is to explain where the equation comes from. Is it from boundary conditions? Is it something about Kirchoff's laws? $\endgroup$ – sammy gerbil Mar 2 '17 at 7:01
  • $\begingroup$ I believe he has identified a concept: the reason why that equation is true (if it is true). Though perhaps we're getting lost in terminology differences. The bigger point is that when the HW policy uses the word "conceptual", it's referring to exactly the kind of question Daniel is asking. We could argue whether there's a better way of describing it than "conceptual", but the intent of the homework policy is not to render questions like this off topic. (Also note we have two separate issues: should the question have the HW tag, and is it on topic? "Conceptual" relates only to the latter.) $\endgroup$ – David Z♦ Mar 2 '17 at 8:30
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    $\begingroup$ If that is the meaning of conceptual then every problem-solving question which asks "Show that the following answer is correct" is also conceptual. The reason we are having this discussion is because the issue is either not clear or not logical. The point I am making is that the meaning of the policy seems to depend on whether you are a highly respected user like DS or a low-rep user. $\endgroup$ – sammy gerbil Mar 2 '17 at 9:41
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    $\begingroup$ No, I believe there is a key difference you're missing between "Show that this equation is correct" (which is not conceptual) and "Why is this equation correct?" (which is conceptual). The former asks for a proof. The latter asks for physical understanding. $\endgroup$ – David Z♦ Mar 2 '17 at 19:42

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