The voltage for transformer is given by  $\frac{V_1}{V_2} =\frac{N_2}{N_1}$  if we use ohms law and assume resistance are same for both inductors,  $\frac{I_1 R} { I_2 R}=\frac{N_2}{N_1}$  but   in my book they derive using power equivalence $I_1 * V_1 = I_2 V_2$ which gives  $\frac{V_1}{V_2}=\frac{I_2}{I_1}$  where have I made the mistake?
In transformers, the ratio of the voltages equals the ratio of the turns - so double the output coil's turns and the output voltage doubles. Then, in order to conserve energy, current halves.  This makes perfect sense in terms of $\mathrm{P=VI}$, but what happened to $\mathrm{V=IR}$? Doubling voltage and halving the current seems to completely contradict this basic law. That is, of course, unless the resistance in the output circuit changes, with R proportional to $\mathrm{V^2}$ - but I don't see how this is possible.  So how can a transformer obey both laws? Can resistance change or am I missing something else?
How to redirect STDIN of background process? In my Ubuntu, i run java application in background. I use bash script to run it and now it looks like:  nohup java -jar app.jar &amp; exit 0   The problem that i want to be able to write an input string to my application, without making it foreground, from different terminals/sessions. Something like  echo "mytext" &gt; /appdir/in   How should i change my script? Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist? Hot chicken soup takes hours to cool I made a big pot of a very hot chicken soup. I put it in my small extra fridge at 11 PM, and it was still warm 9 hours later, at 8 AM.  Do I need to throw it away? Use of Website Category Landing Pages OK, here's the situation: A reasonably simple website with a primary navigation menu including drop-down list of sublevels on hover. Each navigation level may have 3 - 6 sublevels below it, none more important than the other. For example see this mockup:    My question is: What should happen if the user Clicks on one of the primary navigation options (such as 'News') instead of just hovering over and choosing a sublevel?  My instinct tells me that I should allow a click of this navigation option; it's expected user behavior to be able to click navigation options. If clicked then a landing page of some sort will be present listing all the sublevels (latest news, blog posts, case studies'). However there is no content to add to this landing page other than presenting a list of links, which is pretty useless. I could pad it out by adding iconography and descriptions of the sublevels, but that's just content for the sake of it; does 'Latest News' really need a description in order to understand what it is?  If I don't include a landing page then clicking this primary navigation will have to open something but if I open the 'Latest News' page that risks the user not knowing about the other sections of the site.  (The landing page will be useful for breadcrumb navigation too, so I don't really want to do away with it).  Is my thinking that a landing page showing the list of sublevels actually useful even though there is no actual content to display, or is there a better alternative to go with? For example,   If this van's a-rockin', don't come a-knockin'  (song title)   (song title)   I have a few related questions:   What is the "a-" or "-a" called? Is there a function beyond a rhythmic one? Why is "a-" attached to a word at all -- and why attach to a word at all? tikz trees: How to not draw a single edge General integral to find resistance My question is: is there a simple and truly general equation for the resistance between two electrical equipotential surfaces?.  Obviously, if so, what is it, and if not, why?  It would be very difficult to solve, granted, but I just want to see a calculus equation that is fully descriptive.  I have two frameworks under which this could be entertained, I'll write those out and then explain the motivation.  To start with, we need propose that the volume separating the two surfaces has a volumetric resistivity, $\rho$ in units of $(\Omega m)$.  Single Volume Framework  We can limit the discussion to a defined volume, then the surfaces reside in that volume or on the surface of it.  This volume may have a constant resistivity $\rho$ while everywhere outside the volume is completely electrically insulating.  Infinite Volume Framework  An alternative to the above approach that might make the task more or less difficult would be to replace a constant resistivity with a spatial dependence $\rho(\vec{r})$ and no longer require a boundary condition.  In that case we only have 3 mathematical inputs to the problem, which is the resistivity defined for all $\vec{r}$ and a definition of the two surfaces, $S_1$ and $S_2$.  Known Algebraic Analogs  The  that I find insufficient is:  $$R = \rho \frac{\ell}{A}$$  Where $l$ is the length of the restive material that is any shape which has translation symmetry over that length, and $A$ is the cross-sectional area.  Obviously, this is a rather simple equation that won't apply to more complicated geometry.  Even more  seem to give equations that fall short of what I'm asking.  For example:  $$R = \rho \int_0^l \frac{1}{A(x)} dx$$  I think it's obvious that an equation such as this is built upon a myriad of assumptions.  For a thought experiment, imagine that the area starts out as very small and then pans out to very large quickly.  Well, accounting for the larger area in the above sense underestimates the resistance, because the charge has to diffuse out perpendicular to the average direction of flow as well as parallel to it.  I have some reasons to suspect this might actually be rather difficult.  A big reason is that all the approaches I'm familiar with require the flow paths to be established beforehand, which can't be done for what I'm asking.  So maybe this will result in two interconnected calculus equations.  Motivation  I had an interest in , and it occurred to me that I can't quickly and simply write down the equation for resistance between two points.  The unique thing about Squishy Circuits is that it calls for two types of dough, one that conducts and one that is mostly insulating.  However, the recipes aren't perfect and because of that, the young children who play with these circuits regularly encounter the limits of conductor and insulator definitions.  If you make your conductor dough too long and/or too thin, you will encounter dimming of the light you connect with it.  Similarly, a thin insulator layer will lead to a lot of leakage current which also dims the light. What is Quantization? comment.sty and UTF8 encoding I noted that if I use comment.sty and a there is a block of text containing UTF8 characters inside a comment environment, the compilation aborts!  Minimal Example  \documentclass{article} \usepackage[T1]{fontenc} \RequirePackage[utf8]{inputenc}%this file is stored as UTF8 file! \RequirePackage{comment} \specialcomment{privateSolution}     {\begingroup\itshape\noindent\textbf{Solution}\\}     {\endgroup} %\excludecomment{privateSolution}%Use it to remove solutions!  \begin{document} \title{Comment.sty and UTF8 test file} \maketitle \section{UTF8 character test} In which alphabet characters àìùòè are common? \begin{privateSolution}     The Italian alphabet contains àìùòè. \end{privateSolution}  \begin{comment}     The Italian one! It contains àìùòè. \end{comment} \end{document}   Has anyone the same problem? Any workaround?  Thanks in advance. Is there a way to achieve the equivalent of a  in javascript regular expressions?  I need to match a string that does not start with a specific set of characters.  It seems I am unable to find a regex that does this without failing if the matched part is found at the beginning of the string.  Negative lookbehinds seem to be the only answer, but javascript doesn't have one.  EDIT: This is the regex that I would like to work, but it doesn't:  (?&lt;!([abcdefg]))m  So it would match the 'm' in 'jim' or 'm', but not 'jam' I am not mathematician by any means so this question might be rather stupid. I came across this Wikipedia article on  and found this bewildering formula,   $$1 + 2 + 3 + \dots  = - \frac1{12}$$  The article also says that "Ramanujan summation of a divergent series is not a sum in the traditional sense". I am wondering then what this summation actually implies?  Is there any interpretation of this confounding result in the physical world that someone not so math-savvy can understand? I have some files that Ubuntu can't read it ( ANSI encoding ) but Windows can read it well.  When I open it in gedit or notepad++ it seems like this :     Êã ÇáÊÍæíá áÜÜ   How can I make Ubuntu read ANSI encoded files well? 14.04 - Network manager stopped working When I started my laptop, there was no network service, and also no network icon in the top bar. It gives an error when I start OS like "Sorry, Ubuntu 14.04 experienced an internal error". When I click details, it says the error is occurred in the executable path usr/sbin/NetworkManager. Also, when I try to enter Network in the System Settings, it says "the system network services are not compatible with this version"  How can I solve this shocking issue?  p.s. I didn't install any third party packages/apps related with networking. Only system updates are installed. Is a differentiable function always continuous? Continuous Functions are not Always Differentiable. But can we safely say that if a function f(x) is differentiable within range $(a,b)$ then it is continuous in the interval $[a,b]$ . If so , what is the logic behind it ? Does the series $\sum \limits_{n=2}^{\infty }\frac{n^{\log n}}{(\log n)^{n}}$ converge? Why is the ROC curve two-dimensional instead of three-dimensional? How to send a header using a HTTP request through a cURL call? I wish to send a header to my Apache server on a Linux box.  How can I achieve this via a cURL call? How to serialize a JObject without the formatting? Cannot change backlight brightness Ubuntu 14.04 Incorrect whitespaces or list item size in Android SE app Noticed that sometimes when there are 10+ answers to a question - some answers look like they have \n\n...\n line breaks in the end, so the body of the answer has incorrect height.  It probably has something to do with ViewHolder or adapter not setting correct row height. Although as far as I know, it should do this according to text amount/length.