Suppose we have simple circuit in which a battery of EMF $E$ is connected to a capacitor of capacitance $C$.  Work done by battery $W_{b}=CV\times V$ and energy stored in capacitor $=\frac{1}{2}CV^{2}$. Therefore the difference, which I'm assuming to be energy loss due to battery's internal resistance $=\frac{1}{2}CV^{2}$.  My question is why doesn't the energy loss by internal resistance depend on the chemical nature of the battery used? How do we define the quality of a battery if same energy is lost irrespective of their chemical composition in all of them ?  If my approach is wrong, what does this remaining $\frac{1}{2}CV^{2}$ signify?
A uncharged capacitor $C$ is connected to a battery with potential $V$. It becomes fully charged and has a charge $Q=CV$ stored on it.   Now the polarity of the battery is reversed. The capacitor will have the charge $Q$ still but with polarity reversed too.  My question is: What is the work done by the the battery?  According to me, during 1st charging it will do a work of $QV$. The energy of the capacitor is also not changing, then what is the work done to change its polarity?
how to reduce DC voltage using resistors? How would one go about using a 12 V DC power source to power something which needs 4.5 V DC using resistors? Is there a way to determine how much adding a resistor would drop the voltage? I’ve run into a limitation in the cURL bindings for PHP. It appears there is no easy way to send the same multiple values for the same key for postfields. Most of the workarounds I have come across for this have involved creating the URL encoded post fields by hand tag=foo&amp;tag=bar&amp;tag=baz) instead of using the associative array version of CURLOPT_POSTFIELDS.  It seems like a pretty common thing to need to support so I feel like I must have missed something. Is this really the only way to handle multiple values for the same key?  While this workaround might be considered workable (if not really annoying), my main problem is that I need to be able to do multiple values for the same key and also support file upload. As far as I can tell, file upload more or less requires to use the associate arravy version of CURLOPT_POSTFIELDS. So I feel like I am stuck.  I have  about this problem in more detail on the cURL PHP mailing list in the hopes that someone there has some ideas about this.  Suggestions or hints on where I can look for more information on this are greatly appreciated! Processing time/speed for Mosaic to New Raster I have a question on speeding up “Mosaic to New Raster” or finding an alternative.  After completing a suitability analysis we are trying to define movement corridors.  We used a modified CircuitScape that left 4 folders, each containing 1080 raster tiles across our study area.  We now need combine all 1080 rasters in each folder then combine these 4 combined rasters into a final raster which will be analyzed for paths.  I tried a python script that just wouldn’t work so I went on to Model Builder.  It iterates through the grids in the folder, collects the values (raster names), then mosaics all to a new raster.  It has been running for 5 days now and the results window indicates it is working.  I’m hoping it will conclude in the next day or 2.  But, we still have 3 more folders, each with 1080 rasters, that need to be mosaicked.  So….is there a way to speed up Mosaic to New Raster or is there an alternative I could use to produce the final grid?    The cell size is 270 meters, 540 x 540 columns and rows, 1 band, 32 bit floating. How can i integrate one SFDC org to another SFDC using Rest Api I am trying to integrate one Salesforce org to other org by using Oauth setup, I wanted to use  use consumer key and consumer secret key in my REST class to connect with the org, after connection part completion, I want to access Get(), Put(), Post(), etc. Including the ability to set Oauth and Authorization headers needed for Salesforce Rest API calls.  Actually I'm new in REST implementation so can you please explain me by using code samples. How to set timeout for web service call I want to call out my web service after the insert process of a custom object with a delay of 2 minutes. But i am getting that exception FATAL_ERROR|System.CalloutException: Read timed out How can i fix that problem ? Here is my implementation.  Callout class:  public class HttpCallout{     @Future(callout=true)     public static void getContent(String url){         Http h = new Http();          HttpRequest req = new HttpRequest();         req.setEndpoint(url);         req.setMethod('GET');         req.setTimeout(2000);          HttpResponse res = h.send(req);         String response = EncodingUtil.urlDecode(res.getBody(),'UTF-8');         System.debug('***response****'+response);     }      public void serviceCaller(){         getContent(url);     } }   Trigger:  trigger AfterInsertOrUpdate on Sales_Order__c (after insert) {     System.debug('Making future call to update account');     HttpCallout httpCallout = new HttpCallout();     httpCallout.serviceCaller();     System.debug('After Insert'); }   Any help would be appriciated. I'm trying to write a simple bash function that takes, as its arguments, a number of files and/or directories. It should:   Fully qualify the filenames. Sort them. Remove duplicates. Print all that actually exist. Return the number of non-existent files.   I have a script that almost does what I want, but falls down on the sorting. The return value of the script as it stands is correct, but the output is not (unsorted and duplicates). If I uncomment the | sort -u statement as indicated, the output is correct but the return value is always 0.  N.B. Simpler solutions to solve the problem are welcome but the question is really about why is this occurring in the code I have. That is, why does adding the pipe seemingly stop the script incrementing the variable r?  Here's the script:  function uniqfile {     local r=0       for arg in "$@"     do           readlink -e "$arg" || (( ++r ))      done #| sort -u    ## remove that comment      return $r } How do I convert or upgrade roads? I'm trying to optimize my road system a bit, mostly converting regular small roads into one-way roads. But the only way I can see to do that is to remove the old road entirely and build a new one. I can't seem to just build over the old one.   I can understand that limitation in cases where the new road type is larger, but it should be possible to upgrade to roads with the same size without tearing down the old road manually.   Is there an easier way to convert or upgrade roads, or do I have to manually remove the existing road every time? Add layer to a QGIS group using Python Who is this running kid wearing a shirt with Uchiha symbol? There's a kid wearing a shirt with Uchiha symbol, but I have no idea who s/he is.    Who is this kid? What happened to Finn's blaster at Maz Kanata's? When entering, we see that Finn has the blaster that was given to him earlier:    However, when the fighting begins, Finn tells Maz that he needs a weapon and no longer has his blaster with him.  It seems unlikely to have been lost in the first shots, given how it is secured across his body.  Also, Han and Chewie didn't lose their weapons and they are arguably less secure.  Now, when the team gets to the Resistance base, Finn again has his blaster:    So where was this blaster during the battle? Cannot install vim I am running Ubuntu 11.10, as Xubuntu, in an AMD 64 pc, configured as dual boot with Windows 7.  I tried installing vim with this:  sudo apt-get install vim   I got this error message:  The following packages have unmet dependencies:  vim : Depends: vim-common (= 2:7.3.154+hg~74503f6ee649-2ubuntu2) but 2:7.3.154+hg~74503f6ee649-2ubuntu3 is to be installed E: Unable to correct problems, you have held broken packages.   I only have a very faint idea of what the problem is, and none whatsoever on how to correct this. Hope you guys can help. Well I thought this is obvious. since $\gcd(a,b)=1$,  then we have that $a\not\mid b$ AND $a\mid bc$. This implies that $a$ divides $c$. But apparently this is wrong. Help explain why this way is wrong please.   The question tells you give me two relatively prime numbers $a$ and $b$ such that $a$ divides the product $bc$, prove that $a$ divides $c$. how is this not obvious? Explain to me how my "proof" is not correct. What does each AMS package do? In my view, any document with a substantial amount of mathematics should load the packages from AMS-TeX. Hence, most of my document's preambles contain  \usepackage{amsmath, amsthm, amssymb, amsfonts}   (I could add to that the non-AMS mathtools, etc.). What do each of those packages do? Do I really need to list all of them, or do some of them load others? In particular, does any package load all of them, so that I can simply type  \usepackage{ams-everything}   shorter than the current list? How to Disavow Bad Backlinks Automatically? When editing really long code blocks (which should definitely be refactored anyway, but that's beyond the scope of this question), I often long for the ability to collapse statement blocks like one can collapse function blocks.  That is to say, it would be great if the minus icon appeared on the code outline for everything enclosed in braces.  It seems to appear for functions, classes, regions, namespaces, usings, but not for conditional or iterative blocks.  It would be fantastic if I could collapse things like ifs, switches, foreaches, that kind of thing!  Googling into that a bit, I discovered that apparently C++ outlining in VS allows this but C# outlining in VS does not.  I don't really get why.  Even notepad++ will so these collapses if I select the C# formatting, so I don't get why Visual Studio doesn't.  Does anyone know of a VS2008 add-in that will enable this behavior?  Or some sort of hidden setting for it?  Edited to add: inserting regions is of course an option and it did already occur to me, but quite frankly, I shouldn't have to wrap things in a region that are already wrapped in braces... if I was going to edit the existing code, I would just refactor it to have better separation of concern anyway. ("wrapping" with new methods instead of regions ;) Show all of my question/answers to me even if they are deleted Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal.   However, today I'm doing a homework considering a potential like this:$$V(r)=-V_0\quad(r&lt;a)$$$$ V(r)=0\quad(r&gt;a)$$ and found that there is no bound state when $V_0a^2&lt;\pi^2\hbar^2/8m$.  So what's the condition that we have at least one bound state for 3D and 2D? Re-install Ubuntu without losing data in home folder I've been reading the  and it mentions about virtual terminals which, if I understood it correctly, it is a Linux-specific feature (not in Unix) to allow multiple login consoles in a non X11 system. You create virtual terminals by pressing ALT-F2. I'm running Linux Mint and in my /dev folder though I see many tty devices and I don't know what they are for. Here is the grepped output:  crw-rw-rw-  1 root tty       5,   0 Jan  2 19:45 tty crw--w----  1 root tty       4,   0 Jan  2 19:10 tty0 crw-rw----  1 root tty       4,   1 Jan  2 19:10 tty1 crw--w----  1 root tty       4,  10 Jan  2 19:10 tty10 crw--w----  1 root tty       4,  11 Jan  2 19:10 tty11 crw--w----  1 root tty       4,  12 Jan  2 19:10 tty12 crw--w----  1 root tty       4,  13 Jan  2 19:10 tty13 crw--w----  1 root tty       4,  14 Jan  2 19:10 tty14 crw--w----  1 root tty       4,  15 Jan  2 19:10 tty15 crw--w----  1 root tty       4,  16 Jan  2 19:10 tty16 crw--w----  1 root tty       4,  17 Jan  2 19:10 tty17 crw--w----  1 root tty       4,  18 Jan  2 19:10 tty18 crw--w----  1 root tty       4,  19 Jan  2 19:10 tty19 crw-rw----  1 root tty       4,   2 Jan  2 19:10 tty2 crw--w----  1 root tty       4,  20 Jan  2 19:10 tty20 crw--w----  1 root tty       4,  21 Jan  2 19:10 tty21 crw--w----  1 root tty       4,  22 Jan  2 19:10 tty22 crw--w----  1 root tty       4,  23 Jan  2 19:10 tty23 crw--w----  1 root tty       4,  24 Jan  2 19:10 tty24 crw--w----  1 root tty       4,  25 Jan  2 19:10 tty25 crw--w----  1 root tty       4,  26 Jan  2 19:10 tty26 crw--w----  1 root tty       4,  27 Jan  2 19:10 tty27 crw--w----  1 root tty       4,  28 Jan  2 19:10 tty28 crw--w----  1 root tty       4,  29 Jan  2 19:10 tty29 crw-rw----  1 root tty       4,   3 Jan  2 19:10 tty3 crw--w----  1 root tty       4,  30 Jan  2 19:10 tty30 crw--w----  1 root tty       4,  31 Jan  2 19:10 tty31 crw--w----  1 root tty       4,  32 Jan  2 19:10 tty32 crw--w----  1 root tty       4,  33 Jan  2 19:10 tty33 crw--w----  1 root tty       4,  34 Jan  2 19:10 tty34 crw--w----  1 root tty       4,  35 Jan  2 19:10 tty35 crw--w----  1 root tty       4,  36 Jan  2 19:10 tty36 crw--w----  1 root tty       4,  37 Jan  2 19:10 tty37 crw--w----  1 root tty       4,  38 Jan  2 19:10 tty38 crw--w----  1 root tty       4,  39 Jan  2 19:10 tty39 crw-rw----  1 root tty       4,   4 Jan  2 19:10 tty4 crw--w----  1 root tty       4,  40 Jan  2 19:10 tty40 crw--w----  1 root tty       4,  41 Jan  2 19:10 tty41 crw--w----  1 root tty       4,  42 Jan  2 19:10 tty42 crw--w----  1 root tty       4,  43 Jan  2 19:10 tty43 crw--w----  1 root tty       4,  44 Jan  2 19:10 tty44 crw--w----  1 root tty       4,  45 Jan  2 19:10 tty45 crw--w----  1 root tty       4,  46 Jan  2 19:10 tty46 crw--w----  1 root tty       4,  47 Jan  2 19:10 tty47 crw--w----  1 root tty       4,  48 Jan  2 19:10 tty48 crw--w----  1 root tty       4,  49 Jan  2 19:10 tty49 crw-rw----  1 root tty       4,   5 Jan  2 19:10 tty5 crw--w----  1 root tty       4,  50 Jan  2 19:10 tty50 crw--w----  1 root tty       4,  51 Jan  2 19:10 tty51 crw--w----  1 root tty       4,  52 Jan  2 19:10 tty52 crw--w----  1 root tty       4,  53 Jan  2 19:10 tty53 crw--w----  1 root tty       4,  54 Jan  2 19:10 tty54 crw--w----  1 root tty       4,  55 Jan  2 19:10 tty55 crw--w----  1 root tty       4,  56 Jan  2 19:10 tty56 crw--w----  1 root tty       4,  57 Jan  2 19:10 tty57 crw--w----  1 root tty       4,  58 Jan  2 19:10 tty58 crw--w----  1 root tty       4,  59 Jan  2 19:10 tty59 crw-rw----  1 root tty       4,   6 Jan  2 19:10 tty6 crw--w----  1 root tty       4,  60 Jan  2 19:10 tty60 crw--w----  1 root tty       4,  61 Jan  2 19:10 tty61 crw--w----  1 root tty       4,  62 Jan  2 19:10 tty62 crw--w----  1 root tty       4,  63 Jan  2 19:10 tty63 crw--w----  1 root tty       4,   7 Jan  2 19:10 tty7 crw--w----  1 root tty       4,   8 Jan  2 19:10 tty8 crw--w----  1 root tty       4,   9 Jan  2 19:10 tty9 How do I make a WinForms app go Full Screen I have a WinForms app that I am trying to make full screen (somewhat like what VS does in full screen mode).  Currently I am setting FormBorderStyle to None and WindowState to Maximized which gives me a little more space, but it doesn't cover over the taskbar if it is visible.  What do I need to do to use that space as well?  For bonus points, is there something I can do to make my MenuStrip autohide to give up that space as well?