What does 50va mean on a 24 volt transformer.
What exactly goes into a transformer's VA rating? At a fundamental level it seems that there has to be a limit to what the VA rating can represent.  For example if I draw 2 Amps-RMS from the secondary of a 30VA rated transformer at 15 Vrms this makes sense as the maximum Complex Power I can draw. Still, at a power factor of 1 my maximum current in the transformer would be sqrt(2) * 2 Amps.   But what if my power factor is abysmally low (ie in a DC rectifier) due to harmonic distortion and while I still draw 2A-RMS I have brief current spikes of 15 Amps? Surely the transformer's magnetics couldn't handle these spikes as I'd expect the core would saturate.  My question is what is the practical limit for VA ratings of transformers? Would brief current spikes that reduce to only 2A-RMS in this case be fine? Obviously the secondary/primary copper losses play a part in the rating but how do the magnetics factor in?  I ask this because I am designing a simple bench power supply using a 125VA transformer with a 24Vrms secondary and am trying to figure out how much power I can draw before the current spikes into the inductor are too much for the transformer. I also don't want to have to resort to active PFC as I don't want to risk messing up any HVAC PCB design.  Thank you
Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$   Obviously $(2,1)$ and $(1,2)$ are two answers. But I was unable to manipulate the equation algebraically giving a useful form for finding all other possible answers! I also tried to view it as a quadratic equation in terms of $x$, but forming the Delta of that equation didn't help much other than if $y=1$ then certainly Delta would be a square and equation would have answer for $x$... Get most common value for each value of another column in SQL I have a table like this:   Column  | Type | Modifiers  ---------+------+-----------  country | text |   food_id | int  |   eaten   | date |    And for each country, I want to get the food that is eaten most often.  The best I can think of (I'm using postgres) is:  CREATE TEMP TABLE counts AS     SELECT country, food_id, count(*) as count FROM munch GROUP BY country, food_id;  CREATE TEMP TABLE max_counts AS     SELECT country, max(count) as max_count FROM counts GROUP BY country;  SELECT country, max(food_id) FROM counts     WHERE (country, count) IN (SELECT * from max_counts) GROUP BY country;   In that last statement, the GROUP BY and max() are needed to break ties, where two different foods have the same count.  This seems like a lot of work for something conceptually simple.  Is there a more straight forward way to do it? Install a .NET windows service without InstallUtil.exe How to float until on left (or right) page? (In, On or At) GitHub? What's the difference between say:     "The project will be on GitHub",      "The project will be in GitHub" and      "The project will be at GitHub"? What happened to Yachiru? According to the , Yachiru disappeared leaving her belongings after the fight with Gremmy. She is said to be "gone" by Kenpachi in the penultimate chapter of the original series.  I use "original" because there might be extra chapters announced as the other big announcement.  So, what happened to her? Was she part of his Zanpakutou or something? Received an email intended for another person I'm not really sure how email routing works, but someone ordered something on Amazon and I received the email instead of them.  Or maybe we both got it, I don't know.  The order doesn't show up in my account, so I'm certain I wasn't charged for it, but I shouldn't be getting other peoples' emails.  We'll say that my email is johndoe1@gmail.com, and somebody who's email is john.doe1@gmail.com places an order on Amazon.  The confirmation email is sent to me at johndoe1@gmail.com.  I checked the email header, and it did say To: john.doe1@gmail.com which is not my email address.  At first I thought that Google ignores periods in email addresses, but I tested the account setup and it doesn't give any error when you put a period in the address.  I didn't create the account; I just used the "check availability" function and the address I chose with a period was fine.  Maybe someone with knowledge about how Email works could tell me why this happened.  Is this a bug in the way Amazon sends emails?  Or is it a bug in how Google receives them?  Who should I report this issue to? Is there to make the login screen appear on the external display in 18.04? On Ubuntu 18.04, I have connected my laptop to an external display and I am able to set the external display as primary and external display only mode. But when I turn on my laptop or log out from my session the display login screen is displayed only on my(internal) laptop screen. But once I login the display switches to external only and my laptop screen turns off as expected. Is there a way I can make the login screen appear only on the external screen on bootup or on logout as in 16.04? Also the login screen does not follow my cursor as in 16.04. Dependency error while installing WINE Every time I try to install "WINE" VIA the Software Center on Ubuntu 12.10, I get this error:  The following packages have unmet dependencies:  wine1.4: PreDepends: dpkg (&gt;= 1.15.7.2~) but 1.16.7ubuntu6 is to be installed          Depends: libc6 (&gt;= 2.14) but 2.15-0ubuntu20 is to be installed          Depends: wine1.4-amd64 (= 1.4.1-0ubuntu1) but 1.4.1-0ubuntu1 is to be installed          Depends: wine1.4-i386 (= 1.4.1-0ubuntu1) but it is not going to be installed   When I try installing it VIA the terminal, this is what I get:  Reading package lists... Done Building dependency tree        Reading state information... Done Some packages could not be installed. This may mean that you have requested an impossible situation or if you are using the unstable distribution that some required packages have not yet been created or been moved out of Incoming. The following information may help to resolve the situation:  The following packages have unmet dependencies:  wine1.4 : Depends: wine1.4-i386 (= 1.4.1-0ubuntu1) but it is not installable            Recommends: gnome-exe-thumbnailer but it is not going to be installed or                        kde-runtime but it is not going to be installed            Recommends: ttf-droid            Recommends: ttf-mscorefonts-installer but it is not going to be installed            Recommends: ttf-umefont but it is not going to be installed            Recommends: ttf-unfonts-core but it is not going to be installed            Recommends: winbind but it is not going to be installed            Recommends: winetricks but it is not going to be installed E: Unable to correct problems, you have held broken packages.   how do I fix this? Clicking leave closed shows the reopen pop-up Extracting extension from filename in Python Is there a function to extract the extension from a filename? If/Else with Selenium IDE - when confirmation message comes up I have a scenario, in case of the user registration successful, it will display a success message on the next page otherwise an error message shows on the same page. How to automate the test case to return as passed if it is success and failure in case of error message comes up.  Please help me out here. An investigator wishes to produce a combined analysis of several datasets.  In some datasets there are paired observations for treatment A and B.  In others there are unpaired A and/or B data.  I am looking for a reference for an adaptation of the t-test, or for a likelihood ratio test, for such partially paired data.  I am willing to (for now) to assume normality with equal variance and that the population means for A are the same for each study (and likewise for B). Work out the type of c# application a class contained in a DLL is being used by Is there any way to know in C# the type of application that is running.  Windows Service ASP.NET Windows Form Console  I would like to react to the application type but cannot find a way to determine it. Why are Perl 5's function prototypes bad? Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$ Let $G$ be a finite abelian group and let $\phi: G \rightarrow G$ be a group homomorphism. I am trying to show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$.  I know that since $G$ is abelian we have that $\ker(\phi^{k})$ and $\phi^{k}(G)$ are normal subgroups of $G$ for any $k$  I also suspect we have the following towers which stabilize at $m$ and $m'$  $$\phi(G) \unrhd \phi^{2}(G) \unrhd \cdots \unrhd \phi^{m}(G)=\phi^{m+1}(G)=\cdots$$  $$\ker(\phi) \unlhd \ker^{2}(\phi) \unlhd \cdots \unlhd \ker^{m'}(\phi)=\ker^{m'+1}(\phi)=\cdots$$  I know that if given a group of the form $HK$ where $H$ and $K$ are normal subgroups of $HK$ and $H\cap K=1$ then $H \times K \cong HK$. I want to apply this to this situation but I am unable to show how write $G$ as a product $HK$  Resolution One of the comments directed me to the following article:  The last part of which answers the question. Below is what is says:  Choose $n=\max(m,m')$, then we have for $x \in \ker^{n}(\phi) \cap \phi^{n}(x)$, this means that $x=\phi^{n}(y)$ for some $y \in G$. This gives:  $0=\phi^{n}(x)=\phi^{2n}(y)$ which means that $y \in \ker^{2n}\phi=\ker^{n}{\phi}$. and then we have that $0=x=\phi^{n}(y)$.  The answer below kindly points out that every element $x$ is contained in one of the cosets of $G/\ker^{n}(\phi)$, this means that $x=k+g$ for some $k \in \ker^{n}(\phi)$ and $g \in G$. We also have that $g=\phi^{n}(h)$ for some $h \in G$. Writing $x=k+\phi^{n}(h)$ essentially shows that $G=\ker(\phi^{n}) + \phi^{n}(G)$. Using the fact above, the claim follows. When is "self" required? Since the last update (v1.0.85), I am getting all the question pages blank on the Android app. For those who are confused with the image, I'm using RtL (Right-to-Left) layout.        If I scroll down (quite a bit) I can see the question. But even then I cannot see the question title, the related comments or answers.         App Version: 1.0.85 Device Manufacturer: LGE Device Model: LG-D620   OS Version: 5.0.2 (152541901f156) What is the difference between DX format and FX format lenses, and which to choose for what purpose? What is the difference between DX format and FX format lenses, and which to choose for what purpose?  What are the pros and cons of both? Is C++ CLI a superset of C++? Would a C++  compiler be able to compile some large sets of C++ classes without modifications?   Is C++ CLI a superset of C++?