Why We use Current in the Ohmic Heating Formula Instead of Voltage Recently I have been learning about the primary differences between AC and DC current and, as an extrapolation, the reasons for where they are used in technology. One of the primary benefits given for AC power in power transmission is that through the use of transformers we can step-up the voltage (and by the same token step down the current) so that less energy is lost due to Ohmic heating. In doing this, given the formula for power being, $P = I^2R$ , and so the formula for Ohmic heating becomes $P = I^2R$.   Where my confusion lies, then, is in the fact that this can be re-written as $$P = V^2/R$$ As we step  down the current to lower ohmic heating, we at the same time are stepping up the voltage, which the above equation seems to imply will have the same effect as not having changed it at all. The way I see this as working is that given the circuit is in series (imagining a very simplified model of a city, the power grid and transmission wires), current will be constant throughout the circuit, regardless of where we look, whereas potential difference will not. However I'm having a little trouble visualizing this - why exactly this inconsistency vs consistency will effect the results for Ohmic heating in the transmission wires - that is, why does stepping up the voltage change anything at all if the formula can also be written as $P = V^2/R $ ? Would this mean that circuits connected in parallel would experience different effects - If anyone could help clarify this that would be great. I found this question a little hard to phrase so if it needs further clarification please let me know.
Ohmic Heating in Wires please could someone tell me why Ohmic losses are always referred to as $I^2 R$ losses? Here is my problem. If the power coming from a power station is fixed then you can either deliver this power as high voltage, low current or high current, low voltage. But isn't $I^2R$ equal to $V^2 / R$, therefore if R is constant doesn't the power depend on the square of the voltage so surely it doesn't matter whether it is high voltage or high current. The only way I can reconcile this is that a high current must cause a greater heating effect than a high voltage. I can't figure why though. If this is the case then is there a reason why a high current causes more heating than a high voltage?
Is there a constraint that restricts my generic method to numeric types? Can anyone tell me if there is a way with generics to limit a generic type argument T to only:   Int16 Int32 Int64 UInt16 UInt32 UInt64   I'm aware of the where keyword, but can't find an interface for only these types,  Something like:  static bool IntegerFunction&lt;T&gt;(T value) where T : INumeric Now that experience does something besides render regions of a server uninhabitable due to  orb lag, what's the most efficient and safe way to get those excellent enchants?  A mob farmer may rank highly, but what about without tons of setup? Show path of a body of where it should go after linear impulse is applied I am making a game with Andengine and Box2D. I have a dynamic body and I apply linear impulse on the body to move it around when the user have touched the screen.  Now I want to show the path where the body will go when the user have touched. If you have played Angry Birds or Basket Ball Shoot or any other which have projectile motion with a path shown you will get my point. I want to show the white dots which are shown in those games. Why is James Bond less tech savvy in the Daniel Craig movies? Every once in a while, someone comes to Meta to report a bug about something not working and it turns out that person is visiting one of the network sites over HTTPS/SSL. The problem has been growing since browsers started to outright block mixed content instead of showing a warning.  The usual answer is that HTTPS is not yet fully supported, and the person should try again using HTTP. Sometimes things get fixed, improving the situation a bit.  Is there a roadmap for full support? Partial support has been there for  now.  Is this actively being worked on? If not, what are the reasons to partially support it instead of disabling it completely to avoid these problems? Why wont my 'background' render? I'm having this problem in Blender that it is only loading the text, I am very new to this and don't know why it is cutting out what is even in the camera view and making it black. If you could help me, I would really appreciate it.   It's only rendering 'Kenny Miller" and not the green/black back:  [ Compile error with \href ToC and \apacite I would like to edit my document but I have a compile error somewhere between the \href and the apacite but can't locate it. I've tried blocking out code and taking out references, with varying results.  \documentclass[a4paper,12pt]{article} \usepackage[english]{babel} \usepackage[utf8]{inputenc}  % TOC, Citations, Refereneces, and Appendicies \usepackage{apacite} % \cite{ref1,ref2} %Warning - unsupported tocstyle code \usepackage[tocindentauto]{tocstyle}     \renewcommand{\thesection}{\Roman{section}}      \renewcommand{\thesubsection}{\arabic{subsection}.}     \renewcommand{\thesubsubsection}{\roman{subsubsection}.} %\usepackage{hyperref} %\urlstyle{same} %\hypersetup{ %   colorlinks=true, %   urlcolor=cyan, %   linkcolor=blue, %   citecolor=green, %   filecolor=magenta, %   pdftitle={Sharelatex Example}, %   pdfpagemode=FullScreen, %} \usepackage[toc,page]{appendix}  \begin{document}    ...to be installed \cite{church13,hershkowits97}. \bibliographystyle{apacite} \bibliography{bibliography} \end{document}   Here are the bibliography.bib entries then  @ARTICLE{church13,    author       = {K.H. Church and H. Tsang and R. Rodrigiguez and P. Defembaugh and R. Rumpf},    year         = 2013,    title        = {Printed circuit structures, the evolution of printed circuit boards},    journal      = {Circuit Insight},    volume       = {},    number       = {},    pages        = {},    howpublished = {},     url          = {http://www.808multimedia.com/winnt/kernel.htm}, }  @ARTICLE{hershkowits97,    author       = {N. Hershkowits and R.A. Breun},    year         = {1997},    title        = {Diagnostics for plasma processing (etch plasmas) (invited)},    journal      = {Review of Scientific Instrumentation},    volume       = {68},    number       = {1},    pages        = {880--885},    howpublished = {}, } I would like to install Ubuntu  for almost 120 users. But it's very difficult in using USB and drives.  Any suggestions? Calling a method in java and returning beer cost Is there a general way to change the font of a particular symbol without switching packages?  For example, suppose I'm using Computer Modern for my entire document, but I want the "subset" operator to look as it does in mathabx.  How can I redefine it to appear in this way? How to disable captive portal detection? How to remove exclamation mark on Wi-Fi or signal icon in Lollipop? When connected to the Internet, the system checks if it's in a walled garden, which is simply trying to connect to Google. If it fails, in Android 5, there'll be an exclamation mark on the WiFi icon or signal icon.   In some situations, this is annoying. Say, in China, Google is blocked, the exclamation mark will always be there, which is meaningless.  How can I disable this check, and make the system assume, connected WiFi/mobile data is connected Internet? Now that I've reached 2k on Stack Overflow, I get access to the "Suggested Edits" review queue.  Although I only have 20 edits per day, the "suggested edit awaiting" icon in the top bar is always there and it bothers me a lot!  My suggestion is to apply one of three solutions:   Remove the suggested edits icon when we reach the maximum (50) edits Remove the Highlight (orange) on the suggested edits Remove the suggested edits part when we click on it   What do you think? What would be the sum of the following series?  $$\sum_{n=1}^{\infty} \frac{1}{n \cdot 2^n}$$  Thanks When a lattice is a lattice of open sets of some topological space? When a lattice $(L,\leqslant)$ is a lattice of open (or closed) sets of some topological space $(X,\tau)$? Which conditions have to be satisfied? We may assume that $X$ is $T_1$. Can I enter other Schengen countries with EU residence permit but without passport? I have some travel plans to go from Netherlands to France by car. I possess Dutch residence permit, but I am non-EU citizen. The problem is that I might need to submit my passport to get visa to another country I plan to go to later. So I have: residence permit and photocopy of my passport. Is it    legal to cross borders by car with this set of documents what are possible fines and other repercussions if police or other authorities ask for my documents in France or Belgium? How to interpret decomposition plot and check for seasonality $X$ is a Hausdorff space and $\sim$ is an equivalence relation.  If the quotient map is open, then $X/{\sim}$ is a Hausdorff space if and only if $\sim$ is a closed subset of the product space $X \times X$.  Necessity is obvious, but I don't know how to prove the other side. That is, $\sim$ is a closed subset of the product space $X \times X$ $\Rightarrow$ $X/{\sim}$ is a Hausdorff space. Any advices and comments will be appreciated. I would like to open all chapters of my PDF ebooks in the same window but neither evince nor okular seems to be capable of doing that (at least not out-of-the-box).  Is there a way to work this out? A deck of 52 cards is shuffled, and we deal a bridge of 13 cards. Let $X$ be the number of aces and $Y$ be the number of spades. Show that $X$, $Y$ are uncorrelated.  Here is what I did:  $Cov(X,Y) = E[XY]-E[X]E[Y]$   uncorrelated means $Cov(X,Y) = 0$, hence  $E[XY]=E[X]E[Y]$   $E[X] =  \sum_{k=0}^{k=4} k \frac{\dbinom{4}{k} \dbinom{48}{13-k}}{\dbinom{52}{13}} $   $E[Y] =  \sum_{k=0}^{k=13} k \frac{\dbinom{13}{k} \dbinom{39}{13-k}}{\dbinom{52}{13}} $   Are the summations above correct? and how do I calculate $E[XY]$? How far does a rogue move when dashing twice using Cunning Action? A rogue receives a bonus Cunning Action, and one option is to Dash. My understanding is a Dash allows a player to move up to twice his speed for his turn.  If a rogue is using a regular action to Dash (hence, is already dashing) can he also use his cunning action as a bonus to Dash again — effectively moving 4 times normal speed in a turn?