Further in my textbook it is stated that the ends of all three resistors are under the same potential difference. how is that possible?
I know how to detect when resistors are arranged in parallel or series arrangement and I can also find their equivalent resistance in simple circuits or when resistances are connected in form of triangle but what happens when the arrangement is complex like this :   Which resistors are parallel and which are in series ? How can I find the equivalent resistance in such cases ? Is there rule or method for figuring this out ?
What is C# analog of C++ std::pair? I'm interested: What is C#'s analog of std::pair in C++? I found System.Web.UI.Pair class, but I'd prefer something template-based.  Thank you! How do I copy Word tables into Excel without splitting cells into multiple rows? I have data in a Word table that includes line and paragraph breaks. When I copy the data into Excel, it splits each line and paragraph I want into multiple cells. How do I copy the data to Excel and keep the breaks? I had two drives partitioned the same and running two RAID partitions on each.  One died and I replaced it under warranty for the same model.  While trying to partition it, the first partition can only start on sector 2048, instead of 63 that was before. Drive have different geometry as previous and remaining ones. (Fewer heads/more cylinders)  Old drive:  $ sudo fdisk -c -u -l /dev/sdb   Disk /dev/sdb: 2000.4 GB, 2000398934016 bytes 255 heads, 63 sectors/track, 243201 cylinders, total 3907029168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x000aa189     Device Boot      Start         End      Blocks   Id  System /dev/sdb1   *          63   174080339    87040138+  83  Linux /dev/sdb2       174080340   182482334     4200997+  82  Linux swap / Solaris /dev/sdb3       182482335  3907024064  1862270865   fd  Linux raid autodetect   Remanufactured drive received from warranty:  $ sudo fdisk -c -u -l /dev/sda  Disk /dev/sda: 2000.4 GB, 2000398934016 bytes 81 heads, 63 sectors/track, 765633 cylinders, total 3907029168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x000d0b5d     Device Boot      Start         End      Blocks   Id  System /dev/sda1            2048  ...   Why is that? What is the best Java email address validation method? What are the good email address validation libraries for Java?  Are there any alternatives to ? I'm preparing for my exam, but I have difficulties in perceiving why there is a $\frac{1}{2}$ in the distance formula $d=\frac{1}{2}at^2$? In a bash script what does a dot followed by a space and then a path mean? I came across this example when trying to mount a usb device inside a openvz container and I have never seen the construct in the second line before. Can you explain what it signifies?  #!/bin/bash . /etc/vz/vz.conf Does being granted a Schengen visa and not going have any consequences? I'm granted a one-entry Schengen visa and now I can't go. Will having an unused visa in my travel passport have any consequences like future visas refusal? Do I need to do anything special? Orange squares appearing on render? I'm trying to render a scene in Blender, and as of yesterday (it was not doing this when I was working on it 2-3 days ago), I am seeing orange squares dancing around the rendered image. Google tells me that these are render tiles (I think), but what are they, why are they there, and how do I get rid of them? Can I use my single entry Schengen visa to go to a different Schengen country than originally planned? My friends and I planned to visit Germany, so I got a single entry tourist Schengen visa to Germany. However, my travel plans have changed since then, because my friends are going to Italy instead. I don't have time to apply for a visa to Italy, but I have been told that I can use my Schengen visa to enter Italy. Is that true? Fullscreen Vista's Command Prompt, or Replacement Opening the command prompt ("cmd") on Vista into full screen causes the application to take up 100% vertical space, but only about 50% horizontal. Is there not a way I can make this fullscreen? If it's simply not possible, what is a good replacement? How to tell if a travel location is "affordable"? Disclaimer: The locations are just examples to set up the question and all prices are made up for the sake of the example and question.  Background: Let's say I want to visit London or Busan, and my currency is USD. While comparing the two locations I notice their exchange rates. 1 USD is 0.60 GBP, while 1 USD is 1,200 KRW.   Question: Are there traveler's tips and/or tools when it comes to currency exchanges where I know how much I can get for my "dollar" in a certain travel location? To use the exchange rate above as an example, consider the following. A bottle of water in London costs 0.40 GBP while a bottle of water in Busan costs 2,000 KRW. How would I know the relative value of goods I can get for my "dollar"?  I found  that provides that information but I'm wondering if there are other travel tips or anything to answer my question.   Edit: I replaced Korea with Busan to give it a more precise location and to keep it on the same level as London. Dynamic dispatch and binding Forcing linebreaks in \url This question led to a new package:      I wish to typeset some relatively long URLs in a piece of text, and when I use \url{..}, the resulting text does not respect the margin boundaries that govern the main text body, instead going all the way to the edge of the paper before wrapping around.   For reference, my preamble looks like this:  \documentclass[12pt]{article} \usepackage{mathptmx} \usepackage{fullpage} \usepackage[pdftex]{hyperref}   and example of the url I'm including is:  \begin{itemize} \item Some text  \url{very-long-url} ... \end{itemize}   I'm compiling using pdflatex, although I doubt this makes a difference. Successfully connected to a bluetooth speaker, but how do i direct sound there? Construct a fourth circle tangent to 3 circles forming a tangency chain I've got the new Canon Pixma MG 3150 and so far, I can't seem to find a driver anywhere. I do have the CD for both Windows and Mac, but this doesn't help me, as I have Ubuntu 11.10. I'd prefer to have it running on the wifi.  I'm really new to this, so I need for you to explain this to me as basically as possible. I would like to pause a render that I have started, with the intention of resuming it at a later time (but during the same Blender session).  How can I do this? Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$ Prove that for all integers $n$, $n \geq 1$,   $$1 + 3 + 5 + \cdots + (2n - 1) = n\cdot n$$   How would I go about proving this? Prove that the additive groups of $\Bbb Z$ and $\Bbb Q$ are not isomorphic.    It is hard to create a map that will show homomorphism. Proposition      Let $\mathcal{P_e}$ be the set of functions $p_e(x) = a_o + a_2x^2 +  \cdots + a_{2n}x^{2n}$, $p_e : \mathbb{R} \to \mathbb{R}$      Show that all $f:[0,1]\to\mathbb{R}$ can be uniformly approximated by   elements in $\mathcal{P_e}$   Attempt:    Since we are talking about polynomials let's try play with Weierstrass Theorem  By definition $\mathcal{P_e}$ is dense in  $C^0([0,1], \mathbb{R})$ , if for every funciton $f \in C^0([0,1], \mathbb{R})$, $\exists p_e \in \mathcal{P_e}$ such that $\forall \epsilon &gt; 0, \forall x \in [0,1], ||p_e-f||&lt; \epsilon$  So we want to show $\|p_e - f\| &lt; \epsilon$  Try something like...since every continuous function is approximated by polynomials i.e. $\forall \epsilon &gt; 0,\ \|f - p\| &lt; \epsilon$, therefore let $p$ be a polynomial, $p = a_0 + a_1x + a_2x^2 + a_3x^3 + \cdots$  $$\|p_e - f\| \leq \|f - p\| + \|p - p_e\|$$  $$\Rightarrow \|p_e - f\| &lt; \epsilon + \|p_o\|,$$ where $p_o$ is an odd polynomial  $$\Rightarrow \|p_e - f\| &lt; \epsilon + \sup_x|a_1+a_3+\cdots+a_{2_n+1}|$$  Stuck.   In any case, $p$ and $p_o$ is poorly defined. What would be the standard approach to prove the proposition?