I know that putting two resistors in parallel will double the wattage from the input to output, but only with half the resistance.  Example Parallel Circuit:         &ndash; Schematic created using   I know that putting two resistors in series will double the resistance, with the same wattage.            However: I need to double the wattage without the affecting resistance. Would this work?:
Is there anyway I can connect resistors to allow them to take more power such as using 4 1/4 watt resistors to get a 1 watt resistors. Or do i just have to use 1 1 Watt resistor.
London Heathrow airport - do I need a transit visa? Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational I tried the methods shown in  but I cannot extend them well into 4 numbers. When to choose checked and unchecked exceptions In Java (or any other language with checked exceptions), when creating your own exception class, how do you decide whether it should be checked or unchecked?  My instinct is to say that a checked exception would be called for in cases where the caller might be able to recover in some productive way, where as an unchecked exception would be more for unrecoverable cases, but I'd be interested in other's thoughts. How do I defeat the Kayran in the first chapter of the Witcher 2? In the first chapter you are supposed to slay the Kayran, this enormous beast:    I'm having a hard time with it. I drank the Mongoose potion for poison resistance and I have the Kayran trap, but it just hits me too often with its tentacles. Especially when the Kayran swings a tentacle sideways, not from above, I have a very hard time evading it.  Is there any trick besides not getting hit by the tentacles?  With a lot of luck I'm getting as far as the point where it's throwing stones. Any idea what I'm supposed to do then? Decoupling caps, PCB layout I guess I've been somewhat ignorant when it comes to the finer details of pcb layout. Lately I've read a couple of books that try their best to lead me on the straight and narrow. Here is a couple of examples of a recent board of mine, and I have highlighted three of the decoupling caps. The MCU is a LQFP100 package and the caps are 100nF in 0402 packages. The vias connect to ground and power plane.     The top cap (C19) is placed according to best practices (as I understand them). The other two are not. I haven't noticed any problems. But then again the board has never been outside the lab.  I guess my question is: How big a deal is this? As long as the tracks are short, does it matter?  The Vref pins (reference voltage for the ADC) also have a 100nF cap across them. Vref+ comes from an onboard TL431 shunt regulator. Vref- goes to ground. Do they require special treatment like shielding or local ground?    EDIT    Thanks for great suggestions! My approach has always been to rely on an unbroken ground plane. A ground plane will have the lowest possible impedance, but this approach may be too simplistic for higher frequency signals. I've made a quick stab at adding local ground and local power under the MCU (The part is an NXP LPC1768 running at 100MHz). The yellow bits are the decoupling caps. I'll look into paralleling caps. The local ground and power are connected to the GND layer and the 3V3 layer where indicated.  The local ground and power are made with polygons (pour). It's going to be a major rerouting job to minimize the length of the "tracks". This technique will limit how many signal tracks can be routed under and across the package.  Is this an acceptable approach? How to import Apple Mail archive files in Outlook 2013? I need to import Apple Mail archived files in Outlook 2013 on Windows, but every time I open the import wizard and reach the file selection step, I cannot select the archived file. It doesn't even show in the dialog box.  I don't know what the issue is. Is it the file size issue as the archive file is large (about 7 GB) or there is any other fault? back commandbutton in jsf I've never really got how chmod worked up until today. I followed a tutorial that explained a big deal to me.   For example, I've read that you've got three different permission groups:   owner (u) group (g) everyone (o)   Based on these three groups, I now know that:   If the file is owned by the user, the user permissions determine the access. If the group of the file is the same as the user's group, the group permission determine the access. If the user is not the file owner, and is not in the group, then the other permission is used.   I've also learned that you've got the following permissions:   read (r) write (w) execute (x)   I created a directory to test my newly acquired knowledge:  mkdir test   Then I did some tests:  chmod u+rwx test/ # drwx------ chmod g+rx test/ # drwxr-x--- chmod u-x test/ # drw-r-x---   After fooling around for some time I think I finally got the hang of chmod and the way you set permission using this command.    But...  I still have a few questions:   What does the d at the start stand for? What's the name and use of the containing slot and what other values can it hold? How can I set and unset it? What is the value for this d? (As you only have 7=4+2+1 7=4+2+1 7=4+2+1) Why do people sometimes use 0777 instead of 777 to set their permissions?   But as I shouldn't be asking multiple questions, I'll try to ask it in one question.  In UNIX based system such as all Linux distributions, concerning the permissions, what does the first part (d) stand for and what's the use for this part of the permissions? A friend of mine asked me the following question:      Suppose you have a basket in which there is a coin. The coin is marked   with the number one. At noon less one minute, someone takes the coin   number one and put into the basket two coins: the number two and the   number three. At noon less $\frac{1}{2}$ minute, he takes the coin   number two and put into the basket the coins number $4$ and the number   $5$ and so on. At noon less $\frac{1}{k}$ he takes the coin number $k$   and put two other coins.       The question is: How many coins I can find in the basket at noon?   Intuitively the answer is $\infty$ because I added one coin for infinite times. But the correct answer seems to be $0$ because every coin numbered $k$ has been removed at noon less $\frac{1}{k}$ of minute. What is the correct answer? Thanks. Portable Ruby on Rails environment I got myself a new 8 gig USB key and I'm looking for a decent solution to have a portable RoR environment to learn on. I did the google on it and found a few possibilities, but I'm curious to hear some real life experiences and opinions. Thanks! Positive operator is bounded For a real Banach space $X$ let $A:X\rightarrow X^*$ be a positive operator in the sense that $(Ax)(x)\geq 0$ for all $x\in X$. Show that $A$ is bounded.   I don't know how to do that, maybe it's an application of the closed graph theorem? How to show that a set of discontinuous points of an increasing function is at most countable I would like to prove the following:       Let $g$ be a monotone increasing function on $[0,1]$. Then the set of points where $g$ is not continuous is at most countable.     My attempt:    Let $g(x^-)~,g(x^+)$ denote the left and right hand limits of $g$ respectively. Let $A$ be the set of points where $g$ is not continuous. Then for any $x\in A$, there is a rational, say, $f(x)$ such that $g(x^-)\lt f(x)\lt g(x^+)$. For $x_1\lt x_2$, we have that $g(x_1^+)\leq g(x_2^-)$. Thus $f(x_1)\neq f(x_2)$ if $x_1\neq x_2$. This shows an injection between $A$ and a subset of the rationals. Since the rationals are countable, $A$ is countable, being a subset of a countable set.    Is my work okay? Are there better/cleaner ways of approaching it? I'm currently working through the book Heisenberg's Quantum Mechanics (Razavy, 2010), and am reading the chapter on classical mechanics. I'm interested in part of their derivative of a generalized Lorentz force via a velocity-dependent potential.   I understand the generalized force   $$F_i = -\frac{\partial V}{\partial x_i} + \frac{d}{dt}\left(\frac{\partial V}{\partial v_i}\right)$$  that they derive from a Lagrangian of the form $L = \frac{1}{2}m|\vec v|^2 - V(\vec r,\vec v,t)$.  However, in the next (critical) step of the derivation, the author cites a theorem from Helmholtz saying      ...according to Helmholtz, for the existence of the Lagrangian, such a generalized force can be at most a linear function of acceleration, and it must satisfy the Helmholtz identities.   The three Helmholtz identities are then listed as:  $$\frac{\partial F_i}{\partial \dot{v_j}} = \frac{\partial F_j}{\partial \dot{v_i}},$$  $$\frac{\partial F_i}{\partial v_j} +  \frac{\partial F_j}{\partial v_i} = \frac{d}{dt}\left(\frac{\partial F_i}{\partial \dot{v_j}} +  \frac{\partial F_j}{\partial \dot{v_i}}\right),$$  $$\frac{\partial F_i}{\partial x_j} -  \frac{\partial F_j}{\partial x_i} = \frac{1}{2}\frac{d}{dt}\left(\frac{\partial F_i}{\partial v_j} - \frac{\partial F_j}{\partial v_i}\right).$$  I'm trying to understand where this theorem comes from. Razavy cited a 1887 paper by Helmholtz. I was able to find , but it is in German, so I could not verify whether or not it proved the theorem. Additionally, I could not find it in any recent literature. I searched online and in Goldstein's Classical Mechanics.   The only similar concept that I can find is in the  where we have three equations known as Helmholtz conditions. Are these two concepts one in the same? If so, how should I interpret the function $\Phi$ and the matrix $g_{ij}$ that appear in the Helmholtz conditions I found online?   If the cited theorem from Razavy does not relate from the inverse Lagrangian problem, could I have some help finding the right direction? Magic 8 Ball Problem This problem is probably simple enough to have an analogous problem, I just don't know the name so I'm going to describe it and hopefully somebody can point me in the right direction.  The problem is this: estimating the number of sides of a .   Let's say you perform the following process:   Shake the "Magic 8 Ball" and mark down the result If the result has not previously been seen, add it to the set of possible results and label the trial "N" (for "new") If the result has been previously seen, label the trial "O" (for "old") Repeat all steps   I imagine the following kind of sequence occurring: NNNNONNOONOONOOONOOOONONNOONOOONNOONOOOOOONOOONOOOOOOONOOOOOOOONOOOOOOOO...  Now imagine we don't know there are twenty sides to a Magic 8 Ball. Or imagine that you have a Magic 8 Ball with 1000 sides. As the number of "new" trials approaches the actual number of sides, we'll get increasingly more "old" trials showing up in the mix. Once we've seen all of the possible results, we'll always get "old" results. But we're never 100% sure we've seen every single possible result.  So here are the questions I'm interested in:   As we proceed with trials, can we estimate the total number of "sides" of the Magic 8 ball based on the number of "new" and "old" trials up to this point? Can we calculate a probability that our current estimate is correct, or a probability that some bounded estimate is correct? Can anyone suggest a book on using complex numbers to solve geometry problems? Can anyone suggest me a book which includes everything which is needed for solving simple geometry problems through it? I only know about simple calculations on complex numbers. Need for a side book for E. Soper's Classical Theory Of Fields I am reading now E. Soper, Classical Theory Of Fields, now and sometimes it is very hard to follow the equations. So I need a side book on  to read it comfortably. Landau &amp; Lifshitz's book is not helping as its content and topics are very much different. Capture characters from standard input without waiting for enter to be pressed How do I get list of all tables in a database using TSQL? I really miss the graphical "Services" tool from older versions of Ubuntu, but I understand why it had to go. I always have terminals open anyway, so I use (because I have to now, I guess) service --status-all to see what services are running. This would be ok except that the command produces output like the following:   [ + ]  winbind  [ ? ]  wpa-ifupdown  [ - ]  x11-common   I'm guessing that those symbols mean something like listening, blocked, or stopped, but which is which? More importantly, why doesn't the man page say? Erf as term for plot of land in a town or city. Is this word only used in southern Africa? The Free Dictionary website states and so does Wikipedia:     erf [ɜːf]   n pl erven [ˈɜːvən]   (Engineering / Civil Engineering) South African a plot of land, usually urban, marked off for building purposes   [Afrikaans]   The term erf is used in legal documentation and technical English throughout South Africa and Namibia, maybe even further afield in the region.  Is it used anywhere else, except maybe the Dutch/Flemish regions in Europe, where I assume the term originated?  An example:      The client purchased Erf 132, Windhoek for a large sum of money. He intends to build a house on this erf.   The capitalisation of "Erf 132" is commonplace, since it is a definition of a location. This is similar to capitalisation of towns or cities. I find it slightly awkward, but that is how it is done.