I've been studying DC circuits recently, but I've run into some confusion concerning how batteries deliver energy to circuit elements.   From what I've read online, it seems that energy in circuits comes from waves that propagate through charges rather than the charges themselves. However, my book seems to convey that charges "pick up" potential energy at a battery and lose it in circuit elements.   These models of how energy is transferred seem to contradict each other. Which is right? And if the wave theory is right, then what does current or voltage have to do with it? Rather, how do current, voltage, and resistance explain the strength and properties of this wave?  If this matters, I'm using Halliday-Resnick-Krane 5th Edition Physics textbook.
I will give this question a little context. Firstly, as I understand it, as soon as I "close the switch" on a circuit, electric current pretty quickly establishes a steady state where, at any given cross section along a wire, the average kinetic energy of that slice is both constant and equal anywhere along the wire. (Please correct me if I am misunderstanding).   If the average kinetic energy is constant anywhere throughout the wire in the circuit (which confuses me, as I would think that the electrons should all accelerate after exiting the resistor since they are no longer being impeded as much), that means that the average velocity is constant. So, in the example of a simple circuit with a battery of v Volts and a resistor of o Ohms, my question is the following:  Because a 'voltage drop' is known to occur across the resistor, what type energy is being "traded" to generate the heat that radiates from the resistor? I would think that the reflexive answer is "electrical energy"...hence the VOLTAGE drop (the sacrificed energy is clearly not kinetic, as the velocity is constant everywhere). However, I find this confusing. Does this mean that if I had a positive test charge, it would be easier for me to bring it to the beginning of the resistor as compared to bringing it to the end of the resister?     Further, if the correct answer IS "electrical energy", why exactly DOES electrical energy get "dissipated" as the electrons pass through the resistor? I always here the comment Oh! It's because all the electrons are running into densely packed crap which impedes their flow but that to me sounds like a reason for their KINETIC energy to be reduced. However, clearly that's not the case. So, ultimately, I guess the real question is:  **What goes on in the resistor that is literally removing electrical energy **. I am sure that this is a quantum mechanics question, but my quantum mechanics knowledge is not terribly strong. If I could get an answer that is devoid of crazy wave function equations, I would greatly appreciate it. Thanks!
Packaging a bike for flying with a bike bag I am doing a cycle tour of Japan starting from Fukuoka and ending in Tokyo. I will be flying with the bike and as my start and end points differ I will not have the opportunity to use a box (unless anyone has any ideas?). I will most likely use one of  bags and I have been told by the airline that nothing is necessary by way of packing the bike but I would naturally like to see my bike in one piece at the other end. The bike is a Specialized Tricross with disc brakes. Does anyone have any pointers as to the safest way to package something like this. I think I will definitely take the rear dérailleur off and wrap bubble wrap along the length of the bike to protect the wheels, pedals etc but other than that I'm not sure what lengths to go to. Does anybody have any experience or ideas? Open Source Command Line Tools to Remove Hyperlinks in PDFs? Are there any Open Source Tools to Remove PDF links in Ubuntu.  I use PDFtk and i am not able to find any internal links in it. Due to the Internal links my python script that uses PyPdf to merge the PDF files into one file fails. How do I simplify and evaluate the limit of $(\sqrt x - 1)/(\sqrt[3] x - 1)$ as $x\to 1$? Consider this limit:  $$ \lim_{x \to 1} \frac{\sqrt x -  1}{ \sqrt[3] x -  1}  $$  The answer is given to be 2 in the textbook.  Our math professor skipped this question telling us it is not in our syllabus, but how can it be solved? Find the number of solutions of $x^2=x\mod m$ for any integer $m$.  I was thinking about bringing the $x$ over to the other side and somehow apply chinese remainder thm. $G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$ Let $G$ be a simple group and there exists a subgroup $H$ of index $n \in \mathbb{N}_{\ge 3}$. Show that: $|G|$ divides $n!/2.$ I saw a similar question .   There was written: "The proof is really simple. Let $X$ be the set of left cosets of $H$. Consider $\phi: G \to \text{Sym}(X)$ given by $\phi(x)(aH)=(xa)H$. Then $\phi$ is a homomorphism. Consider now $K=\ker \phi$. Then $K$ is a normal subgroup of $G$ contained in $H$. Finally, $G/K$ is isomorphic to a subgroup of $\text{Sym}(X)$, which has order $n!$, where $n=[G:H]$. Thus, $[G:K]$ is finite and divides $n!$."  In fact, I don't understand the last sentence. "Thus, $[G:K]$ is finite and divides $n!$." Also did I understand it right that $ker(\phi)=H$?  Can you also give me an advice how to proof it for $n \ge 3$. (maybe induction)  Thank you for taking your time. I'm having trouble with a proof by induction SSH tunnelling with multiple dynamic port forwardings I am trying to monitor multiple JVMs running on different servers through an ssh tunnel.  Thanks to one of the UNIX gurus here, I have managed to get this running for a single server by:   Run jstatd on the target server Set up Visual VM to use 9696 as its socks proxy port. On my local PC, run:  ssh -L 2222:server1:22 bastion-host  On my local PC, run:  ssh -o port=2222 -D 9696 -L 1099:localhost:1099 localhost    This does the trick. Now when I try and tunnel to a second server I try:   On my local PC, run:  ssh -L 3333:server2:22 bastion-host  On my local PC, run:  ssh -o port=3333 -D 9696 -L 2099:localhost:1099 localhost    However, the last step complains with:  bind: Address already in use channel_setup_fwd_listener: cannot listen to port: 9696   Has anyone managed to do something similar?  Update:  The reason this is so complex is that jstatd is an RMI server application:    As with RMI applications, these register with an rmiregistry. Using rmi through a firewall requires me to use SOCKS as described here:    Unfortunately, visualvm only lets me set the SOCKS proxy port once, and the -D option won't allow me to forward the same local port to both servers... 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