EdX and its Members use cookies and other tracking technologies for performance, analytics, and marketing purposes. By using this website, you accept this use. Learn more about these technologies in the Privacy Policy. × MITx: 6.002.1x Help Circuits and Electronics 1 Basic Circuit Analysis Course Progress Dates Discussion Notes petarin1a1213 FAQ All Topics Add a Post Search all posts Search Audit Access Expires Mar 23, 2022 You lose all access to this course, including your progress, on Mar 23, 2022. Upgrade by May 16, 2025 to get unlimited access to the course as long as it exists on the site. Upgrade now Noddy's Guide to S2E5 for Dumbbies and Simians~ Filter Topics filter topics discussion posted about a year ago by NoddySparks All Discussions Howdy, my science monkey companions! If you're scratching at your noggins and trying to force your brain to do the required gymnastics for this problem, then not to worry, for Noddy is going to help you limber up and get you to your brains gymnastic best.* Posts I'm Following * Please be advised that actual brain gymnastics are not a thing, and this is a euphemism.) General So to start off, it looks like most people have breezed through the first part of the example problem with relative ease. If you're one of these people, this tutorial is probably not for you, as only dumbbies like me should be reading this comprehensive guide. Feedback Now, for the rest of us, by which I mean the dumbbies, lets start with Noddy's patented move number 1 to solve any circuit! Troubleshooting Draw that damn thing out! Live Interactions By now, most of you should have no troubles drawing a circuit, and properly labelling all your perty whatsits. If you're drawing doesn't come out looking something like this; Final Exam Audit Track Introductions Welcome to 6.002x Math Review Complex Geometry Complex Exponentials Complex Replacement then you may be having more issues with the content of this course then this guide will be addressing. I suggest going back at least to the S2E3 problem, where I first started my tutorials. Or if my tutorials are still too advanced, or neausiatingly incorrect, then Kahn Academy has a significant amount of free and interesting content that closely mirrors these courses, and walks through similar problems. People who read my previous tutorial on the last problem may be frowning at me right now, because of the fact that I've ignored the use of the 'current convention' for our Nodal Analysis Tool. Which is just the current convention of kirchoff's law) Instead, I've gone with drawing our currents under the Associated Variables Convention. The reason for this, is because it's a matter of preference! It doesn't actually matter, because our current directions are intirely arbritary. The purpose of the convention, is to make math-magic easier on our brain ligiments while doing mental gymnastics! Now that we've discussed some nonsense only marginally related to the problem, lets get down to some sciencing! The first problem is asking us for the Node Voltage of e1. Notice how I've called it the Node Voltage. It's important that you recognise that there is a difference between your regular Terminal voltage (the voltage measured across the terminal (plus and minus signs) of a circuit element), and the voltage measured from one node to another!. In larger circuits, this distinction matters if you ever decide to work with nodes seperated by multiple elements! Not only does it matter in larger circuits though. You'll see at the end of my tutorial why it's important to differentiate Node Voltage and Terminal Voltage properly in your mind! It should be obvious then that my next course of action is going to be to find some way to determine the relationship between these variations on the voltages! Because there is only a single element between each Node and the Common node in this circuit, that will actually be super easy! In math terms, you could say that the relationship between element voltages and node voltages, will look something like this; V0 e1-e3 V1 e1-e2 V2 e2-e3 This will be true, regardless of which Node I make my Common. Speaking of which, when we finally do pick a Common, then we introduce a variable to those Voltage relationships. For the sake of argument, lets use e3 as our Common Node. Which conviniently just so happens to be the common for the first part of this problem! When we make a node our common we are basically saying that when we measure every other node, where going to be measuring the difference in voltage between that node, and node e3. That also means that when we measure the voltage between e3 and e3, then we are naturally going to get a 0. Which in math-magic terms means; 0 (this will change depending on which ever node you pick as your common! If i picked e2 as the common, then e2 would equal 0 instead. Dont forget this! e3 Great! So we have a variable that we can plug into our Node/Terminal voltage relationships now! Which will look something like this; V0 e1 0 e1 V2 e2 0 e2 V1 e1 e2 That's not super important just yet though! Instead, whats important is the; V0 e1 part. Which just so happens to answer the first question! Simple, right?! Now that we're starting to get warmed up, lets jump straight into the next part of the example problem. 'Write an equation for the node e2, then write down the value for e2 in volts'. So, if you're still confused as to what nodal analysis is and how to do it, you've probably read that question and said, 'Huh?' Well, you're not alone. I too stared blankly for many minutes after reading the question. If anyone asks, I was doing it in my head! Okay? I wasn't confuseded! That was when I remembered Noddy's patented rule number 2 for hard problems! Start at the damn begining! If you've actually been studying, (like Noddy should have been), you should know that the first step in Nodal Analysis method uses kirchoff's current law! Which should be obvious! Why else would I be using my 'Nodes' otherwise! Nodes Current Laws) I1 I2 I3 Well, what can I do with this? The only current I know is I3. Which reminds me! My current convention is going the oppisite direction of the ideal current source arrow! That means; I3 I 3 And if we pop that into our kirchoffery we get; I1 I2 3 Great. Now what can I do? Well, I need some variables for those currents, right? The best way to do that is pull out my good ol' ohms law, so I can use some known resistances as variablez! V1/R1 V2/R2 3 V1/3 V2/5 3 Okays! So now I have some more variables, but where the hells am I supposed to get them voltages from? Well, it just so happens that we already figured out how the Element Voltages are related to the Node Voltages! V1 e1 e2 V2 e2 V0 e1 If we throw all that into our equation we should get; (e1 e2 / 3 e2/5 3 Wowzers! Hey look! There's another variable I know! e1 5-e2 / 3 5, right?! e2/5 3 Now the only variable I don't know is e2! Which also just happens to conviniently be precisely the node voltage I was looking for! Now we just have to rearrange this mess so that e2 is all by his lonesome! 5/3 e2/3 5/3 3 e2/3 4.6666 e2/5 5*e2/15 4.6666 15 e2 e2/5 3 5 3*e2/15 3)e2 XXXX volts! Coincidentally, if you did the question as intended and determined an equation for e2 (which would be basiaclly the same process as we've just done but without inputing variables), you should have gotten something that looks like; e2 R2*e1 I3*R1*R2 / R2 R1 Well done team! My maths teacher always told me I'd never sum up to anything! I always told her that was because she was being negative and it was unbalacning my sum! Looks like I proved the both of us wrong! Ahem! Dad/maths jokes aside, lets move on! The next question should be as easy as the first question. Espeacially because we're hardworking science monkeys and wrote out our Element/Node relationships before we did anything else! V2 e2 Ok, so now onto the next part of the problem! Some of you may be thinking "Hey wait a damn minute! We just did all that hard sciencing and now we're just tossing it out and starting again from scratch! What the booger?! And what in the bean countering is this stuff about e1 e3 V!" Well, not to worry my fellow simians! I too have these mind twisting questions! It's a good thing we limbered up for the brain gymnatstics, right!? Now first off, not everything we've just done is useless. For example, the very first thing we did, which was to determine our Node/Terminal voltage relationships, (which look something like this incase you're like me and already forgot! V0 e1-e3 V1 e1-e2 V2 e2-e3 already told us that V0 e1-e3. Which any fellow simian will happily remind you can quickly become e1 V0 e3! This is a good reminder that those Node/Terminal voltage relationships are going to remain the same throughout the circuit, regardless of where we put our common node! Infact, this is (presumably? citation needed-) true for every circuit where we employ Nodal Anylsis! You may be wondering then, "what has changing our 'Common' node done?" Moving our 'common' node only changes what's going to be our 0 when we want to start adding variables! "But wait a minute!" some of you are no doubt shouting! "If our Node/Terminal voltage relations havn't changed, then doesn't that mean that all that work I've just done still counts!" Those of you screaming that at the top of your lungs would be mostly correct! However, what you have to remember, is that we've just 'inverted the polarity' that we're measuring our voltage across. That means, we're now measuring between e3 and e2, as if the positive end is node e3! For those of you that have a voltmetre, or have used one, you know exactly what I'm saying. And this would be the part were we'd all share a conspiritorial wink of acknowledgement between eachother! For everyone else, what you must remember is that the voltage is the difference in potential between two points. In this case, between two nodes! That means if you measure from a node with higher potential to a node with lower potential, then your voltage will be positive. If, however, you measure from a node at a lower potential to a node at a higher potential, then the voltage you get will be negative! In mathimatical terms, all that nonsense I just rambled on about would look something like; V2 XXXX and V2 e2-e3 and e2 0 therfore; e2 e3 0 e3 e3 XXXX XXXX XXXX The last question should be painfully easy, given I just gave you all an enourmous exposition on how Node/Terminal Voltage realtions won't change just because we moved our Common Node! If you can't get the last question with all that in mind, then Noddy's Guides are probably all nonsense and you should seek help elsewhere! Try Reading the text book, asking the TA here in the comments section, or finding another tutorial source. Kahn Academy is quite good at walkthroughs.) Regardless, everyone else who managed to slog through that word salad from Noddy can give themselves a pat on the back! WOOHOOO!!! Look at us go! Smashing out 720 front flips with our brains and landing with 9.8's from the russian judges! Great job team! See you at the next problem! Noddy Related to: Week 1 / Node method example This post is visible to everyone. 2 responses Add a Response Samanth_aa about a year ago Thank you so much Add a comment MIT_Lover_UA Staff) about a year ago This is helpful to many students! Add a comment Showing all responses Add a response: Preview Submit edX Legal Connect About Terms of Service & Honor Code Blog Privacy Policy Help Center edX for Business Contact Us Accessibility Policy © 2022 edX Inc. All rights reserved. | 深圳市恒宇博科技有限公司 粤ICP备17044299 号 2
