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Complex Circuit Lecture

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A complete walk-through of calculating the equivalent resistance of a complex circuit, the current through the battery, the current and voltage drop associated with each individual resistor. It might be necessary to pause or rewind sections of the video.

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you had your circuit by the way we live here and I want you to find the four things one I'd like you to calculates what the equivalent resistance is for the whole circuit that's a say the battery has a certain voltage 20 in this case and the current goes through it so what's the requisite resistance that the battery sees what once I know that then I can just go be equals IR de casa current the batteries once I know the current of the battery that I know or can calculate how much current goes across each one of these resistors cuz I have the guys coming out the battery and they'll go across to the five that the green section and someone will go up the top and some of them will go to this middle section and come on back to the blue so I can figure out how I can split that current and finally once I know how much current goes across the resistor I can is a relationship of equals IR to figure out how much voltage has to be across that resistor to push that much current through it but the whole key is finding out how much resistance to the original circuit has cuz you can't do that you done cuz you can't answer to three and four until you've done one and not because one is one but yet you have to have that information so here we go my bottom left-hand Corner over here I have a 2 and a 5 in series know how do I know that you and five is a series because the amount of current that goes to the to hassle to go to the 5 there's nowhere else for it to go if you have to pay for it every guy that goes to to also goes to five than those two things are in series so I could simplify this guy here as a seven what y'all redraw over here with this guy over here the seven. Okay current goes across with now currently at 7 comes up the green leg and it has a choice and go up to the 1 or come down here for the three in the four if it happens to go through the three it will go through the four go karts for 3 and then turn around say just kidding and head back the other direction these are one-way streets show my free in for Orangetheory so I can say hey those guys are like a 7 also salsify three in the four and just get rid of the 4 and call it the seven you'll notice now that the current will come out of the battery oh by the way which is the positive the black or the blue the blackest is it the bigger one this guy was a plus here let me have it in their super plus right away so I have over here that the current goes out of the closet and over here cuz current the flow of positive charge cruises along comes across the seven hits the green and then he splits now this green wire I want to think of it as a cable a cable just a bunch of wires kind of wrapped around each other you're just like a string strings wrapped around each other you call that rope see how the Rope or cable in this case here which consists of two wires and once it reaches this point right here this joint juncture sometimes are called you unravel it so that's one wire goes down the other wire goes up same way with this blue cable the blue cable that runs it reaches this point you take one of the wires you connected to the side and can if the other way are going up and around to the one ohm resistor so the one ohm resistor has a blue on the left and a green on the right I said that backwards the seven has a green on the left on the right they both have the same wires on both sides therefore there in parallel that's how you tell something's in parallel or not if they have the same wires on the respective sites why is there a parallel you go 100 + 1 / + 1 / Michael Let's Lose the whole thing and lose the sneaky ear listen to music thing I hook it avoid the appearance + 1/1 which is this resistance oh by the way this is going to be one of the three buttons not Choi Siwon 7 + 1 is 8/7 flippant show the equivalent resistance of the circle parallel area is 78278 right here now my 7/8 and my sevens are in series because well they connect to I hear that every guy that comes here they got to go through the 7/8 so he's got no choice but to go through them so the net effect of that is of course 7 and 7/8 now I know it seems gif possible it seems impossible but every year I have about three to four kids in a. Can't add fractions 5 like one third plus one fourth and those how many is 1/7 and I just stare at myself in complete utter deer-in-headlights bewilderment thinking where were you in fourth grade when we learn to add fractions but it happens I know how to do you have brain cramp has been so long what you got to get the right answer okay so the answer number 1 the equivalent resistance is 7 7/8 also known as 7.875 can I get a finger count please the procedure for coming up with 7 7/8 questions to ask you can record it question was mr. Duncan basically can you go to the procedure did again on the on the parallel hear what I did is I got rid of this section right here Delores that's not here done and I got rid of just the one on resistor and replaced it with another resistor so that would be the equivalent of the one and the seven in parallel and equivalent resistance is 7/8 okay I now know that the resistance of the whole circuit how to say the whole big mama coming around here coming here kind of those splitting thinking back to hear all of that all together if I got rid of the to the 5 to 3 before 1 if I got rid of all five of those resistors I could replace it with a single resistor they have the value of 778 into the battery it would look the same so the battery has a voltage of 20 the resistance from the batteries point of view is 7 7/8 so the current from the battery to three sig figs is 2.54 amps equals IR next I have 2.54 amps that are leaving the battery what we've all got to go through the too and although guys have to go to the 5 but once it reaches this joint up here it has a choice they can come across the top guy or can come across the bottom section here that the equivalent of 7 not what I said equivalent of 7 remember the 3 and the 4 and Siri Siri says the same as a 7 we simplified that play from here to the purple guy hey those guys right there are going to Series so I got rid of the purple and the four and just made him into a 7 play a 2.5 for reaching this joint right here summer going to go up imma go down why do more take the top guy text and the bottom guy gets so you can think of this like I have a hose and then I put like a coupler on it so explicit and one cup has a diameter that's really big and the other coupler has a diameter that's really small the book have the same pressure but the big guy forces going to get more water truck in fact the big guy has an area that seven times is big as the little guy please not the one that has a bigger area on the hose is the one it's kind of gauge on the wire or gauge and shotgun 20 gauge is what you use to shoot like a quail K 12 gauge what you just like to take down a rabbit or something like that and 8 gauge is what you wanted to use of I'm going to stop you know crazy man coming at me. They knock you backwards type 20 is just going to take the guy I make them bleed a little bit and then he's going to get really take that check I got away from you and hit you with it just remember that okay not that you'll ever have to know that play should be recording this anyway so I've got a certain amount that comes across the bottom part how much is that how much was the cross the top guy 7 times as much 7X so I got exitos cross the bottom 7s it goes across the top that's a total of 8x + 8 text has to split into 2.54 amps do I have a 2.54 amps and it split in eight parts but one part to the bottom with seven parts of the top oh by the way I can do this with this will be like next year level stuff let's suppose it just for Giggles that I put like say 3 in your no next we have a parallel with the 1 and 1/3 supposed now what would do is I said have a 1 1/6 at 7 plus three more that's 10 and I would say great now I need to split this guy into his different parts and next year I'll teach you how you would split that apartment pause for a moment. Once again I got the a tax by saying that the top guy has get seven Parts in the bottom guy gets one part because the bonds that has 7 on the top guy has 107 + 1 is 8 okay so 7/8 of the total amperage 2.54 works out to be 2.2 to 1/8 of my total amperage is .32 and you'll see that if I add those two numbers together .32 and 2.22 it works out to the amperage of my battery 2.54 by the way I mean knowing that you guys will only email this but the I'm not going to email you the avi file you can load that you can download that cuz it's going to be huge I'll take it while I'll see if you can press it okay now for the fourth question and I'll ask you guys right now just to pay attention don't actually write it down it's not going anywhere this is our last page now we have found the current through each resistor 2.5 for 2.5 4.32 at 7 I would like to know the voltage across that resistor well I know what i is 2.54 here I know what the resistor of a choo resistor is so I said again I know what the resistance of a 2 ohm resistor is that's right too long that's why they call it to him resistor voltage is equal to the go to the Chalmers Esther times the resistance of the 2 ohm resistor V equals IR the current 2.54 the resistance is 2 voltage drop SP 5.8 just Ma same game here are spies amperage is 2.54 multiplied together voltage drop across here to hear is 12.7 although it's only one resistor this car gets most of the voltage drop this is the guy that the pressure kind of backs up the most they were like putting your thumb over the hose you still in some water but I'll but it's going to back the pressure up I have seven altogether with the three in the four shouldn't he have most of it he would if he got rid of the one but you got like an escape valve it's really easy to get through it so the pressure doesn't back up so much okay. across this guy of courses 2.22 now pay real close attention here the voltage drop across the 3 on guy this guy right here that guy voltage drop across Tim is the current that the current you have to use is .32 you don't use the 2.5 for used .32 cuz that's been out of current that actually going through 2.32 * 3.96 on the floor guy is 1.28 and there's your voltage drop across each one of your guys now we have answered all four questions but let me point something out to you when the current goes across a resistor the resistor heats up it gets hot sometimes you want that like in a toaster oven or a hair dryer or one of those little space heater things you like plug into the walls got electrocuted being in for about 25 bucks down at Walmart the energy that the battery is supplying goes into heat when the resistors heat up so let's suppose that I had 20 joules of energy for every coulomb electrons that I had coming from the battery well this guy is going to lose energy this guy is going to lose energy and then this one's going to lose energy and then he'll go on back so if I add the this resistor plus the five plus the one that's why I did right here if you add those voltages you know what they add up to 20 as they should or I could say what if it came across the two than the 5 and it took the middle whoop okay voltage drop of the two plus two 5 + 3 + a 4 + mens back into the blue wire goes back to the battery if you add all those 20.02% round off that is round off because this isn't actually .32 it's like three 17 I just rounded it yeah yeah just rounded it so once every few kept all the numbers in a calculator it would come back to exactly 20 questions so the question is mr. Duncan if I just want to see if I can get 220 do I add all of the guys together no you just pick a path to say I'm going to pick route a to get from a back to me I want to think of this like what Roaring Rapids except right here imagine that you had the big old White River and it split into two channel she had one channel that was like say 12 feet wide and the other was like I don't know 40 ft wide most of the inner tube things are going to go down the black path that doesn't really fat one but once in awhile wants to go see how the skinny or what okay

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