 Homework from last day number four sure So which resistors are in series? this is a Series means the same skiers go through them both for example the what what that? Okay, okay. That's so wow What's going on here? You know pink thingy there Let's do this Let's turn that back on again, and let's see if it's a there we go. That was a little weird Okay, I think I saved it Series means same skiers go through both these two here are in series with each other because as I look at this The same skiers go through both of those so I would say in terms of series R7 and r8 are in series with each other Can you find any more resistors where the same skiers have to go through and no more no less Exactly the same skiers have to go through both You see it selling In other words if I was analyzing this circuit, I could just add those two together and treat them as one I could add those two together and treat them as one The rest of these are all sorts of parallel and so this is a this is a nasty circuit They actually gave me this with numbers It would take me a while to analyze it unless they were nice enough maybe to give me total current and a lot of Extra stuff somewhere along the way R2 is in parallel with both of those combined R6 is in parallel with both of those combined R5 is in parallel with this whole mess Okay, is that all right? So that's the difference between series and parallel good question any others so less than five and the title is Mixed resistor circuits all we're gonna start doing is just practicing Using Kirchhoff's laws and the rules for parallel and series Resistors so mixed resistors miss mixed circuits have both series and Parallel parts and to solve them First thing we're going to do is make sure Sally and this is why your question earlier was so nice We want to make sure that we identify let's make it nicer number one mister do it first thing we do is we Identify what series and what's parallel because we're going to be using a different strategy for each of those And then we're going to simplify the circuit to find total equivalent resistance our total and to do that If they're in series we just add them up if they're in parallel one over our Parallel equals one over the first plus one over the second plus one over the third So that's the second thing we're going to do. Oh another late-comer. Let's see here Got a note. So we're going to try and find the total resistance Then we're going to try and find the total current and to do that almost always we're going to use v total equals i total our total and Then we're going to walk our ski rule Kirchhoff's rules We're going to walk through the circuit filling in what we can't so Example one and Sally again. This is great practice for the question you asked me It says identify the resistors in series or in parallel Well Those two are in parallel, right and then if I went one over this plus one over this and then took the reciprocal Then I would have this and whatever equivalent resistance This is Gordon would be in series and I could just add them up and find the total. What about here? Which resistors are in series in this second one? Can you see them? You know what? Let's give these names Let's call this R1 R2 R3 R4 and R5 Which of those are in series? 3 4 and 5 are in series In other words Dylan if I wanted to just combine this as a single resistor I could just add those three up Then these two this one and my mystery combined resistor would be in parallel I could go one over this plus one over this and get a parallel Combine it with that and then I could get a single solitary little resistor and go v total equals i total r total What would you say these two are series or parallel? Parallel what would you say these two are series or parallel? Parallel so hopefully that helps you spot the difference between them now We need to practice the actual math the actual physics the actual solving of the circuit. Oh No, I got one more still so what we're gonna do for this one instead as a little twist Is I'm gonna write up here Find our Total and I'm gonna make up numbers these numbers almost certainly will be yucky. I'm gonna say that this is 10 ohms I'm gonna say that this is 8 ohms and 4 ohms And I'm gonna say that this is trying desperately to do some math in my head Hoping desperately to make this work out evenly. I doubt it though. I'll call this 18 ohms How could I write that as a single solitary resistor? Well, the first thing I would do is anywhere that's in series I Would probably combine those can you see any that are in series right now? sorry the 8 and 4 and in fact what I would probably do is I would probably if I could change colors or I might you know what you guys can't change colors I would guess I would probably quickly resketch this and I would say right now I have and I would draw it pretty small 10 10 mr. Do it And I would get really sloppy. I wouldn't even put the resistor symbol in there. I just put a 10 right there And then I would say I got a 12 And I got an 18 Now I see I think I have two resistors in parallel. Can you see them? Which two Tyler? So I would say 1 over our parallel equals 1 over 12 plus 1 over 18, and I would bust out my calculator This is what I was trying desperately to make work out evenly, but I doubt it will 1 over 12 plus 1 over 18 and again the most common mistake Kieran is kids think oh, that's our parallel. No, no, no, that's 1 over our Parallel so I busted out my calculator. You guys might want to get yours out and follow along just a thought Where's your calculator? I? Was working my way up to that sir. Where's your calculator? Not here. Where's your papers? Not it. Where's your binder? It's yeah, yeah, yeah, you know it's you gotta be crescendo to it. Okay build up to it. Yeah, okay So a reciprocal. Oh, that's not bad. I Thought it was gonna be a long usually they're repeating yucky decimals this one actually not too bad So this is the same as a single 7.2 own Resistor in other words and here's where I would really start mucking up my scratch diagram over on the side here I would say hey, that's the same as a single 7.2 Because now I can tell you are total This 7.2 is in series with this 10 now now I could say our total is gonna be 17.2 ohms, and I can deal with whatever I need to deal with Boy those numbers actually worked. Okay Jordan does that make sense? That's how we're gonna handle these now all along We're always trying to look for shortcuts. Did they tell me total current then probably I don't need to nest this I might not even need to rewrite everything or is there some resistors that have two up two things because if I know two I know four But if they give me something bare bones like example two Where it says find all voltages and currents and there's nowhere where they've told me two things and there's nowhere Where they've told me total current then I've got a fall back on We write this as a single solitary resistor and use v equals i times r. So let's try this Says find all voltages and currents draw a summary diagram I think the first thing that I would like to do is I would like to combine this as a single these two parallels as a single solitary resistor So the work that I show for this Justin I go one over our parallel equals one over 10 plus one over 15 I draw a little arrow and I write our parallel equals So on your calculators Assuming you have them here. Oh, that's nice six. Yes so right now here is my equivalent circuit and Eventually, probably you'll stop redrawing them You'll get good enough to keep track of stuff in your head and if you do fine, but for now I'm gonna say right now I have 20 volts and I've told you I get sloppy. I just put the resistor in like that and what are these parallel resistors the same as Six I got a four and I got a six Sally these two resistors in series are in parallel Now this resistor this six isn't actually part of the circuit, but it is the equivalent mathematical of those two by the way, look up How big was this resistor? Not a trick question. You can how big 15 how big? Anytime you're combining parallels your answer will always be smaller than the smallest resistor There's a built-in error check. I knew this is going to be less than 10 always will be So oh and you know what? If I combined a two-ohm resistor right there So now I have three in parallel. It would be one over 10 plus one over 15 plus one over two You know what the answer is gonna be smaller than two Try it if you want to go one over 10 plus one over 15 plus one over two and then take the reciprocal guarantee It's smaller than two. It's a built-in error check along the way So here's my question Megan. What's my total resistance? See it these two are in series. So what's my total resistance? 10 I can now say okay our total is 10 ohms, and I know the total voltage. They did tell me the chair lift that battery 20 So I total equal well actually you guys haven't probably memorized stuff yet because then you haven't done the homework V equals i times r except we're talking total total and total and I've said to you once we find the total current these usually fall apart. Let's see um. Oh How would I find the total current? Get the it by the total by itself the current by itself Mitchell current by itself. What is it? I equals I? Equals the total over our total and this one's really nice if I make these up. They won't work out nice because it's yucky math 20 over 10 how many amps are there to now since this is part of one of the things they asked me to find I'll go sig figs just to be careful, and I'll go two amps. I'll draw a box around it So Gordon that means how many amps are right here? To how many amps are right here? How many amps are right here if I'm and if I know 2 I know 3 What's the voltage drop going through this resistor? How many volts do I lose 8? Now it looks like if I'm a skier I can go down this ski hill and then if I hang a right I can go down this ski hill and end up at the bottom. How many volts must I lose going through this particular resistor? Gordon got to be 12. Oh, if I know 2 I know 3 What's the current? 1.2 is that right? 0.8 over here because the skiers got to split up if I know 2 I know 3 if I go Oh, you know what? I don't need to go I times R because can I not go through this ski hill and end up at the bottom or better yet Are these two can we not shake hands and meet up? What must the height of this resistor be also 12 volts has to be oh, and could I tell you the wattage now? yeah, 12 times 0.8 and 12 times 1.2 and 8 times 2 I could tell you if these were bulbs which bulb was brighter Because brighter wattage is brighter bulb That would be actually to me a nice question would be giving you something like this and instead of saying find everything I could say call this bulb 1 bulb 2 bulb 3 which one is brighter and prove it Well, you're gonna have to find everything to prove it Usually what they'll do though is they'll say find the current in this resistor Which you'd have to find everything else to get there anyways example 3 Find all voltages and currents it says and draw a summary diagram Again drawing a summary diagram some of you will reach the point where you don't need to redraw the circuit You can kind of keep track of stuff. That's fine. I Think the first thing that I would look for whenever possible is are there any resistors in series? Are there any resistors in series? Okay, so Gordon. I think mathematically I can redraw this as a six ohm right there a five right there and and What's this whole set of hills the same as 12 6 and 20 yes, and then Jordan. I think these two are in parallel So I'm quickly gonna go one over our parallel equals one over five plus one over 20. Oh Don't put an equal sign there mr. Do it because you're flipping it. They're technically not equal yet one over five and one over 20 I'm good at fractions, but even first thing in the morning. I'm not gonna try that for Four ohms and this is where if you wanted to this is our scratch diagram I've tried to keep my original circuit clean if you wanted to Regan you could redraw or what are these two combined the same as Regan You know what? I'm gonna do I'm just gonna go scribble scribble scribble, and I'm gonna put a little four right there and say that's my new circuit If you're looking for shortcuts Because now I think I can tell you the total resistance What is the total resistance? What is the total current? I think it's gonna be 30 divided by 10 total current is Mr.. Do it go to two sig figs just in case 3.0 and Now we use Kirchhoff laws start at the chairlift usually Sally. What's the current right here? Three amps. Oh, hey, what's the current right here? Let's write that down Do I know to I know three? What's the voltage drop going through this resistor? 30. I don't think so Go I times are right vehicles I times are we know I we know current we know resistance It's got to be couldn't be 30. Otherwise the skiers couldn't go down these next few hills There wouldn't be enough voltage. So I agree 18 volts This five ohm resistor. What's the voltage drop going through here? Let's see random Got to be 12 because I can get to the ground from there. Can't I so I'll put a little 12 volts if I know 2 I know 3. What's the current in this particular resistor? 12 divided by 5 2.2 2.4 it's what I said 2.4 amps. Oh my total current was 3 amps. How many amps going through here then? 0.6 0.6 0.6 amps Now the voltage drop in each of these is not 12 volts Oh, but they're gonna add to 12 volts because these three small hills have to equal this great big hill I times are I times are I times are what's the voltage drop through the first resistor? 7.2 volts Voltage drop through here 3.6 Voltage drop through here 1.2 Double-check do those three add together to give me 12 volts? Yeah. Oh great. Oh What if they wanted the power loss in one of these? Let's see I times there's V times I 18 times 3 I'm willing to bet this is the brightest bulb 54 watts, but let's see 7.2 times 0.6. Yeah 3.6 times 0.6. Yeah 1.2 times 0.6 Yeah, oh, what's the dim? What's the what's the dimmest bulb here? Justin says my mom says I'm the dimmest. No, no, no, I mean in the circuit here Yeah, not the not the brightest bulb on the tree. Um, I think sorry this one's the dimmest one point seven two watts Right not very bright at all where How many amps total no how many amps total Three they split up here. How many went down this way because we knew we figured out the 12 volts We knew 2.4 must mean 0.6 gears went that way, right? True cause love really when you wrap your brain around them Tyler really nice It's one of those boy circuits really could have been ugly. Actually the rules are pretty clean. Oh Also, you'll notice Using the old method that I used to teach the non skier method systems I did need about this much room to solve everything we're now we're doing most of the math almost in our head We're getting a few things here, and then it's fill in the blanks So thank you. That was the teacher that I was with over at SRT on Thursday He's the one that gave me this method and I say to him. Thank you very much So here's a using principles of physics right to explain kind of a question And yes, there's going to be one of these on your desk are using principles of physics question One of the questions they love to ask in circuits is hey, what if you add a switch and close a switch? So what happens to the total current in this circuit as measured by the ammeter When the switch is closed well total current is Total voltage divided by total resistance Now I don't think our total voltage is going to change that's the chair lift We're stuck with a hundred volts whether this switch is open or closed doesn't matter. We're stuck with a hundred volts So the real question is when this switch closes What happens to my resistance? Does it get bigger? Overall or smaller? overall Now a lot of students would say oh you're adding it when you shut this switch Dylan You're adding an extra ski hill. You're adding an extra resistor. I think it gets bigger. Let's find out Let's do a before Before I think I only have two resistors and I think Evan They're both in parallel because before I close the switch all the skiers have to go through this one and this one Sorry, that's a parallel series. They're both in series. I think before my total resistance 25 ohm When I close the switch What's my total resistance? Well, I have these two in parallel Let's find the equivalent of those two. It's going to be one divided by five plus one divided by ten reciprocal oh Plus this 20 ohm here When it's closed our total is 20 plus 3.3 repeating it's 23.3 ohms so as it turns out and this is very strange, but it's just true if you add a resistor if It's in parallel. You're lowering the overall resistance actually making that kind of makes sense because actually what you're doing Even though you're adding a resistor you're giving the skiers an extra hill to go down We can fit more skiers on our ski slopes So if this gets smaller if this gets smaller Our total decreases the total is constant therefore What happens to I total stays the same increases or decreases Increases in fact it goes from four amps to whatever 100 divided by 21 I can do that 100 divided by it goes from four amps to 4.3 amps so if these were light bulbs Strangely enough when you close this switch this bulb would get brighter This one would get dimmer because now it's splitting current with this one And if you don't believe me you can actually well initially there's four amps going through here when it's closed You can work out how much current was going through there if you wanted to it's less current So shut the switch dimmer dimmer brighter homework two three four Five so so far everything Number six is a nice twist instead of giving you the chairlift. I'm saying find the chairlift. Oh I do notice over here. They gave me two things. That's probably gonna be my plan of attack if I know two I know three I know four as a matter of fact and what else can I get from there? So six is good. Yeah, seven eight. Am I gonna assign them all? Let's see Nine air resistance, which is nice review, but I won't worry about number nine. So right now one through eight It's a short lesson. What we're also gonna do today is go through our electrostatics test finally