 Here's my circuitry tutorial from the big review package. Are there questions you would like me to go over? Go ahead. Let me draw a circuit. Okay. What's that? Okay. And I'm going to draw a fairly simple circuit. I'm just going to put in one big resistor here. And I'm going to make that resistor, I don't know, 15 ohms. Okay. And I'm going to temporarily do that. I'm going to add another resistor right here, but we'll just scribble it on. All right. If I tell you that this has an emf of 30 volts, what I'm really telling you, because I haven't given you a built-in internal voltage, I'm telling you the terminal voltage. That's why I usually use the letter V there. So if I wanted to find the current, I would go, what's my total voltage of this circuit? What's my total resistance of this circuit? 2.0 amps. Okay. Now I'm going to take this same circuit, but I'm going to break this battery apart. I'm going to show you the inside of the battery. So I'm going to have the same battery, same 15 ohm resistor, but inside here there's a little tiny resistor as well, an internal resistor. I'll make it a 3 ohm resistor. Now I've already told you that when we hooked this circuit up, I told you that the terminal voltage was 30 volts. That included that there. So when I went R total, the total resistance of this circuit really isn't 15, really it was 18. So let's see if we can do a little bit of arithmetic here. When we just looked at this overall battery, we found that the current was 2 amps, right? How many amps go through here? What's the voltage drop here? How many amps go through here? What's the voltage drop here? Six. Now look at this then. Here's my chairlift. How many volts do I lose here? How many volts do I lose here? So how high is my chairlift? Now this we call the EMF. This is what it would say on the side of the battery. On the side of the battery, it would say 36 volts. That's what the battery gives you before you hook it up to anything. Hook it up to something and now you have your terminal voltage. Your terminal voltage is your maximum theoretical minus whatever you lose going through the battery. That's where the 30 comes from. I don't know if that helps or not. I hope that does a little bit and we'll do some more questions. I know it was the last lesson and it is actually probably the single more confusing lesson. EMF, maximum theoretical voltage, what it says on the side of the battery, that never changes. The terminal changes depending on what resistor is right here. What if that was a 20 ohm resistor? Good question. So now I know this battery has an EMF of 36 volts. What do we say the internal resistance was equal to? What did I say? Three ohms. Now you pull out that 15 ohm resistor and you replace it with a 20 ohm. Sure. What's my terminal voltage going to be now? Well, first thing I would say is I need to find total current. It's going to be a decimal. Sorry, I was trying to make these work out evenly but there's only so much I can do with these numbers. I should have made this 21 ohms and that would have been 24. That would have been a little nicer. What is 36 divided by 23? 1.57. So now the total current is 1.57 amps. That's 1.57 amps. How many volts do you lose going through here? 31.3 volts. This is also 1.57 amps. How many volts do you lose going through here? 4.71 volts. So the terminal voltage is going to be that original 36 minus what you lose going through the battery. What do you lose going through the battery? 4.71. Now here's the equation that we can see. This is the circuit version. The equation you're correct that we came up with was maximum theoretical voltage minus total current and we use a little R to symbolize it's a small resistor inside the battery. Where did that 4.71 come from? I times R. So the terminal voltage would be 36 minus 4.71. 31.3 volts is your terminal voltage. If I put a different resistor here terminal voltage would change because I'd get a different total resistance, a different total current, a different voltage drop through there, a different maximum theoretical which never changes minus terminal voltage. So does your EMF change? No. That's what you see on the side of the battery. So if I look at these I think these are the little tiny ones in here. I think they're 1.5 volts. That's an EMF. I'm not getting 1.5 volts out. Now for what it's worth you'll notice here our total was this plus this. Because I hadn't given you an internal resistance, I'd just given you the battery, I'm giving you the terminal voltage here. So this voltage already includes what you lose going through. What was our ski hill analogy? We said what you lose going through is like the bump after the chairlift that you ski down. Does that make sense? I hope that cleared it up a little bit. For the second one if I wanted to find terminal voltage I could have then said 15 plus 3 is 18. So there's where my 2 amps came from from my EMF. 36 divided by 18. So that works if I started with this and worked my way backwards I could have found the terminal voltage. Here I told you the terminal voltage we worked our way backwards to find what the EMF had to be. I hope that helped. I don't know. I think so. Can you come to the office please? Feel free to pick ones if you find one in there that has the little resistors and this dotted rectangle around the battery. That's a terminal voltage question. I'll happily do it. Anyways which one would you like to do? 48? Jimmy you are great. You're conscientious about the homework. Everyone else appreciates that because you've probably done questions that they haven't got to yet. Oh and I'm seeing a terminal resistance. Sorry a terminal voltage. Internal resistance. choice. Okay they want me to find how much power is dissipated as heat inside the battery. Do batteries heat up when you use them? Yeah. Why? Right there. Power is VI. Now that's the one that's on your formula sheet. Also remember power is I squared R and V squared over R. You can get those two Jimmy by plugging in that there whichever variable you get by itself. Okay. How do I solve any circuit? Try and find the total current. Did they tell me the total current? No. My next step is I go find any resistor where they told me two things because if I know two I know four. Wait a minute I thought it was three. No no we said also now if I know power there's four things. Resistance, voltage, current and power. I'm gonna start here. So let's see what I can figure out. I think I can figure out the current because if power is I squared R, I is gonna be power divided by resistance square root. The total current is gonna be 3.2 divided by 10 square root. Let's try that again. Square root. The total current is 5.657. So what's the current right here? 0.5657. Hey Pat what's the current inside this little resistor then? 0.5657 amps. If I know two I could find power I don't know another one yet. Well what else can we figure out here? Now that we know I and R I think we can figure out the voltage drop. What's the voltage drop? I times R. I think I can multiply by 10 in my head. I hope I think I hope I think 5.66 volts. So then are you ready? They didn't give me terminal voltage. They gave me chair lift height. How high is the chair lift? 6 volts. How high is the only ski hill? So how high must the bump off the chair lift be? 0.34? 0.34 volts. By the way that means the terminal voltage of this is 6 minus 0.34. The terminal voltage of this is 5.66 volts. That's the terminal voltage. They're not asking that. They're asking for the power inside this resistor. Power is VI. It's gonna be 0.34 volts. That's what we lose going through that resistor times the current 0.5657. 0.19 watts. Terminal voltage is the voltage after you've gone down the bump off the chair lift. And if they don't mention a bump off the chair lift then we just assume I guess it's a smooth chair lift and there was no bump. Yeah they wouldn't you if they didn't have if they didn't show me the little resistor if they just had a battery they wouldn't have used the E symbol there. They would have used V because it would have been the terminal voltage. Good question Jimmy. Does that make sense the way we handled it? Okay. Anymore and don't feel bad if you're the only one asked but whoever wants to ask. Pat you got one? I'm not sure. Chica you alive? Kevin and Lingling anybody? Number 9. I don't remember number 9. Let me see. Number 9. 12. Getting closer. 8. Oh 9. Great question. This also ties in terminal because they want me to find the EMF chair lift height and then there's a part B. Make sure Kevin I do part B as well but I'll do part A first. What's my strategy going to be here? Now they want me to find the EMF. They want me to find how high this chair lift is. It's going to be that voltage plus either of these guys plus that voltage that's going to be my chair lift height. Find total current. Did they tell me total current anywhere? No. Step 2. Find any resistor where they told me two things. Haha right here. Okay I'm working right here because if I know 2 I know 4 but I'm really interested in voltage. What's the voltage in that resistor? 7? What's the voltage in this resistor then? Has to be 7. Has to be 7 because the skiers can break apart and join together. They have to be able to break apart and join together at the same height. Same voltage. Oh I know 2 in both of these. Now I know 3. I can find the current. Current is voltage divided by resistance. So here it's going to be 7 divided by 33.2121.212. Here it's going to be 7 divided by 68.103 and ta-da I now know the total current in this circuit don't I Kepp? The total current is going to be 0.212 plus 0.14 plus 0.103 0.455 amps. 0.455 amps. That means 0.455 amps up there and that also means oh I times R I can multiply by 10 in my head. 4.55 volts lost. Oh and that means 0.455 amps there 0.364 volts lost. I times R. So now I can walk an entire ski run and end up at the chair lift. Starting here if I go through there through there and there will I end up back at ground zero. That means that this chair lift has to have a total height of 4.55 volts plus 7 volts plus 0.36.364 11.9. In fact I'd be willing to bet that's probably a 12 volt battery but I'll put 11.9 because that's what I got mathematically but I'm willing to bet the sticker on the side says 12. That's what they'd call it even if it wasn't an 11 volt battery 12 volt battery. No no no EMF is the height of the chair lift. EMF is the maximum theoretical voltage of your battery and the way to find it is add up all the hills in one path and don't forget to include the little bump at the bottom of the chair lift because your chair lift was a little higher you lost a little bit of voltage going to so the EMF is going to be dope. EMF is going to be 0.364 plus 4.55 plus 7 11.9 volts. I would say when you're dealing with a circuit that's one of the ways to find it yes. I can think of other I can think of other questions where this method wouldn't work so I can't say I'll do it all the time but but probably that'll get you there but I can think of other weird circuits where this method wouldn't work specifically I guess I would say this okay Angie if you can do a closed path ending starting at the top of the battery ending at the bottom of the battery going through the resistor internally and always going downhill then yes but I had to add those conditions because otherwise some kid might say well why can't I go like this well no that's not going to get you there is that okay? B what the heck was B oh find the power in the internal resistance I times Vi right so 0.364 times 0.455 there's the power or you can go I squared R or you could go B squared over R but I got V and I good enough is that okay cap for part B I'm guessing you were wondering about part A yeah yeah yeah you're assuming I know what we're talking about give me a second okay five this one is so easy that it's tough is part D okay let me uh let's go look at number five then Mr. Duke number five what the heck was D what do you get for C so about 60 watts light bulb they will somewhere on the provincial and I have during your unit tests asked you to quantify certain values you'll notice every swap and I've said you should have a good idea of what a really big number and what a really small number is so I have seen them on the provincial for example say a resistor is exerting a power of 2000 watts which appliance is this resistor most likely to be in A a light bulb B a hairdryer C a washing machine probably the fact that microwaves are like you know a thousand watts so it's something that pulls out a lot of heat or they've done stuff with um I've seen them do it with momentum or energy for that matter you know magnetic field will we do magnetic field I'll be talking about well here's the earth's magnetic field so this is what a big magnetic field this will kill you this is a small magnetic field this is what would cause something to stick to something else and then here's the earth's magnetic field that we exist in all the time it doesn't affect this at all okay so yeah how many marches is worth by the way one and it's a fairly I mean it's almost close to 60 watts yes so I don't think that's a stretch certainly calculated would be a bad idea I don't think the least your calculators don't glow and get hot so well you know what a bulb is though right see I think the kettle they just put on there as a distractor a kettle would probably take more though because does it use way more heat so it burns more energy per second and that's the definition of watts right power was worked per second it must be more than a light bulb does that make sense yep 21 this one you'll notice no internal resistance savanna on number 21 did they use a letter e next to the battery so technically they're asking me to find the terminal voltage oh they just called it the potential difference it's voltage in this case it is because they didn't give me an internal resistor potential difference is voltage they want me to find v they didn't include an internal resistor or a letter e I'll do it anyways for some reason I'm missing that line there so what would I do and start here right I know the voltage here as well v equals i times r 60 volts what's the voltage have to be through this resistor then 60 volts in fact I think this is the same diagram I gave you on your quiz but I changed the question I think I can't remember now um oh what's the current have to be six amps what's the total current then 1.5 amps 6 amps yeah 7.5 amps so you're ready up here is 7.5 amps and what's the voltage drop through this resistor 6 times 7.5 what's that 45 someone's already got the numbers for me oh and down here is 4 times 7.5 amps 30 is that right let me down here 4 times 7.5 it is it is 30 right and now yeah we can walk a path that's got to be the total voltage the potential difference okay now what you have found is the terminal voltage here's how I know first of all did they give you the internal resistance here anything like that did they give you the emf no and also because they told me what kind of current I'm getting from this circuit I'm willing to bet that current includes whatever we lost going through this internal resistance so fine okay uh what do we get uh 45 60 and 30 100 135 oh number eight by the way 135 volts that's probably a plug that's a 140 volts I think is what you get out of your plug so probably plug with an adapter to give you direct current so probably what I'm getting from this number eight and then 12 sure eight total power okay uh total power is going to be the power here plus the power here plus the power here because power is a scaler so I'll just add it up um oh they told me two means I know four let's see what we got here uh power equals i squared r I know it's vi but it's also i squared r right lingley and they gave me the power they gave me the resistance so I can find the current it's going to be the power divided by the resistance square rooted it's going to be 30 whoop 9.2 divided by 33 square root of that looks like the current is 0.528 so right here I have 0.528 amps oh what's the voltage right here well i times r times 33 17.4 you know what the voltage through here has to be then 17.4 volts right um oh you know what the voltage has to be here then if i'm starting by the way this is a terminal voltage not an emf because they didn't give me the internal resistance that's fine that's why they use the letter b uh 24 I lose 17.4 24 I lose 17.4 how many are left for the final hill this has got to be 6.6 volts I know two now I know three current is voltage divided by resistance the current is going to be 6.6 divided by 10 which I think I can do in my head 0.66 amps that's total current haha now this question fell apart because if that's the total current and I got 0.528 coming from that junction I bet you it's going to be 0.66 minus 0.528 the amount of current over here is going to be 0.132 amps and now I'm almost done well what's the power in the first one voltage times current 6.6 times 0.66 that's how many watts are in the first one what's the power in the second one 9.2 what's the power in the third one 17.4 times 0.132 I times V or V times I so 2.3 watts plus 4.4 watts plus 9.2 watts the total power in this circuit 15.9 I bet you the answer is 16 yep and then sorry which one 12 ooh nice twist finding a resistor well I'm going to start where they gave me two things obviously here they gave me power and resistance it's really handy I have this one memorized that power equals I squared R which means that I equals P over R square root P 0.4 divided by 10 square root I think it's gonna work out evenly ah a lovely current of 0.2 amps oh and what's the voltage if I go 0.2 times 10 in your head two volts by the way how many volts are we starting out with and that would include the bump off the chair lift apparently since they didn't bother separating it 12 I lose two this and this better add to 10 because I gotta get rid of my 10 volts somehow oh um what's the total current here Pat no no no no no no no no no no no no no no no no oh what's the total current here then what's the voltage drop here I times R at 3 I lose two volts and I lose three volts I start with 12 volts. How many volts must I lose through here? Not only that, because these guys are identical. Point one amps, point one amps. The same current will go through each of them. Do I know two? I know three. R equals V over I. I never do baking fun you guys for doing that. R equals V over I. So that's how you got through science tan. I just, my beef against them is that I would rather teach a student how to do the algebra so that whatever equation, like haven't you got way better at your equation solving this year to the point where you're doing stuff you never thought you could do in your head, in your head. So let's not push them that way instead of giving them the crush. But I understand that. Seven divided by point one, I think 70. I think each resistor is 70 ohms. That's how I would handle that one, I think. Pretty sure. Next, 45. Love to. So here's an example of a recharging one. I said it shows up once in a while as a multiple choice. Are you having a head? Stick around for two minutes and I'm gonna do hints about the test. Can you? I'll do this question and then remind me and I'll do the hints thing. I always do that for the people that show up for the tutorial, right? Or watch it online. People that actually take the time to put in an effort to want to improve their grade. And what was your question? Will there be one like this on the test? I don't think I did. It's clearly fair game, although this is from 1997 and the course has gotten easier in some ways. Which is the bigger battery? That's the winner. The current is going to flow that way. Which kind of makes sense. Bigger chairlift, higher mountain or whatever, okay? As a matter of fact, your net voltage is three volts because this is in the opposite direction. It's sort of like gaining eight but then climbing down five volts of stairs. What's your total resistance? They're all in series, right? 11 and 1 and 2. 11 and 1, 14 ohms. What's your total current which happens to be the current going through the 11 ohm resistor? It's going to be V over whatever the heck that is. That to me is a fair game one as a multiple choice because I don't think that one was too unreasonable. What they're not gonna do is that one of the last ones I did with you that had like the two batteries and they all over it, they're not gonna go up on you like that, okay? The review that I gave you is a pretty good indication. There are a couple on that review that have multiple batteries. That's about the level difficulty they'll throw at you if one shows up and they hardly ever show up. Is that okay, Enge? Is that the right answer? I hope, I think. What is the correct answer? What do you get? A, B, C, or D? A? That's how I'd handle that. Hints about the test and I'll still take more questions. Hint number one, if you're not sure what to do, draw the circuit. I type this test up. Sometimes rather than do the graphic circuit, I just described it. Hey, you have a battery that's this big. You have one resistor that's this big. An eternal resistor that's this big. Find B. So draw it if you're not sure. Make sure you know how volt meters and ammeters are supposed to go. That was from like lesson one. There's several of those in your review anyways. No, kilowatts and no. Make sure you know the difference between current and electron flow. Current is which way the positives would flow if they could. That's which way of battery we point the battery, but the electrons flow in the opposite direction. So yeah, here's a fairly standard circuit to analyze. It has an EMF as well as a terminal voltage. So we've done a few of those so you knew that was going to be on there. It's a pretty straightforward test. I'm trying to give hints that I could give you weird stuff, but I kept it pretty straightforward. There's a question. Be prepared for switches opening and closing that those are good ways to do using principles of physics right to explain questions. That's probably what you're going to have. And if you're doing a use of principles of physics and you're not sure of the theory, make up numbers or crunch the numbers and see, oh, is there more power or less power? Is there more current or less current? Is there more voltage or less voltage or I guess the resistance wouldn't change. But don't be scared to crunch numbers. I think you'll find the written very straightforward. I have a lot of kids get perfect on the written multiple choice. So even be more specific, how many multiple choice questions are there? 11 multiple choice and one, two, three written questions. On the multiple choice out of those 11, I think six of them are pretty conceptual. Of the remaining five, two are tricky. Not nasty, nasty tricky, but tricky. Draw the circuits is my advice to you and I'll be giving you the same advice tomorrow on the test. You asked me, will I do a question with more than one battery? There is a question on here where I have more than one battery, but they're not facing each other. They're in series, which is just like two chairlifts in a row. Yeah. Okay. We did, we did do that. For me, I think in this case, I think in the one that I'm thinking of, each of them also has a little internal resistor. So you'd have to say, oh, what's the EMF and then minus what I lose, plus what's the EMF and then minus what I lose. And that's how high I am. Right? Makes sense. So there's your hints back. Not really many hints because I think it's a straightforward one. Jimmy, which one? 1616 power. Okay. No problem. Bluff, I say. This one is as tough as it'll come because did they tell me total current? No. Did they give me any resistor with two things? No. Then I have to rewrite this as one resistor. It's the only way I can do it. They did give me the voltage, the terminal voltage of 80. So let's see. I have this parallel resistor right here. I'm going to say that's going to be one over R parallel equals one over 12 plus one over eight. One divided by 12 plus one divided by eight. Okay. The parallel resistor is 4.8 ohms. Terrible ohm signal. Let's try that again. So what's the total resistance, Jimmy? Well, the total resistance is, this is the same as a 4.8 ohm resistor plus I hit a 10 plus I hit a 12 and these are all in series so I can just add them up. Total resistance is 26.8 ohms. And now I can find total current. Total current is going to be total voltage divided by total resistance. What's my total voltage? 80 divided by 26.8. What's my current? 80 divided by 26.8. And I get two point, you know what? I'm going to use 2.985. I'll carry an extra sig fig. Amps. All right. So Jimmy, how many amps are going through this resistor here? Yep. 2.985. And how many amps are going through this resistor on the top here? 2.985 amps and amps. Now they split up here. I'll figure that out in a second. Ooh, but since I know two, I know three. I can get the voltage of each of these two resistors. I times R, I can do this one on my head. 29.85 volts and then 2.985 times 12. 35.82 volts. How high is our chair lift to begin with? 80. Going through here we lose 29.85 volts. Going through here we lose 35.82 volts. You know how many volts we have left to go through either of these ski hills? How high either of these ones has to be? This is 14.33 volts. Jimmy, do I know two? Then I know four. I can find the power. Now I know resistance and voltage. Let's see. Power equals VI, but I also know that I equals V over R. So power equals V times V over R, or V squared over R. It's going to be 14.33 squared divided by 8. 25.7 watts. That's how much power that particular resistor dissipates. I'd take it, but I would also say try not to round off partway through. Don't go stick bigs until the very, very, very, very, very end. 26. This one hopefully won't be too bad because they told me total current. Although to be honest, usually when they do that there's going to be a curveball later on because otherwise it's just three. Let's see. How high? Back to zero. How high? How high? Oh, here I know two, so I know three. What's the current here? So do I need to draw the triangle? Please don't make me draw the triangle. 1.5 amps. And Savannah, what's the total current in this circuit? So if I got 1.5 amps that went this way, how many amps went that way? I don't know what you're trying to do, but it's 27. I think this is a question that I hate. And I think the reason I hate it is because when you round off, the rounding off numbers that you get are confusing. Let's see if this is the one that I remember. Did I write a note about that? Okay, you know what, Jimmy? I'm going to show you my answer to that question and I'll talk about it. Did they give me a picture of the circuit? So I drew it. Okay. Yeah, I wrote bad question. Here's why. All right. Actually, no, I didn't draw it. I used the formula. It says the cell has an internal resistance. They gave me terminal voltage and they gave me... So I wrote this down, which is the EMF equals terminal plus IR. I just rearranged it. It said, okay, I need the total current. The total current is going to be the total voltage that they gave me, the terminal voltage, divided by the resistor that they gave me. Now, this terminal voltage, I'm not going to use the 5.5 ohms total resistance because that terminal voltage already includes the bump off of the chairlift. So total resistance, 5. Is that okay? What I didn't like about this is I get an EMF of 1.54, which to two sig figs says my maximum theoretical voltage is 1.5 volts. Then, we replace this with a 10 ohm resistor and they want me to find the new current. Now, I know the EMF is 1.54, so I'm going to use 1.54 because I'm using an EMF. I'm going to include that 0.5 in this. When I did that, I got a new current of 0.146 repeating. When I use that to find the terminal voltage, I got 1.5 volts. Here's what I don't like. What's my voltage before I start? 1.5 volts if I go to two sig figs. What's my voltage after I start, after I hook it up? 1.5 volts if I go to two sig figs. I don't like that question because you already said, oh, so the voltage is always small. Yeah, it should be smaller once you hook it up, but here because of just the weird rounding, it's not. I don't like that question. I understand what they're trying to do. I just want to pick different numbers. In hindsight, if I was doing this again, I would draw a circuit so it would be clear. When I first did this answer key, I still wasn't very good at the ski lift method. 24, A or B are both. Oh, they just isn't A. I didn't include B. B used to be there, but it got thrown out. B, they closed the switch and then they asked you some questions. The problem was when you close the switch, what you've actually done is you've created a short circuit because skiers can get from this height to that height without going through a ski hill. It was just that's a bad circuit. That's the definition of a short circuit. It's going to get really hot and it's going to burn. So they threw that question out. Apparently I found that out. All right, let's see. Eight volt battery. Oh, each bulb has five watts. I guess I have 1.5 amps going through this internal resistor. Oh, how many amps are going through this lamp? It won't, gotta be. Do I know two? Now I know four for this one. What I like to find, I'd love to find the voltage here. So 3.33. It's gonna be 5 divided by 1.5. I agree. So this is 3.33 volts. How many volts must this be then? Oh, I don't know because I'm losing a little bit going through here too. Oh, wait a minute. How many amps go through here? Also 1.5 because none can go through there as long as the switch is open. So that means this is going to have the same voltage as well. 3.33 volts. Right? So Kevin, I have this starting out with 8 volts and I'm gonna lose 3.33 volts twice. Is that okay? So when I get right to here, I still have 1.34 volts that I need to lose in order to get to the bottom of the chairlift. Do I know two? I know three. R equals V over I. 1.34 divided by 1.5. Internal resistor is 0.893. I hope that's the answer. I think that is. 0.89 ohms. Does that make sense? Okay. Okay. Deep breath. Which one? 30. Oh, too far. 30. 120 volt power supply is connected to a heater of resistance 15 ohms. Okay. We want the same power output if we connect it to a 240 volts. Let's look at this first one here. Power for this first one is VI. I don't know. You know what? It's going to be V squared over R. It's going to be 120 squared divided by 15. The power that we're talking about here is 120 squared divided by 15. 960 watts. Which sounds high. No, wait a minute. It's a heater. That moves a lot of heat. That probably would take a lot of power. Now, here we're also going to use power equals V squared over R, except they want us to find the resistance. So the resistance is going to be the voltage squared divided by the power. What's the voltage? 240 squared divided by what's the power? Same power as they told me we were drawing originally 960, because they said same power output. 240 squared divided by 960. Oh, this would have to be a 60 ohm resistor. That would give you the same power output. 39 and 41. Here's another good EMF kind of a question, but this time Savannah, they're wanting us to find the internal resistance. Kevin, what's the current flowing through this bulb? Do I know 2? I know 4. Let's find the voltage. Power equals VI. The voltage is going to be power divided by current. 3.5 divided by 0.4. I lose 8.75 volts through the bulb. What's my EMF? How high is my chairlift? 9. So Savannah, what must I lose going through here if that's my terminal voltage? And that is my terminal voltage because that's the only other skill that shows up. 0.25. Oh, and Kevin, what's the current going through here? Equals V over I. 0.25 divided by 0.4. 0.25. Try that again Mr. Duke. 0.25 divided by 0.4. 0.625. 0.625 ohm. That's part A. What did B ask? Here is a good using principles of physics question. We replace the bulb with a lower resistance. So this resistor here gets smaller. If this gets smaller, if this gets smaller, what happens to your total resistance gets smaller? If that's smaller, total resistance is the 0.625 plus whatever resistor this is. Total resistance gets smaller. Now if total resistance gets smaller, what's going to happen to your total voltage? Well, actually first of all, what's going to happen to your total current? Your total current is going to be your maximum theoretical voltage divided by the little internal resistance plus this new resistance here which is now smaller. You know what's going to happen to your total current? If this number here gets smaller, EMF doesn't change, 9. If this number here gets smaller, what's going to happen to your total current? Total current gets bigger. So terminal voltage is your maximum theoretical unchanging voltage minus I times little r. This hasn't changed. This can't change. That's a physical part of the battery. What has changed? Current went up. So if this number gets bigger and you're subtracting, what's going to happen to your terminal voltage? Now that's the algebraic approach. I didn't like that. No problem. Here's what you also could have done. Do you know current? Do you know voltage? What is the resistor of this bulb? Well, it would be V divided by I. It would be 8.75 divided by 0.4. This bulb right now has the resistance of 21.875. In the using principles of physics, it says replace it with a lower resistance. Fine. What's its resistance right now? Make it a 10-ohm bulb and now re-crunch the numbers. Let's make it a 10-ohm bulb temporarily. What's my total resistance in this circuit then? 10 plus 0.625. Total resistance would be 10.625. Of course, I'll carry a few extra sig figs just for the heck of it. Total current is maximum theoretical total voltage 9 divided by total resistance. Total current is going to be 9 divided by 10.625. 0.847 amps. What was the current before? What was the current before? What is it now? Would the current get bigger or smaller? Okay. Now, 9 minus 0.847 times little r, little r, little r, 0.625. 9 minus that answer times 0.625. I get a terminal voltage of 8.47 volts versus, what do we say the terminal voltage was here? 8.75, wasn't it? Because it was 9 minus 0.25 volts. Originally, 8.75. New one, 8.47. Definitely less than that. You could also crunch the numbers. But it's kind of a weird one because strangely, by lowering the resistance, because that made the current bigger, the bump after the chair lift somehow also got bigger, your net terminal voltage got smaller. And you said 39 and 41. Is that what somebody said? Hey, Savannah. Terminal voltage. Savannah on the circuit diagram, terminal voltage is this minus, sorry, let's try that again, Mr. D, is this minus whatever voltage through there. That's terminal voltage. Okay. And that's probably how I'm going to end up finding it. Let's see. Have they told me the total current? Have they told me anywhere with 2 going to have to say total current is going to be total voltage divided by total resistance. Now my total resistance is 2.7? 2.7, isn't it? Total voltage is, total current is, I'll carry a few extra digits just in case. So you know what the terminal voltage is? It's that 6 minus i times r, little r. Oh, did I do it times? Sorry. Chair lift minus bump at the end. 5.56. 5.6. 36B, probably. 36, there's A. Well, I'm probably going to have to copy the circuit to do it anyways. So let's do that, Mr. D. Heck, it's good practice for you. What's the current? 1.5 amps. What's the voltage down here? It's going to be 2.7, I'll bet you. Yeah, you know how I knew that? Because they told me the terminal voltage. Since that's my battery and this is my only other voltage drop, this has to be exactly equal to the terminal voltage, 2.7 volts. Let's see. 1.5 amps. How many volts do I lose going through here? Can you go i times r here for me? 0.3. So the EMF, let's see. How high is the chair lift? Well, I lose 2.7 going through the ski hill, but I also lose 0.3 just getting off the chair lift. That chair lift must have been, there's my EMF. That's a 3-volt battery, it's what it's out of the side. Okay, now let's do part B and C. The 1.5 ohm external resistance is replaced by other resistors, and the current and the terminal voltage are measured in each case. Which graph best represents terminal voltage versus current as these resistors are chained? Say what? Well, terminal voltage equals EMF minus IR. I can't remember how I explained this one, let me check my answer key. I'm having a long day. What number was that? Okay. So I said terminal voltage equals that. I said as your current increases, that also automatically gets bigger because your EMF doesn't change. So as your current gets bigger, this answer should decrease. So I picked a graph where as current got bigger, terminal voltage decreased. That makes sense to me. As this gets bigger, this gets bigger, this can't change. In fact, eventually you can have such a big resistance, sorry, such a big current that your terminal voltage is zero, your battery is going to overheat pretty quickly because you're using all of the energy just across the battery. Does that make sense? Sorry, I blanked on that. Long day. This one, and number 13? Question 13? I don't know what question 13 is, go find out. Ohm's law is just v equals i times r. So Ohm's law is v equals i times r. So what are we comparing here? As that gets bigger, what's going to happen to that? Are there any squares or anything like that? So it's linear. Ah, very nice. Yes, as it turns out. I think there's one later on where they give you one of those graphs to analyze and I think you have to clue in. Oh, the slope of this graph is the internal resistance or something to the battery. One down. Okay, I'm going to hit stop first of all.