 Questions from the homework number seven I would love to okay. I said this The amount of electric energy we said yesterday was power times time and Since they want to how long I said I'm kind of leaning towards time being however much energy it takes Divided by however much power we supply. Is that okay Sally? This is maybe not the question to do right before lunch, but that's okay Hot dogs. I'm still a kid enough. I love hot dogs. Oh 10,000 joules 10 kilojoules apparently we need that much energy Divided by now power is measured in watts. I said I don't have any watts here However They did tell me that the resistance is 30 ohms and the hot dog is connected to 120 volts So I said I can certainly go v equals i times r I can tell you how much current is flowing through this hot dog the amount of current that's flowing through this hot dog is going to be 120 divided by 30. I said oh, we got four amps flowing through this hot dog. I Didn't quite know what I was going to do with that, but I figured we're gonna let me find something. Ah, wait a minute I said aha We also said yesterday that power was Right So down here instead of power. I'm going to put Do I know the voltage that this hot dog is wired into? 120 did I just figure out the current? Oh, that's why they told me the resistance that I just figure out the current Yeah, four amps. So it's gonna be 10,000 divided by 120 times 4 and I think that should work. It's gonna be 10,000 divided by I think 480 is 120 times 4 And by the way, that's how many watts of power. I guess we're using to cook this hot dog is 480 watts of power Good. Yes, 2028. Yeah Okay Nice little question in terms of it reminds you don't forget to kind of plug and chug and use the two equations To find missing stuff But I'll be honest most of what I've assigned so far is not what I'm going to be primarily asking you In fact today is the meat and potatoes. So With that, let's move on to today's lesson continue So the laws for analyzing circuits Krikov was a russian physicist and he wrote Very nice mathematical rules for analyzing circuits And I learned the mathematically and the way I taught it my first couple of years when I taught physics 12 was mathematically And I'll be honest I almost prefer that because I'm a math nerd it involves systems of equations Oh, it was lovely And then I think I told you I talked to a physics teacher who gave me a better analogy this idea of a ski hills I'm going to use that because it's much clearer for those of you who are not math nerds and even the math nerds like it So the first law we're going to learn is krikov's current law And the author abbreviates this as key kcl and it's basically a conservation of charge. Here's what it says Krikov's current law states that at a junction between wires if you come to in a circuit diagram a fork a junction The current flow splits or combines and it continues to flow downhill So we're always going to ask ourselves Where's the battery? Where's the top of the battery and the current is always going to flow downhill from there When the current splits or combines no charge is lost So that the total flow into the junction equals the total flow out of the junction. Here's what we're going to say the sum Of all of the currents into a junction has to equal the sum of all the currents out of a junction What we're saying is electrons and protons can't magically vanish in our ski hill analogy The skiers can't leave the hill without getting to the bottom and walking off if you have two amps Coming this way and one amp coming this way. Do you know how many amps you have leaving? three So let's use that to analyze the current says find the unknown currents So here is our circuit diagram Here is the top of the battery the uphill. So the current is flowing this way How many amps are in this wire? 1.75 that's our total current. How do I know it's our total current? Because that's what left the chairlift it may get split up along the way But when they join back together, you know what our total current's always going to be? 1.75 So here how many amps are flowing through there? Have there been any other paths for the skiers to travel on? Then it's 1.75 amps What about here? Have there been any other paths for our skiers to travel on? Then it's 1.75 amps And in fact when they get me to analyze a circuit one of the first things I try and find if I can find Total current inevitably the question falls apart Next one Here's our battery I usually start at the top of the chairlift at the top of the battery What's my total current in this circuit? three If 0.8 amps go this way How many amps go this way? 2.2 Follow them follow them follow them follow them follow them follow them follow them When I get right here, what's the current? Still 2.2 and what's the direction? That way downhill I had 0.8 amps going this way 2.2 amps going this way when they meet again. What's my current? And that is going to be my total current because they all meet at the bottom of the chairlift Three amps. What's the direction that way? That's kurkov's law for current It's basically a conservation of charge dylan. It says you can't lose electrons along the way Except instead of the electrons because that's such a small unit of measure we'll use amps and current Example two Says show the direction of each current and find the unknown currents. Okay Right here the current would be traveling that way off of my chairlift. That's downhill So as I follow through here If I go through this resistor, which way is this current up or down? It's got to get back to the bottom of the chairlift. It must be traveling this way in this resistor As I travel, let's look down this junction here Which way is the current flowing here to the left or to the right if I follow from my chairlift from my battery Which way must it be flowing over here? To the right and you know what how many amps right here? Five how many amps right here? How many skiers did we start out with them? Does that make sense codder? Yeah Oh Which way is the current flowing through this resistor up or down? down So if two amps went here and I have five amps coming in How many amps right here? Must have broken up into three amps and it must be flowing this way and down and Let's keep walking. Let's keep walking. Oh, how many amps must there be right here? Must be three And they joined together. How many amps must there be right here? Five to the left Oh, and how many amps must there be right here? 13 The amount of current flowing into a junction has to equal the amount of current eventually flowing out of a junction Electrons are neither created or destroyed. Oh, by the way, this is the direction of the current Which way is the direction of the electron flow? In the opposite but we said we're going to talk about positive current because it allows us to use this downhill analogy and it makes more sense So current up electrons down Current left electrons right next one Okay, this one's a bit trickier here I'll start out by adding some directions. So here's my battery. Which is the positive side the left side or the right side Right side. So the current is flowing this way Which way is it flowing in all three of these resistors upwards or downwards? Upwards I'm going to go like that. I'm going to go like that. I'm going to go like that Which way is it flowing right here? Left ah, and this is an important number because look look look Is that not all the skiers do not ever does not every skier have to go down this hill follow it Do all the skiers join back together? Do they all follow here? There's my total current See it Total current Dylan is Five amps now. I can go back and fill in some blanks Oh, and if I had two amps right here and point five amps right here How many skiers went down this ski run went through this resistor? 2.5 Blah blah blah blah blah blah blah Okay, which way is the current flowing in this two amp current up or down? down How many amps must be in this resistor then? three Also down and they joined together at the bottom of the ski lift bottom of the chair See the ski run analogy actually worked really well I used to do this all with systems of equations. We would call this i1 We would call this i2. We would write us. It was nice, but it was way more complicated First thing I try and find always if I can is the total current has this diagram told me the total current anywhere What's the total current? 4.5. So there's my reference point and it looks like it's flowing this way looks like it's flowing this way How many amps are in this particular junction? 3.5 Because I got one amp going down How many amps are in this particular junction this particular resistor right here? 3.5 How many amps are at the bottom right here? 3.5 How many amps are right here? One amp how many amps are right here? Back to 4.5 So as long as they give you a little bit of information You can hop scotch your way to filling out the rest The nicest to find you can see it falls apart as soon as you know total current It really falls apart and so I almost always bend my efforts to I'd like to find total current That's kerkov's law for current. It says that current n equals current out How do we decide how much current goes where? Well, the amount of flow along a particular path Depends upon the resistance How many amps is there in this particular circuit ran total? 6 If each resistor is identical The current will split exactly in half because you can think of it as identical ski hills. Hey, you guys go that way We'll go this way. We'll meet up at the bottom, but it's the same hill So how many amps are flowing through this resistor? 3 amps how many amps are flowing through this resistor? 3 amps If one path has more resistance What can we say about the splitting of current? So here's our diagram. We have a small resistance And a big resistance More skiers can fit through the small resistance hill because it's a wider hill That's going to be our analogy. There's not as much resistance We can get more skiers on it wider hill lower resistance will have a bigger current We would say this i1 is going to be bigger Than i2 Bigger resistor smaller current Smaller resistor bigger current which kind of makes sense smaller resistor. Yeah and pack more skiers through In fact, we can even do more than that dylan if the resistors are simple ratios of each other We can relate the currents via the same ratios For example, here it says that the second resistor is twice as big as this one Smaller resistor will have more current, but the ratios will be the same But opposite it would be four amps And two amps it'll be a two to one ratio, but the opposite ratios of the resistors What if it this said what if this had been three r? There would be a three to one ratio I have to do a bit of math to figure out what that would look like, but okay But two to one work nice In fact, we can do even more than that Kirchhoff's voltage lock Which the author abbreviates kvl It's basically a conservation of energy because we did say that voltage was energy per coulomb. It says this As charges flow around the circuit They experience voltage gains in the battery The chairlift lifts them higher remember we said voltage like your height And they lose voltage across the resistors they go downhill through the resistors For every path through the circuit the voltage gains equal the voltage losses the sum of all the voltage gains Equals the sum of all the voltage Losses This looks confusing, but when I bring in our ski hill analogy, you'll go. Oh, yeah, that just makes sense Here's what it says If the chairlift takes you to the top of the mountain And you've gained six volts you have to lose all six volts to get to the bottom of the mountain You can't somehow lose four volts and end up at the bottom of the mountain You couldn't be at the bottom of the mountain because volt is like your height You have to go through another two volt loss to get to the bottom of the mountain It's much easier to see in the circuit so Here's our chairlift. Here's our battery What voltage gain do the skiers have when they leave the chairlift? How many volts? 20 volts Before they hit this ski hill how high are they still? 20 volts But they lose eight volts going through this resistor So once they get to the bottom of this first ski hill, what would the voltage in this circuit be if we measured it right there? How high are they now? 12 Because they've lost eight volts going through the resistor. They've gone down an eight volt high ski hill So now they have 12 volts left to span What does this drop have to be? Well, if this is my last ski hill How high am I at the bottom of the chairlift always? Zero so how many volts must I have lost going through this resistor? Must have lost 12 volts going through the resistor and at the bottom of the resistor megan I'll be at zero volts now because I've gone through all the ski hills Start out 20 volts high lose eight lose 12 in fact, what we say is If you walk a ski run Which means you get back to where you started from the change in voltage is zero Start out with 20 Lose 12 lose eight gain 20 back here. You're back to where you started from. That's what kerkov's voltage law says It says on a mountain if you end up back to where you started from you have to be at the same height as you were five minutes Like where you started Evan how many volts is this battery giving us? 10 so what's the voltage right here? 10 we haven't lost anything yet Let's go down now. There's two possible ski hills. We can travel down the skiers have options So the first path we're going to take evan is this one. This is our first ski run of the day We're 10 volts high. How high are we still before we hit the hill? 10 volts high Now how much do I lose? Well, I notice evan that I can go down this one hill And end up at the bottom of the chairlift So how much must I lose going through this particular resistor? 10 volts. How many volts do I have right here? zero There is a second possible path brendan that I can take. I could have gone through this ski run here So when I get to the top of this ski run brendan, how many volts do I have? 10 Can I lose and end up back at the bottom of the chairlift going through this one hill here? Then I must lose all my voltage. How many volts do I lose? 10 and that gets me to zero In fact, both of these resistors would have a 10 voltage drop So Terminology We say these two resistors are in series We say these two resistors are in parallel. We'll be talking about that next class, but there's a good example So we have a question. I thought I heard something Okay Example five What's going here? 12 I lose eight volts So how higher we would get to the bottom of this particular ski hill this particular resistor How many volts do we have left to play with? four, so how am I at the top of this hill? four volts If I go down this ski run, does that get me to the bottom of the chairlift? Then I must lose Four volts going through that resistor. How high am I right here? How many volts do I have right here? four Dylan, can I lose all of my height and get back to the bottom of the chair lift going through this ski hill? Then I must lose four volts to get to zero volts Let's do a more complicated one with multiple resistors 60 volt battery big battery Megan when I leave the chair lift, what's my voltage right there? 60 Yeah, yeah, go ahead Megan I lose 15 volts through here and looks like every skier has to go through this ski hill However, this mountain is set up. Everyone goes down this hill So how many volts do I have right here? Okay, let's walk this ski run together first of all then we'll walk the outside ski run together So right here. I have 45 How high is this particular hill? It's 18. So what must I have left here? 37 27 sorry I didn't hear you 27 volts and as I keep going now I don't know what this voltage drop is but I do notice I ended up at the chair lift Which is at the zero at the bottom. So how many volts must this voltage drop be? It must be a 27 volt drop. I must have 27 coming in and lose my final height there Let's walk through the outside path now So we already filled in the 60. In fact, uh, what's my voltage right here? What am I going into this particular ski run with? 45 I lose 10 35 Gordon what how did you figure out the eight? It doesn't say oh I know I have to be 27 volts high when I get here still So I can only lose eight volts to get to 27 volts high because the skiers have to be able to join together on the same height This is where kerkov's voltage voltage law really shines note There are two useful conclusions to draw from kerkov's current law For any complete Loop around the circuit. Actually, this is not from kerkov's current law. This is from kerkov's voltage law For any complete loop around the circuit the voltage drops equal the voltage gains And no matter which way you go between two points the drop must be the same in other words Whether I go from here to here or from here to here if I'm starting here and ending here If I lose 18 going through here See the other way I could have done it gordon as I could have said I have to lose 18 going through here If that's 10 that better be eight so I can lose 18 going through here I could have looked at the end result or I could have looked at the corresponding ski hill Doesn't matter same answer no matter what? Very nice Believe it or not That's all we're going to be using for the next three or four lessons We're going to be doing more and more complicated circuits and more and more accurate circuits But we're going to be using kerkov's laws and ohm's law v equals i times r. Yes Uh, are we ever going to work with resistance and wires? No Sadly Uh, that's the fib almost no sorry The author says to see the voltage relationships It's sometimes helpful at first to redraw the circuit so that all the resistors are pointing downhill In other words, he might take this and make it look more like a ski hill Everyone goes down this hill and then we split up with our friends and we go down here I'm going to choose not to do that I want you to get used to the regular schematic diagrams And also because I really suck at drawing these sorry so It says five b can be redrawn as follows I guess Example six says write equations We're going to jump to actually solving some of these Suppose we have a 30 volt battery and we have two equal resistors along a path If the resistors are the same What do you think would make sense about the voltage drops? Or me Prove it Here's how we're going to prove it Now we're going to start to combine everything I know that voltage equals i times r remember that one ohm's law This is the total current leaving right here. I'll just label it total current What can you tell me about the current here and the current here? Are they the same or are they different the current has to be the same because kerkov's current law says that Current going in has to equal current going out. There's no other junctions So what I would say is for each of these They both have the same current as well Do you see how we're going to do our proof dylan if they have the same resistor? Which the question told us And they have the same current which I know from kerkov's law and the v equals i times r Then both of these have the same i times r therefore v equals 15 In each Now, uh, I agree with you dylan if they're the same I would have just said it's half and half 15 and 15 But if it's more complicated, I can go with this and actually Calculate it. This would be v equals i times r. This would be v equals i times r That's going to give you a hint for this next one If the resistances are not the same, what can we say about the division of voltage? So if you have a big resistance and a small resistance now, they'd still have the same current because they're still part of the same junction So you would have this v1 equals i big r v2 equals i little r Which one's going to have a bigger voltage v1 is going to be bigger Than v2. So bigger resistance means a bigger voltage in that resistor A larger voltage drop And if the resistors are simple ratios of each other We can relate the voltage drops via the same ratios. For instance, find the unknown voltage drops below if Excuse me If this one is twice as big as this one This voltage will be twice as big as this voltage 20 and 10 assuming my voice holds up um At first although I labeled the voltages all over the place Your diagram gets cluttered. So from now on connor i'm going to be labeling only my batteries and my resistances I'm going to label voltage gains and voltage drops Otherwise the diagram gets really really cluttered So example 8 says find the unknown voltage drops currents and resistances remembering that v equals i times r Okay Let's see The first thing I would do is I would glance at my diagram and I would say Do I know the total current anywhere? Have they told me the total current anywhere? And I think In this diagram, I think they have Current current current current total current four The reason is all the sneakers have to go through here So I'm going to try and see if I can label some currents along the way. What can I label here? Well, if that's three amps How many amps must this be? One amp Oh, and how many amps must this be? Sally I thought you said no four. Yeah, so I didn't hear you Because it's total current back again. Okay, um, let's see what we can do with voltages. How many volts do we lose here? Starting with 18 we lose six. How many are left? So if I walk through this ski hill, can I go down this ski hill and get to the bottom? How many volts must I lose here? Sally 12 Do I know the current here? Yeah Do I know the voltage here? Yeah, good What's the resistance? Let's see r equals V over i from i vehicles i times r. What's the resistor? four ohms Right The rule is as soon as you know two things you automatically know the third one because of ohms laws So if you know two quantities inside a resistor, you know the third one always Oh, how many volts must I lose here? 12 Oh, and by the way, what's the resistance in this particular resistor? 12 ohms Oh, what's the resistance in this particular resistor? V divided by i six divided by four This has a resistance of 1.5 homes Any resistor where I know two I know three b I said again, I always try and find total current first have they told me the total current in circuit b Not blatantly it's not labeled however I think I can make an educated guess because I can figure out what the current is right there when everyone joins together What's the current right here when everyone joins together? You see it? What? 2.5 that's my total current here then 2.5. Oh, by the way What's the resistance there? It's gonna be a decimal 8.4 even Um, if I walk through this particular ski run to get to the bottom of the chairlift How many volts had I better lose here? Well, I'm starting with 35 I lose 21 what's left uh 14. You know what this has got to be 14 volts Oh, and uh for what it's worth What's the resistance of that particular resistor? 14 ohms How many volts do I have to lose going through this ski hill? Also 14 Oh, and how big is that resistor? 9.33 So you said I can't give you a standard approach to solving all of these all I can say Jordan is try and find total current first And once you have that it does usually fall apart But as they get more and more complicated we're gonna have to kind of get a few other approaches as well Let's see here Did they tell me the total current anywhere in this question? Hmm Not blatantly So now I start to fill in what I can but I'm always keeping in mind as soon as I know two things How many do I really know? Three and in particular I'm gonna be saying hey It'd be nice if I can find a current somewhere along the way because the more currents I can find the more likely it is I can get the total current so um Well starting here. How high are we? 40 volts I don't know what that is, but I lose 35 and I can get to ground level. Oh, I do know what this is How many volts must this be as a voltage drop? Gotta be five volts Yay Oh, how many volts must this one be as the voltage drop? 35 And now I smile because do I know two? I know three V equals i times r i equals v over r. Yes, if I get the i by itself What's the current here? Seven amps. Why does that help me? Well, I got one amp here I got seven amps here What's my total current when they join together? So what's my current up here? Because total current's going through it If I know two I know three Uh resistance is what did I say voltage divided by current so five divided by eight point, sorry point six two five Ohms and this one I could have got actually right away Voltage divided by current this has a resistor of 35 ohms Turcos loss very handy This is so much fun. Let's do a few more Okay hmm Oh I know total current That probably is going to help this question fall apart somewhat I know two You know what I really know three What's the current in this particular resistor? Current is v over r three amps And this is why I said if they give you total current the question really falls apart I know my total current is five if that's three. What's the current over here? Two oh, oh, oh and one more thing Look up for a second folks So here's our skiers right here They split up some go down here some go down here. Do they meet up again down here? Then they must have gone through the same height How high is this resistor have to be Sorry, yeah, how many volts is this resistor have to out? It's got to be 15 volt drop Right, otherwise the skiers couldn't shake hands leave and shake hands meet up Do I know two? I know three. What's the resistor here? 7.5 Ohms Oh, I know the current down here. What's the current down here? five amps How can I figure out the voltage? Oh V equals i times r What's the voltage drop here? Not 40. I don't think V equals i times r. It's got to be 20 Right, I know I know two. I know three Ah, but gourd if I start out with 70 And I lose 15 and I lose 20. What must I lose here if I'm able to get back to the ground Justin 35 Justin, do I know two? Then I know three. What's the resistance up here? seven So you hopscotch your way around Filling in what you can along the way Your main goal though your rule of thumb is try and find the total current first because if you find that It really does fall apart Were there other orders that we probably could have done this in probably but we got same answer No matter what I just try and go kind of systematically And generally whenever I know two I write the third one down just because It's easy enough to quickly do on my calculator e um In my diagram this line got moved a bit. This line should really be Right there for the battery, but somehow it got moved partway into the resistor. Sorry the diagrams are getting old But use your imagination So this time the current is running this way You know what I'll just do the arrows like that just to make sure because we've been going in the Opposite direction up until now. I don't want to make a sloppy mistake. It's going from positive To negative. Okay. Did they tell me the total current anywhere? Yes No, they didn't yes, they did Do you see it connor if I know two I know three What's the current in this particular resistor? Four amps and conveniently that happens to be the total current right Okay um well How high is the chairlift? 32 How much do I lose going down this first ski run? Eight, so how high am I now? 24 Can I get to the ground going through this ski run right here? How many volts must I lose going through here? 24 Do I know two I know three What's the current here 2.4 amps What was the total current? four How much went here 2.4. What's the current in both of these resistors? 1.6 1.6, and I know it's the same for both because there's no junctions for the skiers to leave kerkoff's law Oh, and they told me this one was 10 volts. By the way, if this one is 10 volts, how many volts must this be? Got to be 14 because this hill is 24 high. These two hills combined better be 24 high. So 14 volts Oh, do I know two? I know three. Do I know two? I know three. What's the top resistance? 6.25 What's the bottom resistance? 8.75 Is he right? I should ask. Yes Okay One of the ways they love to test your understanding is they love to give you light bulb questions Now light bulb questions involve brightness And the brightness of a light bulb is related to its power use Which depends on power equals v times i If these were all light bulbs Can you go v times i on that one for me, please? How many watts is that bulb? 100 How many watts is this bulb? How many watts is this bulb? 32 Right V times i how many watts is this bulb v times i 7.6. How many watts is this bulb? 16 How many watts is this bulb? So here would be a nice question. Which is the brightest bulb? That one which is the weakest bulb the dimmest bulb Uh this one I think yeah No Uh this one Brightest one is I can't hear you Brightest one's not on your diagram Oh, that's not in no wonder. I'm confusing you guys. That's not a bulb there. So which is the brightest bulb I think this one then yeah, who's the brightest bulb in the drawer? Apparently not mr. Do it shut up. Okay Okay So when they're asking you which bulb is brighter What they're saying is which one has a bigger vi So it says this the two bulbs below are identical. They have the same resistance. So I'm gonna say r R By the way, how many volts must this bulb be taking? What's the voltage drop? 10 volts. What's the voltage drop here? Also 10 volts if the resistances are identical and the voltages are identical. What can you tell me about the currents? So what can you tell me about their brightness if they have the same voltage and the same current same since both have Same vi same power two bulbs wired in parallel Will have identical brightnesses if they're identical bulbs What about these two? Which are wired in series So the two bulbs are identical Same are same are What can you tell me about their currents? Oh Identical for both because they're both part of the same junction If the i and the r are the same, what can you tell me about their voltages? So what can you tell me about their brightness? By the way, what is the voltage if they're the same in each of these bulbs? So they would have the same brightness Since they have the same vi If all four of these bulbs in these two examples were identical Which bulbs will be brighter the bulbs in the first circuit or the bulbs in the second circuit? First will be brighter convince me kerkov's laws What's your homework? I'm going to give you a bunch of these you get good They go fast, but this is the fundamental stuff of this unit. So number one number two number three Number four number five one two three four five Six is good seven is good Eight is good nine is good Yep 10 Oh, yeah 12 falls apart really easy these go pretty fast. So so far everything Uh, am I gonna assign Yeah, 13 is a nice one to think about they gave you a hint Holy smokes am I gonna assign every question? Let's find out What can be said about Yeah, 14 is good. I'll pause there. I won't worry about 15 or 16 They go pretty quick Mr. Duck How do we show work on these and the answer is You sort of don't the way you show work the way I mark these is I look for stuff to be labeled So if you do do a v equals i times r on a test to find something Or an i equals v over r or an r equals v over i show write that somewhere so that I know you did that step But otherwise I look to see your circuits are labeled