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(b) Find the current running through the battery: (5 points)(c) What is the power dissipated by the battery? (5 points)(d) Calculate the current running through the...

Question

(b) Find the current running through the battery: (5 points)(c) What is the power dissipated by the battery? (5 points)(d) Calculate the current running through the 4-Ohm resistor. (10 points)

(b) Find the current running through the battery: (5 points) (c) What is the power dissipated by the battery? (5 points) (d) Calculate the current running through the 4-Ohm resistor. (10 points)



Answers

Consider the circuit shown below. The terminal voltages of the batteries are shown. (a) Find the equivalent resistance of the circuit and the current out of the battery. (b) Find the current through each resistor. (c) Find the potential drop across each resistor. (d) Find the power dissipated by each resistor. (e) Find the total power supplied by the batteries.

No discussion of the seas security. We are different. The first putt we want to find a cougar and resistance or the entire circuit so are equivalent. Since they're always Siri's to each other, we just at all the resistance up. Just what, plus our two plus our tree should get nine homes next to finding current. True, each resistor. Since they are in series again, the current is shared so they have the same current from the total equivalent resistance. So I goes to if you, uh, rotations to total wattage divided by t total resistance, give us to MPs Next the potential drop across issue, sister. Not every Northey individual current. My dish. The chef current can't find the individual potential trump by taking the shed current multiplied by D individual resistance. So fy one just two points You him I want to play by for since his dead ISTEA resistance gets eight votes be to it's just two times one to be towards And victory is the same as we want since they have the same resistance. So this it puts finally the power supply by the battery is close to the you know that power is goes toe ivy. Sincerely, nobody told her current and we know the Toto potential drop across the all off the resistance. All right, so we can finally see politics Bater by the resistor Each off the resisted by taking the current pipe idea potential job. So v one So p one do you power drop across resistance one stick. All right, so it's just not MPs this fault, So this will be 16. What's P two devoted across that is two votes, two votes so two votes times two MPs Guess for what funny Petri is to see map p one The same vote a straw. So they're 16. What's finally P Total power, disputed by a battery or actually supplied by the battery, will be just some off all the powers disputed by the resistance so that 16 plus 16 plus four, two days, 36 what's

For this question about the question you want to find the unknown currents. The first that I can do is to look at loops that you've office small number off unknowns as possible. It's one of loops is over here. So in this looked as the only unknown there'll be involved. It's I fall. Okay, writing Now the jobs look rule. You start off with the battery moving from minus two. Positive. So we get that V two. So this is fight falls. Then we bypass are four in the same direction s to current, so we some tree away Deportation drop. So this tool times I fall every create this 20 so you can find I fought to be quite five MPs. All right. Next unit for other equations. To find the father unknowns, I went to high five. So, Defense Secretary, I'm gonna use T Junction Junction rules made ready. Incoming current must be close to the outgoing current. So, for your first junction, all the rights we have eye for the incoming current and your going will be I five and I treat for a second junction. I tree and I one incoming and I two is the only elk away current. The 30 question We're gonna use the different look, Rose. So if we can do you can look at is over here and for this loop, we start off with the best for you again. And so we are moving from positive to negative. So we got a minus away, V two. So that's minus five. Debbie. Bypass artery. Same direction. Nasty current. So minus Sometimes I tree very bypass are one in the opposite direction. So we plus quit is 20 The last equation Internet Yes, over here. This particular group the start off Tibet tree from minus to plus. So we at the fee one this shelf by plus ah, one witness full time. So for my one Demi bypass, I to which is also subject because it's in the same direction is the current maybe three times side too. Question zero now Too soft for this ik regent's from equation too. We're going to from equation to find ways I won, I want Yes, he goes to my two minus all right tree. We substitute that into both equation tree and four so in equation tree off the substituting in you get minus five minus to a tree, us four times off to my nose, for I treat close to zero. Simplifying debts gets minus five minus six tree plus for two because it was substituting debt into equation for my substituting the equation for I one into equation for get shelf minus for two plus for a tree. My next shii to west with zero get shelf plus four tree minus seven I to close to zero. We have two equations and toe unknowns. It's like yourself. So after substituting, uh, we adjusting the equation I left. We get our i to in terms off a tree and the from the equation on the right. All right. We can substitute the I two into question over here, so we get chop. Thus for a tree minus seven, four times six. Tree bus five, close toe zero. So this is the video expression full I tree and then we bring all the constants to the right hand side. So that's trough doing it. I tree to be close to 0.5 MPs From here, we can find any other values quite easy. I to using the above expression we can't two MPs. Then we can start you to into the equation for I one right over here, which is a goes to I to my nose. I tree should be a 1.5. Finally, we can't get five from the first equation. Jessica's toe I four minus. All right, treat. So this by fine minus my fire, which is two MPs s well, no to find a Pulis applied by the different what age is. We just have to multiply the current 50 voltage. So the current passing Trudy respective for teach We use that current to get power and poets goes to feed times I So the public or city Rotich one get few one times I to write nasty current housing. Truitt. So it'll be journey for what's for P two. The power for the second footage that is V two, which is five votes went Bye bye. I five i five is skipper nous to MPs so this will be 10 watts to find the power dissipated by the resistance. We already have t various currents. So we just have to use the current I square. Uh, my current square time. See resistance to get it power. So power for our first. The sister. Uh, one. We take high one square times the resistance off one first night. What's let me do the same thing for the other resistance, right? So I'm gonna do them directly for you. For our tree. The carbon this point finds a boy five square, perhaps two homes. What fight? What's for the current ISS? I for just 2.5 resistances too. You should get show my fight. What's

In this question of this um Get arrangement for three resistance. There are two parts in this question. You want to find a total power dissipated and the potential drop across each. Okay so in part a find out total power dissipated. Yeah. First is to find a total resistance. So I'm is one two. Okay so we can see that are two and archery are parallel. He then So R. two tree the tool one of our two plus one of our archery and receive boko. And yes. So you'll be getting a there you see almost And then R. one and R. 2 3 in series. And so the equivalent resistance is uh 192 us that you see. Mhm. 288. Okay so the power dissipated is calculated using we square over our are equivalent then numbers. The answer is 51. Okay so this is the answer for part A. Okay next in party. Um So we want to determine the potential drop across the resistor his office so you can find a total current investigates. Okay, so this is equal to V over our total are equivalent. So 100 indeed divided by 288. And this is 0.417 mps. So to be one is equal to I. R. One And this is 0.417 times one night two. Here you get he wants and that have you to and delta bigotry are the same because they are proud of. So it's equal to -501 180 when it's 80. It is. Yeah. So these are the answers. Mm And that's all for this question.

For this question. Uh, question 69 Be one of first. Fine. What if the, uh overall, it could learn resistance, not the sucky, And from there, find the current from the battery. Now, to do that, we will need to simplify the resistors in parallel. I would have to do is to add them up together. So for the R one and R two mine, too. Uh, portion. We can simplify them by adding them up together in reciprocal. So one overnight plus 1/18 in first to find effective resistance across. Ah, this but girl, part of the circuit. We get six homes, we do the same for the artery are for portion. So this 1/10 plus one of the 10 yet firearms, after which we can find all the equivalent resistance by summing them together since they are all now in series. So plus our five. So we get six homes plus firearms, plus it forms from the r five plus one old from the internal resistance off the battery. So six plus five less. It's one. We get 20 homes. This is the equivalent resistance off the entire circuit. From there we can find out what the current by taking I was to feel the Are the HST um f off the battery that he votes divided by the total resistance of the circuit which is to any homes gets 1.5 MPs Right now, The next time you want to do is to find the potential drop across each resistor. And to do that, you will need to No, what is t uh in fact, he across all off this resistance. We can use fee because to ir to find a potential drop for the parallel circuits, we can use the effective resistance to find what is potential drop because they both share the same ah potential drop since they're connected in parallel. So let's start off it. Easiest one riches the potential drop across Ah five, 35 We used the overall resistance which is 1.5 times overall current Sorry, 1.5 MPs, much right by the resistance off our five inches eat and we get shelf faults for our tree, our tree, and are for we used the effective resistance off five homes. Multiply that by 50 current, which is 1.5. We get some quite five votes. Six for our in our to the effective resistance is six or so. We take six times 1.5 you get my vote's right. So this is the potential drops across each of the resistance? Not if I knew devoted drop, of course, is sure to your sister. It's actually easier now to find your current. So we're gonna go back to the part B. The current true is ITRI sister eyes because to V over R. Now we have really found that Ah v right for the first current for the first resistor, the vote eight across is nigh votes. So we take nine photo by nine My home gets one and pierce for our to devote stations the same night votes but the resistance is 18 So we get your 0.5 pierce for tree devoted across is 7.5 and the resistance is 10 So this working fast 7.5 appears sorry 0.75 MPs you see same s I for since they have the same of all teachers as well as se resistance and last but not these For the fifth resistor, it is in the main circuit so it takes the entire current off 1.5 MPs Knicks. We can find a politics abated by each sister using the potential drop right Usti formula. Yes, equals to be square over our all right. So start off with first we sister p one. The rotation crosses nice or nice square and the resistance off our oneness. Nine. So just give us nine watts. We do the same for our to, so it's also nine votes, but you gotta buy 18. So nice squared about. By 18 we get 4.5. What's for our tree? The rotation cost is 7.5, so we get 7.5 square. Divided by is Resistance Richards. 10. Get 5.6 five. What's 5.6 tree. But my 60 what's and this is actually equivalent toe the power disputed by awful right, Since they have the same resistance as well as the same potential drop Knicks we wanted flying for last resistor, which is our five p five. We take again fi square. Ah, you get shelf square, but by eat and just give us 18. What's finally the total power being supplied by the Petrie? They were include the power being dissipated by our internal resistance off the battery. So to ignore that we can simply look at the total voltage off our battery multiplied by the total current off the circuit with just 1.5. So it powers a plate close to 30 with photo boy 1.5 Tookie Fuss, 45 watts.


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