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4_ A bank of resistors are placed in a simple circuit shown below. The total Power expended in the circuit is 250W. Given the information below; a) Determine the cu...

Question

4_ A bank of resistors are placed in a simple circuit shown below. The total Power expended in the circuit is 250W. Given the information below; a) Determine the current leaving the battery b) Determine the equivalent resistance of the circuit2 J5 R 3- N-_AnIJ M10 n4M 6_RAv

4_ A bank of resistors are placed in a simple circuit shown below. The total Power expended in the circuit is 250W. Given the information below; a) Determine the current leaving the battery b) Determine the equivalent resistance of the circuit 2 J 5 R 3- N-_An IJ M 10 n 4 M 6_R Av



Answers

Four resistors are connected to a battery with a terminal voltage of $12.0 \mathrm{V},$ as shown below. Determine the following: a. the equivalent resistance for the circuit. b. the current in the battery. c. the current in the $30.0 \Omega$ resistor. d. the power dissipated by the $50.0 \Omega$ resistor. e. the power dissipated by the $20.0 \Omega$ resistor (Hint: Remember that $P=\frac{(\Delta V)^{2}}{R}=I \Delta V$.)

I mean, especially interested in this particles circuit. And you quite a few things to find about this circuit. You're the 1st 1 would be the equivalence resistance off the entire circuit. To do that, we had to simplify this parallel circuits over here. First, my taking one over r two plus one of the artery University. So that's what you voted by nine. I lost one of over 18. Get six holes. They know the artists. Ah, or in Siris with each other so we can just add up the resistance. So the effective resistance just be six plus 14 us for homes to keep us turn it for office. So they see effective insistence now to find a current you gotta use I goes to V over R where? VC tota voltage across the entire circuit. So we know that Steve Batteries, You wanna be to actually connect it in the same direction so we can assume them to be a single large battery. We've toto voltage off 24 right? Yet I'm not together because science series each other, so it should be 24 votes defended by doing forms to give us what name? This our current is flowing out off the batteries not to find currently Sri sister really have that. The current flowing on the batteries One emp. So this is one and so I want flowing through our one must be one end and I for flowing through our for miles. Also be one m right. Since this is the current off the batteries No. What about occurrence for our our to and treat well, one of the waste they were going to do? Yes, we can find what is the potential difference across this are to an artery First, by using the ah resistance just because 26 homes, you could learn resistance off six arms. So the potential difference, of course, are twin artery just going feed prime. Because to be close to IR, we take the total current breezes. One end. I want to play by six. Here he gets six ports. Next from here, we can find individual current, so I to aspx equals 26 votes developed by nine. Should be joe 0.67 EMS. And from here, we can in four debts. Oh, I tree would be just one minus. This, uh, this value All right, So now we have a current off. Each sister can find a potential drop across each resistor. But we already found that just six votes for artery and are too we're gonna find now is the potential drop for ah one and also for right for R one and r four. You can do that by using Feagles toe ir. The overall current is one m so V one must be close to one M month pipe by de resistance, which is 14 to give us 14 votes. Same with our for on m my public for post four votes. Now to find a participated by each of this resistance, we can either use p equals two pi square are or V squared over r right up to you. So I'm gonna use the easier one, which is just meeskhobar. Teacher, you just use the phone. So p one course toe for you on square for one keeps us 14. What p two. We know the potential difference across this is 24 minus 18 which is six six votes across our to an artery. So they both have the same potential difference. Reaches six through justic, six square foot by nine. Good for what's for Peter? Six square. You gotta by 18 to get towards for Petri. Lastly, yeah, are for a potential difference off four votes or four square. But by four, we get forwards with these already different powers dissipated. Finally, we can find the total power that's being supplied by the Petrie's really known the overall current. So what we can do if you speak was toe I fi your current. This one m the potential difference across you should be batteries is chill faults. So this gives us shelf. What's so they see post black by each off, Demetri.

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

So here we have the circuit and we need to figure out the current end this four ohm resistance. So first we will see the set of equations which will help us to determine the current through this forum resistance. So we have the two batteries here as indicated one, this 12 world battery and the another six world battery. So let us take the current. Let's see here, I want guarantees flowing and this island current I two current is flowing through this two and then I frequent is flowing through this three oh and now across this forum, the current that will be flowing is I won minus I took minus I. So we have applied cultures passed law to get the current through this for all because total current entering the junction, which is Ivan should be equal to total current. Leaving the junction that is I two plus I three plus X. And here we found X coming out to be Ivan minus two minus three. So in order to figure out the value of X because this is the current. Through this forum we will use kale chips voltage law. So we will see and get three different equations because we have three different variables to be solved. I one, I two and I three. So let us consider first this loop. So we are considering the loop B. See D. A. So if you consider the loop A B C D E A. Then here you think ketchups voltage law 12 minus I won minus three. I three will be zero. So this is first equation. Similarly, we use any loop we can take. So here I am taking this loop B C. D be So we start at any point and consider the potential to be zero. So let's say I start at this point. So we are moving now in this manner. So considering the potential at this point be at zero potential act, she will be minus three I three because we are going in the direction of current and potential will decrease and we need to also get the current flowing through this 50 So observing here the junction here I two is flowing and they will combine So through here I two plus this current that will be I want minus I treat. So we will get the equation minus right I one minus I three. So here I'll do plus because we are moving oppose it to the direction of current and potential is likely to increase here. Also we are moving now oppose it to the direction of current so it will be minus six because from positive to the negative terminal we are going so minus six and then again we are moving oppose it to the direction of current, so minus four. Into the current flowing through the forum. That is I want minus I do minus and then it will be zero. So simplifying this equation to get minus three I three plus five I one minus 53 minus 10 minus because the score was multiplied with this. Okay I one minus two minus three. So we get minus six minus four. Ivan minus four to minus four I 30 So we simplified even more. Why I one minus four Ivan that will be Ivan minus three I three minus four I three. That will be minus seven I three and we will combine this so it will be minus 23 minus four. I two minus six is equal to zero. So this is equation do that. We have got let us keep track of all the equations. So we even need equation three because we had three variables. So for that we'll have to consider another group. So let's say now we consider this law. So again we started point B. So at point B zero world and then we are moving in the direction of current. Now the potential at this point will be minus four times I want minus I too minus I treat. And then the potential at this point will be plus six and we are moving oppose it to the direction of current so we will add to I two and this will be zero. So we simplify it even more. Wicked four I two plus two I two, that is six. I do minus for Ivan minus four I three plus six equals to zero. So dividing throughout by two wickets three I two minus to Ivan minus two. I tripped plus three equals to zero. So this is the third equation we have got and here we will have a tree check on this equation to so in the loop of B C D. B potential was zero here the potential was decreased by three I three. So we included that here and then we're moving oppose it to the direction of current so plus five and then minus six. And then here we have to add because here again we are moving oppose it to the direction of current. So I changed the sign here so it will be plus minus and this will be minus only. So four I one minus four. I took minus four I three. So we will change this equation two. So here we get let us combine Ivan's first so 57 plus four Ivan that is nine Ivan. And then I use so minus four I two and then I trees minus three. I three minus five I three, that is minus eight I three minus 12 3 and then minus six equals to zero. So now this is the correct equation. So these three questions we need to solve. So let us collect these three questions here and then we will solve them. So first equation 12 minus I want minus three I three equals two zero. Second equation nine I one minus four, I two minus 12. I three minus six equals to zero. And then third equation three, I two minus two, I won minus two, I three plus three equals to zero. So we need to solve these equations. So in order to solve we will first simplify so the first equation we will figure out Ivan. So this comes out to be 12 minus three I three. Second equation we will find out I took So second question will make it in terms of I 23 so we'll get nine instead of Ivan will put 12 minus three. I three minus four. I too minus 12. I three minus six equals to zero. So the second equation becomes 108 minus 27. I three minus four. I took minus 12. I three minus six equals two zero. And here we simplify and get the value in terms of I do. So here I too will be equal to restaurant will go to the wife or let's take minus four I two to the right so we'll get four right to us. 108 minus 27. I three minus 12. I three minus six. So we get for I two s 10 two minus 39 I three. So we divide throughout by four ticket I twist. Let's keep it was 10 to minus 39 I. Three 54 So we'll take this value of I. One and I two in terms of I. Three and put it in this third equation. So putting it here pick it three I two. That means tree in two 100 to minus 39 I three by four minus two. Ivan Ivan. We will put it as 12 minus three. I three minus two. I three plus three equals to zero. So we hear we solve it we get 06 minus 117 Hi three divided by four minus 24 plus six. I three minus two I three plus three equals to zero. So we solve it further wicket 306 minus 117 I three by four minus minus 24 3 because minus 21 less four I three equals to zero. So we solve it wicked 306 minus 117 I three minus 84 plus 16 I three is equal to zero. So from here we find that 117 I three minus 16 I three is equal to 306 minus 84 So we simplify this and get 117 minus 16 is 101 I three equals two 306 minus 84 That is triple two. So this gives us I three as yeah 2.198 So I'll take it as two point two amperes. So we have got I three and once we have got I three will take this value and put it in this equation. So we saw this we get I two s 102 So we'll keep track of I treat that is 2.2. We have taken so 10 to minus 39 times 2.2 and we divided by four so we get 4.5 amperes. Similarly we'll take this I three as 2.2 amps and we'll put here so we'll get 12 minus three times 2.2. That is 5.4 amperes. So we have got now I want that's right. Here we have got I've won I do and I three so I when we got it us 5.4 amperes I three, we got it us 2.2 m peers and here I 23 is 2.2 amperes and I three is 2.2 and I two as 4.5 amperes. So we required the current through this forum, so current through this forum, what it is, it is Ivan minus I tu minus I three. So if I subtract I two and I three from Ivan, we will get the current coming out to be 5.4 minus 4.5 minus 2.2. That is minus 0.85 amperes. The negative sign indicates that the current will be flowing in the opposite direction, what we have taken. So current will be flowing across this forum in this direction, and that current will be 0.85 NPR's 0.85 amperes. Okay.

So what we want to registrants is So basically, Uh, there is a battery like this one. Okay. And one registrants is over here. Wanted to know what happened And one which took over here. This is a hard one. This is the heart. And this is a hard three. This is battery. And the potential difference of the battery is given the difficult to 14 or 15 gold and R1 equals to what, 10, 15, 20. So this is 10, this is 15, this is 20 only activity. Okay, So first of all we have to do and the equal tradition says then the currents of the register and the total total currently just get. So basically we can clearly see that very simple question. What we can do over here is that since the same current passes through them because they are in the streets are equivalent even do nothing. But just that some of the iron plus R plus R three, that one still plus 15 plus 20. That means the 35 39 45 on in the next part. What we need to do is the current we need to find the current restoration. So we already know that the current through its rays changes will be saying because they are in the street. So I will be nothing but Mm 2015.45. So that will be won by three that once a 0.33 NPR. And it seems we already know that the current through the target will be current through a heated exchange. So current through the entire circuit. That will be also said that the 0.33 NPR. Okay. Thank you for watching. Yeah.


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