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H Gaintheeinere the cunent and potential difterence 9.00 v ` dclivered to 3.00 Q 5 each U00 9 resistor Wv in the...

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H Gaintheeinere the cunent and potential difterence 9.00 v ` dclivered to 3.00 Q 5 each U00 9 resistor Wv in the

H Gaintheeinere the cunent and potential difterence 9.00 v ` dclivered to 3.00 Q 5 each U00 9 resistor Wv in the



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II Find the current through and the potential difference across each resistor in Figure $\mathrm{P} 23.27$.

In this question, we have, ah, this circuit that all the components are connected in Siris and we want to find the potential difference between points A and B. So the voltage that we are looking for is V. Abyan issues the value we want to calculate. And, uh, the value full for each of these registers are is also given to be 75 all, and the batteries are 1.5 rolled, and we have ignored the Internet resistance of the battery. So to do this, we assume a current for the secret in this direction, and we name it I so we can re draw I all around the circuit in the same direction so that we can remember the direction of I. So I is ah, running to the secret encounter clockwise direction and for solving this ah question. We have to use loop rule. So the cruel and, uh or using really prove we have to define a loop, and it's easier to define it in the same direction as the current slowing. So we considered this direction for the loop that we're going to go around and you're starting from point A. So starting from point A The first potential differences caused by this resistor r and it's negative because we are moving in the direction of the current and we're going to this register, are so minus r. I is our first, the potential difference. And then we get to this bad three b go from the negative to the positive terminal, the batches. So we have to add doubles which one point five vote. Then we get to this. Ah, next resistor and we are moving in the direction of Corrine. So again, minus are I will be the potential difference. Then we get to point B and then we go to the next register So another r I and then we go into the second battery from the negative to the positive terminal. So again we have to add 1.5 gold and then before getting to point a b past true, another resistor in the direction of core and so another minus r I is the voltage difference caused by that rather store. So we get back to point A in the loop is complete. So this some should be equal to zero. Okay, Now we try toe simply by a little bit. So we have to constant 1.5 votes. They add up to be troubled and we have 123 and four are eyes and negative Stole, minus, or are I? And there should be equal to zero. Okay. And ah, from here we can ah have this relation for our I. So we take trouble to the other side of the equation so is equal to trebled and as a result, I, the current of the secret, is equal to three bold over four r and R is the value of the already stores in the circuit. So you can simply plank in our from that is given in the question. So three vote, divided by four multiplied by 75 and foremost blind by 70 five is the three hundreds so troubled, divided by 300 0 will be 0.0 one emp or 10 million up. So this is the current of the secret. Now we want Teoh. What we wanted to calculate is the a d. So the voltage difference between point A and B and we want to start from A to calculate this voltage. So first we start from point being going this way. So this is how the direction that we go toe cabinet Ah, the a p. So first we go to the first racist or so the voltage maybe minus r I. Then we go to the bantry. So plus one point I vote, Then you go to the next ah rez a store Some minus are I will be the potential difference and then we get to point A So this would be this term would be the voltage difference between point A and B so you can simply clark in our eye. So 1.5 world minus two are I so to multiplying by 75 0 multiplied by you know 0.1 AM and as a result, the A B would be equal to zero. This is the answer of the question. So you see that there is no both the difference between point a a and B and if you see that between these can divide the secret growing blind between points A and B, and you see that we have the symmetry executed on either side of this line. So that's the reason for the A B being zero

Hi. In the given problem, there is a circuit diagram having a battery off 10 volt connected with resistance 5.0 home which are further connected with three identical resistors in parallel combination like this, all these three identical resistors are having value off 5.0 home. No. First of all, we will find the equivalent resistance off the circuit. Then we will find the net current passing through the circuit and this current after that will be divided into three equal parts. I dash each true these three identical resistors. So we have to find the current passing through each resistor and potential drop taking place across each resistor. So, first of all, if you find the parallel combination, the net resistance of parallel combination R p is given by the rule are divided by n if n identical resistors are joined in parallel, each having a value of our the net Resistance in parallel is given by this expression. So here this rt will be given by five by three home. Now This parallel combination is in Siris with five home so net equivalent resistance off. This combination will be given by five plus five by three means this is 20 by three. Oh, so we can find the value off this current I using arms law. This is given by Absalon by our equivalent. So this is then by 20 by three, um Pier, which comes out Toby 30 by 20. Or finally we can say this is 1.5 am Pierre. So this is the current passing through this five home resistance. Hence we can find the potential drop taking place across this five own resistance. So potential drop across 510 Home sister using homes law visible toe I into our. So this is 1.5 into five and it comes out Toby seven 0.5 world. So these are the two answers for the first resistance. This is 1.5 MPR current passing through these resistance and 7.5 world. The potential drop taking place across this first resistor. No, out off this end world, what as 7.5 world are dropping across this first one tense the potential drop taking place across parallel combination off three resistors is total applied 10 world minus that dropping a roast five world which waas 7.5 fold So this is 2.5 world dropping across five home waas 7.5 world. So this is 2.5 world. So it will be same across each resistors, three resistors. You have been parallel. Yes, potential drop remains same in parallel. So potential drop across each one in parallel is equal to 2.5 volts and the current, which was 1.5 MPs will be divided in two, three equal parts across each resistor. And that is I buy three means 1.5 divided by three. So it comes out to be 0.5 m Pierre. So these are the answers for the given problem.

Okay. So since we need to know the current through East Resister in this figure, we can see that Ah, each resistance has value off three point two five kilograms and the voltage of the barriers to airports. Now, to get the current, we first need to find the total current that's passing through the circuit. Because if we look at this resistance that this is in serious connection with this guy, so that means And since this is directly connected to the battery, that means the whole current is passing through our sick. So that means we need to know the full current and to do so, we can actually simplified the circuit. And as you can see, I've simplified the circuit till this and and, ah, let me explain what I did here. So, first of all, as you can see between A and B ah are one and arteries in serious connections. So I replaced our wanna now to buy our one two and then ah, the rest of the circuit is the same. But then, between point A and B are one to an artery, are in peril connection. So I replaced them with this and are one, two, three. So this is the circuit news target. And then, as we can see that between point A and C are one two, three and our four is in serious connection So we replaced these two guys by this equivalents are good. Witches are one, two, three, four and then we have battle connection of are one, two, three, four with our fight and really place that by are one, two, three, four, five and then this resistor is in serious connection with our six or replace them by, aren't you? Now we can actually find out all the values for these resistors, so let's get on to it. So first we need to find our one two. So that's going to be are one to which is equal to our one, does arto. And since they're all, they all have the same resistance. So that's going to be our plus our, which is two times are then for our one, two, three. This is going to be since it's a parable connection between our one two and our tree, it's going to be this. And then we'LL have one over r one too, plus one over our three reciprocal. And if we plug in the expression for those, we get to over three r, say that should try doing it. Where? Yourself So that you get some practice. Uh, okay, moving on. So now we have a serious connection. So beans are one two, three four is going to be two three. Four is going to be are one, two, three plus our four on DH, which is nothing but five over three are. Then we have a panel connections. So are one, two, three, four five. That's gonna be one over R one, two, three, four plus one over r five. Reciprocal on that gives us five over eight are right and finally are equivalent Cool. And that's going to be a serious connection. Between are one two, three, four five on our six on DH. That's gonna be left to write that down. One, two, three, four, five, six plus R. It's going to be one, two, three, four bye on our six. And that he's gonna be thirteen over eight are right. So now we know we simplified the loop. Now we can go backwards and because we need to go backwards to get the current because so that sorry given resistance. And we know the toll bolted. So, you know, using home so we can get the given current s. So that's gonna be I eat you, which is equal to the voters of the battery over the equivalent resistance. And we plug in the values here. Our let's just plug in this guy over here and we get eight of Salon over thirteen are. And this guy right here is same for our six and are one, two, three, four, five. Because, as we saw that this is a serious connections. So the current passing tow this circuit and this argued with the same. So this guy's equal toe are Isaac's. It is equal to ay one, two, three, four, five. Right, um and then look at the circuit diagram again. We see that the five. So the five is the voltage difference between A and C on DH. So this guy is equal to B one, two, three, four because it's a serious connection. And that's equal toe be one, two, three, four, five Because again, this whole day is the circuit. So let me like that down. So it's going to be the five. This is equal to the one two three four, which is the one, two, three, four five. And according to our own slow, it's going to be one, two, three, four. Five times are one, two, three, four, five on If you replace, the values will get Katie. It's Ellen. Thirteen for our might be applied by five over eight are. So this guy right here is our one, two, three, four, five. And who is this Great? Um, and I five. So I five is going to be V five over our life. Andi, that's going to be five by thirteen Absalon over r What is by Absalon over thirteen are on DH. Yeah, that's that's r I fight and I want two three, four one, two, three, four is so I want to be poor is the one that's passing through this guy. So that's going to be voltage V five or three. One, two, three, four They're they're the same. So v one, two, three, four divided by I want to report and that should give us five over thirteen. Um, Absalon, divided by five by three are on. That gives us three Absalon by thirteen Are it is I for because again this one is a serious connection. Between are one, two, three and our four So I four should be the same as I wanted to port. Okay, Right on off course that's going to be I want to three as well right now we will see this relation. The one two three which is equal to I want to three times are one, two, three. So if we go back to the diagram, it's basically this far so we can again blood in the numbers That's going to be three. It's salon over thirteen are or I want to tree and are one two, three wass to over three are so that should give us two over thirteen Absalon which is be one too. What is it? Three. So we want to three against three. One two three is a serious connection artery and our one toe. So that means the voltage between this and that would be the same. Great. So now from there we can figure out a tree which is passing to our three or here passing to artery. So I three is going to be three over our three and that's going to be too upset on over. Thirteen are great and I want to is going to be if you want to. Over are one, too. And that's going to give us two way thirteen Absalon divided by to our, which a simplified as Absalon over thirteen r and disguise is basically I won and I too, because I want to is a serious connection. Um, between our one and our tow, that means the current is the same. So that's why I won is equal to ay to. So now we know all the currents we can actually plugging all the numbers and I'm going to give you the value so you can actually plug in the numbers. We know that Absalon, in our case, is twelve volt, so we can plug that and are in our case. It's three point two five poems. So are you gonna be three point two five loans? Yeah, Sophie, plugging all the numbers will get the falling values. I want Quinn's too cheese. Zero point two eight four millions. I three is going to be zero point five six eight millions I for it's been hard to hear I fore it's going to be zero point eight five two millions. I fi is gonna be one point for two millions. And finally I six, he's going to be two point two seven Williams and right, And okay, so we need to find the potential difference between point A and point B. So putting their difference difference within this and that. So we're going to use, Let's see, it's going to be three. So we're going to be using this guy, right? So we're going to be used in there trying to find this guy, so is too over thirteen. Excellent. So the A B is to over thirteen, um, at a salon, and that should give us one point five quotes. So, yeah, it's better to derive this, So that gets clear. It's a very simple problem if we actually, um, simplified the circuit. Thank you.

So this problem we was circuit on Do we have a circuit like this? And we're looking for the currents. That air flowing to the different branches we're gonna do is we're generally gonna use care, coughs, loop serum as well as the junction rule not to set up a system of equations to them solve for the unknowns. So in this case, you have four knows that we're looking for. We have I one I two r three and I for and these are directions that air picked arbitrarily for now, we'll see in the calculations if we get a negative or positive number as to whether these directions air correct. So we're first going to do is we're gonna set up our four equation since we have for unknowns, So will apply in the loop rule to these three loops, the left, the middle and the rights as well as the junction rule for our last fourth equation. So when we do this, we're going to get is these four equations So starting with the left loop will have negative 200 times. I won minus 40 plus 80 times I to equal to zero. Then in the middle loop will have minus 80 times I to plus 40 close to 60 minus 20 times I three and for the right loop will have 3 60 minus 20 times I three minus 70 times I for plus 80 on this expression is equal to zero over the junction really can see that we have I one plus I to plus I for equal Teoh i three since we're considering this part here to be the junction that all the currents are flowing into So now that we have our system of equations were essentially just can use algebra two eliminate and substitute in order to find the values currents. So we can first do is we'll go ahead and just label these equations. So we have 123 and four So we can first do is we have I three in terms of I two I want and I four so we can go ahead and substitute I three with this expression And when we do that, we'll get three equations so we'll have to is equal to 2.5 times I won class point fines and for the second equation will have 400 minus 100 times I to when? This 20 times I won minus 20 times I for all equal to zero and then we'll have for 40 minus 20 times. I want minus 20 times I to minus 90 times I for equal to zero. So we're going to continue to take this an expression where we have one of the values, one of the unknowns in terms of the other and will continue to substitute. So in this case, we're gonna be substituting I two with Equation one, and that will eliminate I too. So when we finally continue this process one more time, we'll end up finding that I won is equal to one amp I for is equal to four amps. Hi, two is equal to three amps and I three is equal to eight AM's. So we got positive numbers here, so this means it's direction in this current this circuit right here that we drew over the circuit thes directions will be the correct ones. Since all the answers that we go on, we're positive. And now if we want to find the voltage that is dropping across the 200 ohm resistor, all we have to do is apply. Owns law. So we know that owns law the Delta V. The voltage drop is going to be equal to the current going through the resistor times the resistance when we know that I one is running through the 200 ohm resistor and I want we found to be one amp so one times 200 simply 200. So we have a 200 volts voltage drop across that resistor.


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