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In the clrcult shown below € 76.0 V, Rs 4.00 0, Rz 2.00 0, Rz 2.20 0, Is resistors R1 and Ra.90 A; I4 6.30 A, and I, 12.6Find the current through Rz and R3- a...

Question

In the clrcult shown below € 76.0 V, Rs 4.00 0, Rz 2.00 0, Rz 2.20 0, Is resistors R1 and Ra.90 A; I4 6.30 A, and I, 12.6Find the current through Rz and R3- and the values of theR}

In the clrcult shown below € 76.0 V, Rs 4.00 0, Rz 2.00 0, Rz 2.20 0, Is resistors R1 and Ra. 90 A; I4 6.30 A, and I, 12.6 Find the current through Rz and R3- and the values of the R}



Answers

Figure $27-78$ shows a portion of a circuit through which there is a current
$I=6.00$ A. The resistances are $R_{1}=$
$R_{2}=2.00 R_{3}=2.00 R_{4}=4.00 \Omega .$ What
is the current $i_{1}$ through resistor 1$?$

The total distance. The total distance across the circuit is polity close to our one less are too arty Divide by our gutless party A system last 40 exiting They were both our peoples 15 we get 60 homes the current across our one I is it was too. Were you born? We'll build a distance. We get 1 2016 We get to empty your current You find the current across our to an arty to find the current across r two and r tree We used jobs through to find the voltage across the rule loop Else falling the law it goes to minus I think I would I just want 20 minus two x is being you get to empty words The current across our do is i r two is equals to they know divided by r two musical So zero point Triple six ampere The current 0.666 ampere the current across our three is then I art three is equals to the new Or did you close to divide by RTZ goes to 1.333 And here

In this question we are given that yeah given this uh circuit. Okay. Battery with three resistance. And then uh given that the E. M. F. is 9.0 votes. R. One is 150 homes. R. Two is 250 homes. Our tree is 1000 homes want to find a current in each resistor. Okay so to solve this question first we want to find our equivalent resistance in the circuit. So we see that to an artery in parallel So we can buy our 2. 3 is one of our two plus one of archery and the recipe book of it. Okay and then our equivalent resistance is one plus R. Two tree. Okay so uh of our fast one of our two plus one of archery. The reciprocal substitute the numbers one of 1 15 plus 1/2 50 plus one over 1000. The reciprocal of it and the Cuban resistance you calculate you get 250 once. Okay? And then the current in the circuit current supplied by Petry. If you go to the mm, do I buy the equivalent resistance? So nine by Try and 50 and you get 0.0257 MPS. He then um I won is going to be 0.0257 MPS. Because uh is in series with the battery and then I too Is equal to be to divide by our two and B two is e minus. We won then be one is uh I one or 1 developed by our two. So you can substitute nine minus. So I want 0.257 R one is 115 and then divide by 215. Okay, So you get 0.0206 Mps. And then I three is equal to 1 -2 T. And the answer is 5.14 times 10 to the negative three mps. Okay, so here are the answers for this question and that's all

Good day. In this question we will be solving for the current total current for the given parallel circuit. So notice that the potential difference from a. to b. s. 40 was. So therefore each resistor has also for devotes since it is in Caroline. Karenin surrogate. So solving for edge current. So for current per receive story we have. All right. Our formula is current equals potential difference divided by resistance. So where I do, we have equal to 40 votes Divided by two obs Is equal to 20 years. Where our I five or Carrot at five equals 40 volts. You're guided by five arms. It was eight um fierce. So for our I I ate is equal to 40 worlds divided by eight hugs Is five of years. Since the Current is split into three, our total courage should be the equal of all the, So the sum of all the carrots. So I do bless I five plus I ate. So substituting what we got. We have 20 on fears Plus eight and peers plus five years. Our current is equal to 33. Um, for years

So we're here we have a network of the resistors and we will need to find out the current flowing through each resistors. So let's say the current flowing is I one in this branch and I took in this branch. So applying ketchups, current law, we will get the current flowing through this five home as I one minus. I do. So similarly here the current flowing will be I too. And we take the current flowing through the six home as I three. So the current flowing through the six home will be I tu minus I three. And here these two currents will combine and the total current flowing through the six volt will be I want minus I do plus I three. And here as usual I even current goes out of the battery. So even current will come out here. So we will apply ketchups voltage law across three loops because we have three different unknown variables. So let us say first we apply in this look. So here we start from this point we take it as zero potential. So potential at this point will be 12 and pay attention at this point will be decreased by this five home resistor. And then we are moving from positive to negative. So there will be document of six volt and then this 10 and three are in series. So there will be decreasing potential due to this two resistors. So 13 Taiwan and this will be zero. So this will be the first equation. So let us simplify it even more. So taking five Ivan and 13 islands will get minus 18 Ivan plus five. I do plus six equals to zero. So this is first situation. Now we consider let's sit this look. So we start at this point with zero potential and we are moving oppose it to the direction of current. So potential here will be right, I want minus I took and then potential here will be minus eight I two. And here the potential will be minus before I do. And similarly now the potential will be minus six I three and it will be zero. So we'll simplify it even more. So we get 551 minus five to minus eight. I do. That is minus 13, I do. And then minus four I two. So that will make it minus 17 I took and minus six I three as you should. But this is the question too, let's put them in the box so that we are sure that these are the equations. So similarly will take third. Look let's say I take it this one. So we start at this 0.0. Okay plus six. So the third question from this loop we use ketchup voltage logging so six minus so here we are going oppose it to the direction of current. So it will be plastic society minus six times I two minus three and this will be zero. So simplifying it six I three plus six I three here. So we get 12 I three minus six I two plus six equals to zero. And this is the equation three. So we saw these three equations so we'll take two equation at the time and get the value of Ivan and I two and then substitute in the third to get in I three. So from the first equation we can write I won has five I two plus six by 18. The second equation it is also in terms of Ivan and I two and I three. So we can take the value of I three now and converted in the form of I two. So we get five instead of Ivan we'll write it as five I two plus six by 18 minus 17. I two minus six. I three equals to zero. So converting the second equation we'll get 25 I two plus 30 by 18 minus 17 I two minus six I three is equal to zero. So here we need to calculate them a bit because it's involving quite bigger numbers. So here we get 25 I two plus 30 minus 18 times 17. That is three not 68 to minus 18 times six. That is 108 Hi three equals to zero. So from here we find out a tree. So we combine 25 I two and 306 itunes. So that is minus 281 I two plus 30 minus 108 I three. So from here we get I three as 30 minus 281 I two. Bye one not eight. So we take this value of Ivan and I three in terms of I two and replacing this 30 questions. So let's replace that we get 12 times I three. So you're right 12 times the value of I three. From here there is 30 minus 281 I two over 108 and then minus six I two. We will keep it as it is and then we have plus six is equal to zero. So from here we can figure out I took so we'll get 3 60 minus 2 81 times. Yeah, so that will be 3372 I do minus 108 times six. That will be 648 I two and then again 108 times six wickets 648 he goes to zero. So from here we figured out the value of I do. So we combine like terms, we get one double 08 minus 337 plus 648 We get 9 85 I 20 So from here we can easily get I to ask for one point 02 amperes. So once we have got this I two has 1.2 Let's put it. The situation I two s 1.2 So Ivan will come out to be five times 1.2 plus 6/18. This will come out to be 0.62 NPR's similarly I three will come out to me two point four amperes. Let's take in terms of two DP So 2.3 eight amperes it's coming as negative. So negative sign just indicates that the value of I three, whatever we have considered in this situation, it will be not the same as we have taken, it will be a positive. So this will be the value the direction of three. So we have to figure out the current across all the resistors. So once we have figured out Ivan I two and I three, we can see that the current across four home and it home. Yes, I took So let's list all the resistors here and the currents. So there are different resistors that we have over here in the diagram that is for our own resistance. We will see the current through this forum, we'll see the resist the current through this. A two six on resistance we have another six armed resistance. We have and then we have five own resistance and then 10 homes and three owned resistance. So across four home and eight we can see this four oh mandate. they are in series So current will be I too. So we figured out it was 1.2 NPR's so current through them will be 1.2 amperes. So six on there are 26 on resistance. So six on. Let us say I call this middle resistance. The current will be I three in the upward direction and I threes 2.38 amperes. So this will be 2.38 amperes across the middle one and this through the sixth on the current is I two minus I three. So we have calculated I two and I think so if we subtract, I do minus I three, so 0.62 plus two point 38 That comes out to be three amperes. And across five own resistance it's Ivan minus I took All right, this is the current across five bombs. So I want minus I do so 0.6 to minus 1.2 So it will be 0.4 amperes. Its direction will be again oppose it, oppose it to the direction what we have taken and then finally comes to 10 home and three um there also in series and the current across them would be I want that is 0.62 amperes. So we have figured out the current flowing through each resistance connected in the circuit.


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