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Problem 30 Hard Difficulty

For the circuit shown in Figure P 18.30, use Kirchhoff’s rules to obtain equations for (a) the upper loop, (b) the lower loop, and (c) the node on the left side. In each case suppress units for clarity and simplify, combining like terms. (d) Solve the node equation for $I_{36} .$ (e) Using the equation found in (d), eliminate $I_{36}$ from the equation found in simultaneously for the two unknowns for $I_{18}$ and $I_{12},$ respectively. (g) Substitute the answers found in part (f) into the node equation found in part (d), solving for $I_{36}$ . (h) What is the significance of the negative answer for $I_{12}$?

Answer

a. 13.0 I_{1} 8+18.0 I_{1} 2=30.0
b. 5.00 I_{36}-18.0 I_{12}=0
c. I_{36}+I_{12}=I_{18}
d. I_{36}=I_{18}-I_{12}
e. 5.00 I_{18}-23.0 I_{12}=24.0
f. \begin{array}{l}{I_{12}=-0.416 A} \\ {I_{18}=2.88 A}\end{array}
g. I_{36}=3.30 \mathrm{A}
h. no answer available

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Video Transcript

in this case, three guns that already given determination as I eating a troll I 36. No, these three currents are the branch currents which are flowing. And according Do that I have marked the polarities across the components once again the current entering the polarities plus and the current which is living that polarity is minus. Now ask for this new addition. Let's start with Step A. Frist. We need to find the equation for upper, so just write it down. We need to find here the question four up. Now ask for the gave you mentioned once again this some off potential difference across all the remains in any grow circuit. You is zero therefore, in order to find the question for the group. But it just looked like you were there so is stocked with aiding and will go anti clockwise. So eating minus big dimes I 80 that it's going which is going to minus 11 times. I drove less drugs minus seven times I 12 minus five times I e. D is equal to zero. So therefore solving further. It's a G minus 13 times I eating minus 18 times. I drove last 12 is equal to zero. Finally, we get a question as 13 times I eating bless 18 dimes. I trow is equal to 30. Will mention this as immigration, eh? And this time we're going toe create lot off equations. So that is mentioned the name according no into step, be define equation. So write down in question for the Lord Liu. So therefore, now we'll start with back cream that is 36 were again going anti clockwise. Bless seven times I trow minus tro bless 11 time I drove minus five times I 36 Music would use you. Therefore 24 Yes, 18 times I trow minus five times I 36 is equal to zero. So finally we good day question as 18 times I troll minus five times I 36 is it will do minus 24. Let's mention this as equation would be so these are basically two answers which we are supposed to get in Step eight instead, be that's small for you Step see before that. But it just tried to get the diagram for reference. OK, Now, in order to find the aggression for the node on the left hand side, so just write down here. We're trying to find equation for the node left inside. We make use off Casey Ill. That is scared. Jobs current, low. And according to this particular law, write down some off the currents entering and note, eh is equal. Do some off the currents leaving no tea. This is we need to remember But therefore, as faras Nori's consider I 80 is entering into it and I 12 on i 36 on leaving So right in this fashion will mention this as immigration one. And this is the answer for step. See, now that's right. Down to step to you here using a question one. We need to find the question for current I 36. So what? We're right. Using in question one, we find equation for I couldn't I'd 36 dad four i 36 is, according to I 18 minus I trow we have just moved in terms around and accordingly the signs are changed And this is the immigration to animation and this is answer for Steffy anymore. Father, let's talk about step. You know now to eliminate real first, write down the statement to eliminate I 36 from the equation of the lower loop. Well, put a creation too. Immigration be therefore 18 I trill minus five times I 36 is equal to minus 24. This is the question be which we already have. So therefore, let's put the value off I 36 in there. So 18 I trow minus five times by 18 minus I trow is equal to minus rifle solving further we get therefore 18 nitro minus five times I eating less five times I trow is equal to minus rifle. Therefore, finally we get 23 eyed girl minus five times I, Dean is equal to minus 24. Let's mark this equation on Dhe Caldas Immigration Hey, and this is the answer for Steffy. This is a question with the elimination of the term high 36. No, let's go to step F. We need to find the values off I 18 and I troll estimation. We need to get this to values here. So we need to make youself doing patients to using immigration e and gration Eat. Let's join down the easy questions first for the reference. Therefore, it's 13 times I eating plus 18 times I trow is equal to 30 and minus Fyi, eating last 23 times I trow is equal to minus rifle. So this is a Grecian, eh? And this is aggression. Now we'll try to get the question in the form to find the value for trail. So therefore, eating I troll is equal to 30 times. But I need you to sign 13 times I eating so 30 minus 13 times I 80 so therefore begin to value. If I troll, we just need to do I'd buy a dean so it will be a combination 30 minus 13 i 80 do I did by 80 So now therefore we're right here I trow is equal to the final calculation would be 1.66 minus 0.7 to toe i e t. This is the question that we have got in dumps off I troll Now let us put notice Board the value off I trow in a grey shin ae therefore minus phi times I 80 less 23 times 1.66 minus 0.7 to 80 bracket accompanied is equal to minus training, for we have put the value of Phi to any question solving this. Rather, we get minus phi off I e d less 30 age point on it. Minus 16 points 16 or six times I eating is equal to minus rainfall, therefore minus trained U N 0.606 Aye aye. Eating is equal to minus 62 point on it. Therefore, the value off eating that we get these 2.877 amperes. This is the answer Four step f At the same time, we need to calculate the value for now. I trow so we can make use off question, eh? Should write down using a Grecian, eh? I tried to find the value for I tow. Therefore it's eating. I trow is equal to 30 miners 13 times my eating. We already have the value of fighting now, so that is too pointed 77 amperes, which is coming as I will bye deriding by 18 further, it will be minus 0.411 amperes. This is the answer for the same step with I trail value, which is a current flowing through trial. Um, resistance. Now that's wide step G. To find the value of 5 36 Okay, so here we need the value of 5 36 Will make use off question, too. From the study. Right here. Reville make use off immigration too, from stepped in. So therefore, I 36 is according to my 80 minus I troll. It's for the values 2.877 minus I travel knew which we have got minor 0.411 amperes, which is equal to your point to 88 years to their full. The value of I 36 is equal to 3.28 and years. This is the answer for ST G now. No, the last trip that his edge the significance off *** do sign. So we're writing themselves. Statement the negative sign. Well, write it down. The negative sign off I drove implies that couldn't flows to travel home in a positive direction. In a positive direction through the direction mentioned in the so called Degra off. Be aiding born 30 This we can mention for though if you want that weekend stayed that I drove those from right to left in the brunch. There travel voyage battery is connected. Wait! The magnitude as Cedo, born for 13 amperes. This is a financier

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