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Problem 60 Hard Difficulty

For the network in Figure Figure P 18.60, show that the resistance between points $a$ and $b$ is $R_{a b}=\frac{27}{17} \Omega .$ (Hint: Connect a battery with emf $\boldsymbol{E}$ across points $a$ and $b$ and determine $\boldsymbol{E} / I,$ where $I$ is the current in the battery.)

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Video Transcript

now, in this particular problem, we need to prove that the wordage and the current combination that means a distance between me and be so we'll just write a question for your reference that to prove r A B but a distance between a and B equal do 27 up on 17 0 This is what we need to go through. So what we have done that we have applied gm if that his battery across A and B ash on here at the same time, the main current, his eye, which is getting segregated into two components here, that is Ivan and I to again we have a zoom vertical branch current as I three and according the polarities are mation and the branch current off one that is the horizontal one is Ivan minus I three at the same time. Over here, your summation and Sadie, the current of this branch is off. I do bless I t which is to firearms. Now, according to the current directions, we already mentioned the polarities across to start with. That's considered a step, eh? We need to apply. Gave you Sam writing here, applying a video to the loo now the loop is basically hey, c be but take it as e so a c b e a That is a group supply gave you into the loop A C B e Now we need to think about the gate jobs worded that there is some off. All the world is across the loop is to you So start from terminally so there's gonna be minus one in driving. We need to consider the living polarity minus one into Ivan minus I tweak and bless e m f is equal. Do see you. This is the loop in question with respect. Okay, just for official. So that's all this Father that is going to be minus to Ireland less. I three is equal to minus off in if and photo Oh, we can get it as to Ivan minus I three is equal to uniph. Let's mark this as a gration one. No, for the thanks, Debbie. We need to apply. Gave you through the loop which is a d b e The results Look off the giving problem. So now let us start from C battery. So we're waiting now and clockwise. Sure it is going to be absolutely. Plus you minus tree. I do minus phi and in bracket is going to be. I took less. I three is equal to zero. So therefore, we're right here. That is our resolving this. I'll get minus off Reid. I do. Minus off II three physical toe minus off. Absalom. So therefore, eat. I do. Class 53 is equal to absolutely That's market as equation, too. No, let's say step. See, we need to apply Kubo to the loop, which is a g a c and a A gay. See any? Okay, so we are going to consider these three companies in the world to drop It crosses. So it is going to be minus off me. I do, plus one times I three unless one times Iran is equal to zero. So therefore we get Ivan minus three. I do. Unless I tree is equal. Do zero. Let's mark this as a question tree. No, after solving this serving these to digressions. But you have got before they get the value of Ivan as let's write it down 13 upon 17. Absolute. I do. As for a born 27 that's long and I three as one up on Grandi. Seven capsule now. Father, apply. Okay, Seal their escape jobs, current law and the junction He over here? So according to the case, he'll it's some off entering. Currents is equal to some Off are going current. So with respect to know, eh, I is the gun which is ending. And Ivan and I go Richard leaving. So let this substitute about values in this particular question. So we get 13 but born 27 ups on bless four upon Granny seven. Absalom. So you get it as 17. Absolute divided by 27 on beers. This is what you need to understand. On this gonna end is basically either total current market as talking current supplied by the battery. Yeah, find out. No this to prove that the distance between A and B we already taken location as our baby. So this since Britain and be would be we need to mation total mortgage upon Go to couldn't So, therefore, for the on ABC quickly, what is it really were? Dish that is excellent. That means a mackerel mortgage and go to work and is gonna be I so solving this excellent upon 17 Absalon born Bernie, seven. This is a live picture guard on the left hand side here. So therefore, our baby is equal to 27 upon 17 home where absolute gets cancelled. This is what we have proved.

Top Physics 102 Electricity and Magnetism Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

Farnaz M.

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Aspen F.

University of Sheffield

Physics 102 Electricity and Magnetism Bootcamp

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