in-order-to-ensure-that-no-current-will-pass-through-the-cross-path-bold-in-the-image-above-what-mus

Question

In order to ensure that no current will pass through the cross path (bold in the image above), what must the resistance of $R$ be in terms of
(A) $R=\frac{R_{1}+R_{3}}{R_{2}}$
(B) $R=\frac{R_{2}}{R_{1}+R_{3}}$
(C) $R=\frac{R_{1} R_{3}}{R_{2}}$
(D) $R=\frac{R_{2}}{R_{1} R_{3}}$

Linda Winkler · Accepted Answer

in this example, we&#x27;re going to look at a structure that&#x27;s that&#x27;s often called a bridge circuit With three sisters in it. Um So let&#x27;s suppose that we had the following circuit with four resistors arranged as shown, which looks like a fairly simple structure. Yeah. However, let&#x27;s now put a connector From one side of the one branch to the other. Um And ordinarily this would be called a bridge circuit with that connector being termed a bridge. And usually what you have inside of that bridge is a small resistor with an and meter. And uh you&#x27;re often using the current flow in that bridge to determine whether your bridge is in balance or not. And what you mean by balance is uh no tendency for current to flow in that bridge, no current in this connector. And in order for that to be true, what you must have um is that there&#x27;s a potential difference connecting those two ends, we&#x27;ll call one and one and two, but that potential difference has to be equal to zero. Um And if that potential difference is equal to zero what that means is the voltage drop on each side of the branch is the same. Okay so let me kind of just show a couple of currents in here. Um So we&#x27;ll send I won through the top through R. And R. One and we&#x27;ll send I. Too through the bottom. And for that potential to be the same at points wanted to. What you must have is that I want times are has to equal I too times are three just based on own slaw. But and then what you must also have true is that I won times are one has to be I. Two R. Two. So the the current has to continue to flow in that circuit all the way across through yeah the top and the bottom um circuit branches if you want to call them that. So I one R. 1 has to also equal I. Too, times are too and then that that current will simply split into two pieces um and go its merry way all the way across. Um So we can figure out what are is by taking the ratio of those two equations and what we find that our over our one has to be equal to Our three over art too. And if if we had to solve for one of the unknown ours, for example, are we would just simply cross multiply that relationship. Mhm.

Ze-Han Lee · Answer

All right, so in this problem, we have the waste on bridge. Uh, so there&#x27;s our one is our and this is our two. And this is our three. Okay, so we want to make sure that there is no current in this. Ah, this wire. So when you have said it&#x27;s fly the venison about its equation, our one our free equal are to our right. So this gives us our equal. Are one are three over our two, okay?

Ankit Gupta · Answer

here we have given resistance battle in distance, off food in distance. Therefore, the art total of these two battlers senses given by our are divided by are one place. Now the first part is asking that if our bone is it goes to Penn whom then we had to draw the graph off our duty. Hence the graph off total will be like this. If the equation off our total brother grafts, we need the question that will be 10 are rewarded by 10 plus our too. Then the graph will be like this. Here it is. The graph and that&#x27;s include here is Wyche will suit then Hence we have obtained us. I&#x27;m told in the graph here that&#x27;s endured is in the blue color line, which is why it is a village to. And this is the essence of this question. Now, in the hard part, we have given their value off. I do is to undergo carbon and the value off our totally 17 and we have to find the value of our therefore putting the question it will be 17 are wonder to under root off our one divided by R one plus two underdog are one. After solving this equation, we will get the value of our one similar do. 103.5 Holmes, This is done.

Elizabeth Xu · Answer

so sorry with Courtney, you simplified the expression for our So be a born father by one. Right about Post Grad, or are one plus one Word of my art too. So one of their own leader. Me too. On the to practice together. Even to do that you can do common denominator are one or two. So we have Our two crews are one in the numerator. We know that one divided by a fraction. It was equal to the This is a tumor is equal to the reciprocal attraction. You are one or two. Bye bye. Are two plus or one. So what&#x27;s your introduced Okay now for B? Well, we have to do is just use the formula that any direct above this one and you can just playing with our values are one or two. So you know you are. What do we equal to? Our one used him times or 2 20 right, Abi? 10. Close 20. So then you have 200 too long. In my 30 you&#x27;re equal to 20 divided by three. Yeah,

Suman Saurav Thakur · Answer

you&#x27;d be have and expression for two resistances connected in parallel equal to one by one by r one plus one by r two. The figure must be Ottawa in and are too connective. Certain potential difference we So that is not our area of concern. First of all, we need to solve this denominator, but taking L City off our own out, it will be our one are to benefit. Divide R one R two with our one. We get out with caution. So it will be wanting to are two bless one into our own. Okay, now it will become one work. I went over our hopeless arwen do right away R one r two. No, please remember, if is divided by me by sea, it becomes in to see the world bags be really used. These concept this concept over here it becomes one into I don&#x27;t know too. Do right by I won&#x27;t preside. Are our becomes Ottawa in our to do right by are one place are too. So this is the solution of our first part. And then we are doing first part part over here. No work barred me foot. Partly you have been given are one the value of our 1 10 homes. And I do 20 films just plugging. These values are on our toe in our question. Our on our tooth anywhere by r one plus r two, our only calls to 10. 20 by and bless 20 it becomes 200 divided by 30. So is there a job? You get canceled out. We will be left with 20 way three own or six Dubai 31 motor. The correct answers. Thank you.

Sanjeev Kumar · Answer

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&#x27;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

Problem

The circuit above has two resistors in parallel. …

Problem 9 Easy Difficulty

In order to ensure that no current will pass through the cross path (bold in the image above), what must the resistance of $R$ be in terms of
(A) $R=\frac{R_{1}+R_{3}}{R_{2}}$
(B) $R=\frac{R_{2}}{R_{1}+R_{3}}$
(C) $R=\frac{R_{1} R_{3}}{R_{2}}$
(D) $R=\frac{R_{2}}{R_{1} R_{3}}$

Answer

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