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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) $R=\frac{R_{2}}{R_{1} R_{3}}$

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Chapter 1

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Section 1

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in this example, we're going to look at a structure that's that's often called a bridge circuit With three sisters in it. Um So let's suppose that we had the following circuit with four resistors arranged as shown, which looks like a fairly simple structure. Yeah. However, let'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'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's a potential difference connecting those two ends, we'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'll send I won through the top through R. And R. One and we'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.

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