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The resistance between points $a$ and $b$ in Figure $P 18.54$ drops to one-half its original value when switch $S$ is closed. Determine the value of $R .$

R=14 \text { ohms }

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Rutgers, The State University of New Jersey

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now in this particular sum. First we're right. Let Aro be the It's your talent, right? Distance. When the switch is open, this is the 1st 1 And the 2nd 1 is let r B be the ACU violent resistance when this switch is closed. So we are considering you're a distress here r o R and R B, which I did. Karate resistance is for two different conditions. Now let's start. Would step, eh? But right here, When switch is open, you can see the circuit that there is a switch shown in the middle of the two branches. Accordingly, I have made certain assumptions, such as have considered current island flowing through another vertical branches off our Bernardo and I do is that gun and we're just going through Our three out of four were ticketed number. Now we just need to find you go out and resistance for the first condition. So we start from here that is artists one. The oddest one is something which is with respect to go forth Brunch. So right here, see honest one and right here say artist too. So honest. One, the current I want, which is flowing through nine human gay? No, in the first word is L A branch. So that is they go out under this since father brunch. So consider island. Unless I go, which is coming. Guess 90 homes plus Daniel me's. So that becomes 100 rooms. Similarly, let us consider our is, too. That is equivalent to a distance of the second word good brunch, which is coming as our three bless are for which is equal to 10 plus 90. Because several agree that off artist one that is 100 homes. Now let's draw one guy Grant to understand this. So make a Daggett. I'm here A and B. This is going to be our This is artist one. And this shall be, though, what it's true now, since artist one an artist who are connected in battle in we find a pattern combination with the seam. So write down artist one and honest too, huh? And better. So which is it? Quit. We need to calculate this. That is 100 on Battery 200 which is coming as ultimately 100. My decried by 100 upon 100 less hungry. So R B becomes 50 homes. Let's make it a bracket big moved to base do now. So again, the circuit it comes Everybody draw the circuit first. Hey, a and B which is our which is our P perfumes that we have Court already showed us right down fighting me. Your talent resistance becomes are always in Quito R S R b So our blessed 50 homes so therefore are always equal Do are less 50 Lem's This is a parent a distance when switch s is open. And that is the answer for step, eh? No. Let's talk about step be and rich when switch is is closed. Now I've shown in the figure that the terminals are close okay with Inspector See? So if you want to make any talent diagram with respect to days we can draw something like this You understand that you never did This will be There are no to resistance is 90 And do you know aren't connected in this fashion again? Same from sea to be damn and 90 year old connected in Though seeing fashion because they're the sisters are connected to two different nose. A fresh one is from a to C on the second combination is from C to be so now you must sell industry that oppose it. Resistance is 90 and 10 10 and 90. They are connected in battle. So you saw this further? I just write down 90 home aunt, A gnome in Alan in both the combination. So therefore can we see Our P one is equal to our P too is equal to 90. Battle to eternal mitral 90 Multiparty by 10 upon 90 plus 10 So then becomes 90 Let's jodo die Gonna have mixed. So accordingly the circuit becomes Hey B, our will be there a distance which is there since the beginning, we have no r p one here an RV to here. Okay? Now R p one is a Gordon. I know. I read who has the same value. And the equal in the distance is known as R B. So now the corral and resistance is equal to R B. Therefore, RBZ quit too. No, there are harming your instances. Three of the senses reject getting CDs because it seemed going it's running through it. If we apply a battery to the tools and be two are less R b one less r p too. So it becomes, huh? Yes, nine last night. So are gestating. So therefore, our B in this case is our bless 18 homes. That's more of this. No, to show that the distance between A and B drops to one off off its original value when the sweetest clothes. As for the question, So actually we need to show. So I write down the question here we need to show according to a conventions, as R B is equal to half times are over. This is what we need to prove to. Therefore, let's subsidy. The values are be as are proceeding problems, music working half and value of our zero as our blessed 50 films. So now to our plus 36 is equal to our last 50. Therefore, to our minus. R is equal to 50 minus 36. So therefore value of our is 50 minus 36. Therefore, our as 14 holes. This is the final answer for said B. So this is the way we can calculate the value of our here