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Problem 14 Medium Difficulty

A battery with $\boldsymbol{E}=6.00 \mathrm{V}$ and no internal resistance supplies current to the supplies current to the circuit shown in Figure P 18.14. When the double-throw switch $S$ is open as shown in the figure, the current in the battery is 1.00 $\mathrm{mA}$ . When the switch is closed in position $a$ , the current in the battery is 1.20 $\mathrm{mA}$ . When the switch is closed in position $b,$ the current in the battery is 2.00 $\mathrm{mA}$ . Find the resistances (a) $R_{1},$ (b) $R_{2},$ and ( $) R_{3}$ .

Answer

a. 18 \Omega
b. \begin{array}{l}{\begin{array}{l}{R_{2}=1000} \\ {\Rightarrow R_{2}=2000 \Omega=2 k \Omega}\end{array}}\end{array}
c. R_{3}=6000-3000=3000 \Omega=3 k \Omega

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Video Transcript

in this particular circuit. We need to find the values off. Our one are doing our three registers. No to step A in which, as for the given condition value of the current which is flowing to the circuit, that is, I is equal to one million here. Now when the switch is open, the currently working girl register Arto is you. So this particular register are just connected towards a and the other No. Zero. Why? Because it is open ended so current will not flow to it. So we'll first tried to draw the diagram to show the connections. So here first Absolutely, which is the E M f, which is off six World when the register, which is our run in Siri's with arto the working good resistance are due, should not be taken into consideration now because the current will not be flowing through it since it is open ended. You are one argument. Artie will be in CDs, and the current was just ruling through them. He's off one million Pierre aspirin in human condition. So simply by using arms law, Absalon is equal to I into combination off resistances, which is our one plus our two plus artery because they're connected in series. So therefore six world is equal to one million Pierre in my duplication But the some off three distances dead for I won. Unless I go bless, Our three is equal to sixfold, divided by one million Pierre which is equal do 6000 homes. I will consider this as immigration one we go for the next year. Step be The condition is when switch is at position e the amount of current which is flowing to the circuit He's off 1.2 million years so we draw the circuit first. This is off. Six words are One will be there in cities with art too. Since the searches are positioned a are you working? Go will be into consideration and our circuit will be like this. So the working girls are do is connected between see hey and D points brother, we consider them as nodes Now In this case, both the articles are connected between the C and O. T there in pattern. So just try to find that effective the distance off them. So are effective is a tow are two barrel arto were just considering to read distances, which will be I do multiplied by through upon addition off these two distances therefore, on effect you in this case, maybe 0.5. No, but just try to Georgia circuit for this. So let's draw the circuit for step be. This is the battery. Because our six world we have resistance Ottoman here, the effective combination which is 0.5 Artoo and in cities with our three. And these are the tools that is See and this is G. The effective current is I, which has given us 1.2 million years. So therefore, by using the same or miso, we can definitely get the question as Isaac. Wait too. Six world. What boy? Either one bless our three Placido 0.52 dead, for we're just in terms off red distances. So our 10.5 I do bless. Our three is equal to six world divided by 1.2 million peers and we get the onset as 5000 homes. Well, consider this particle equation as immigration too steps. See Now ask for the human condition. When switch is that was he shouldn't be while you have the current, which is going to the circuit is off two million years. So let's draw the circuit. First asked for this condition, the six world connected in cities with the oven That will be our two. There would be our three as well. But at the same time since the switch is that position B, a wire will be connected. I shown here now, and the world will be between Toby and Jody. I understand the concept behind it when the current is actually flowing through our one eye too. And then it is getting speeded between a wire and our three. We need to just find effective distance offered. So are you think, do you between be truly if you want to find out is equal to the distance Off wire is almost zero and that will be in battle with our tree. So we need to find this combination as zero into our three upon zero class are three, which is coming at zero mes. So we need to draw the effect. You suck it off. This which could be growing as this is a six ward battery that reveal a distance servant. There will be the distance. I do, but there will not be the distance are three because effect you're a distance is just a wire weaken B and e okay for ask for the given condition. Isaac Walton are two million peers. It's made a question Isaac will do. Six. Work do I did buy combination off Carbon and Arto since the same current flows they are in CDs, therefore value five. We already know us two million peers, so I won, unless I do is equal to six fold divided by two million peers. We're just coming asked 3000 homes and this will be our equation. Three. So we have three Grecians now. That's right. The easy questions first, 1st 1 I run. Bless I do bless. Our three is equipped to 6000 homes. 2nd 1 is on the run. Bless 0.5. I do. Plus, our three is equal to 5000 homes, and the 3rd 1 is either one unless I do is equal to 3000 homes. This is a host sicking endit toward Just for your reference, we moved to a step D. We tried to find each resistance now, so let's put the value of the question three in question one some writing, Putting the value. Oh, gration three in immigration one therefore 3000. Bless Our three physique worked with 6000. Therefore, value of party read innately good. He does 3000 homes, and this is a first answer that we have caught. Step. We're putting the value of our three. Any question toe. So right foot the value off our tree in gration two, therefore are one plus 0.5 I do plus 3000 is equal to 5000. There's a question that we have. Therefore, our run plus 0.52 is equal to 2000. This is the equation. Four. The market does a question for you if, well, justice a question for in terms of fireman so right and just thing this equation for and himself right away. Therefore, our one is equal to 2000 minus 0.5 I do on let's consider this as a gration five now well put little book This value off I'd run immigration three day before right here since equation threes are one parasite who is equipped with 3000 homes. Therefore, 2000 minus 0.5 I do and plus our toe is equal to 3000 will get cedar 0.5 are too is equal to 1000. And therefore the value of I do is 2000 homes is the second answer victory of court. Now, using a question Fife using a Grecian five, we put the value of five doing it. Would the value off too, innit? Get Ottoman value. So therefore, Arvin is equal to 2000 minus 0.5 I too. Let's put the value There's 2000 minus 0.5 multiplied by 2000. So which is equal to Tom's in arms? This is the turd. So fine. Annie, we've just tried to write. Does? That's a conclusion. The resistance is Ivan. Come on. Two and our three are How's the nose? 2000 homes and 3000 arms, respectively. This is Ah conclusion

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